This package facilitates analysis of both timecourse and steady state flow cytometry experiments. This package was originially developed for quantifying the function of gene regulatory networks in yeast (strain W303) expressing fluorescent reporter proteins using BD Accuri C6 and SORP cytometers. However, the functions are for the most part general and may be adapted for analysis of other organisms using other flow cytometers. Functions in this package facilitate the annotation of flow cytometry data with experimental metadata, as often required for publication and general ease-of-reuse. Functions for creating, saving and loading gate sets are also included. In the past, we have typically generated summary statistics for each flowset for each timepoint and then annotated and analyzed these summary statistics. This method loses a great deal of the power that comes from the large amounts of individual cell data generated in flow cytometry, by essentially collapsing this data into a bulk measurement after subsetting. In addition to these summary functions, this package also contains functions to facilitate annotation and analysis of steady-state or time-lapse data utilizing all of the data collected from the thousands of individual cells in each sample.

This package provides set of functions aimed at epidemiologists. The package includes commands for measures of association and impact for case control studies and cohort studies. It may be particularly useful for outbreak investigations including univariable analysis and stratified analysis. The functions for cohort studies include the CS(), CSTable() and CSInter() commands. The functions for case control studies include the CC(), CCTable() and CCInter() commands. References - Cornfield, J. 1956. A statistical problem arising from retrospective studies. In Vol. 4 of Proceedings of the Third Berkeley Symposium, ed. J. Neyman, 135-148. Berkeley, CA - University of California Press. Woolf, B. 1955. On estimating the relation between blood group disease. Annals of Human Genetics 19 251-253. Reprinted in Evolution of Epidemiologic Ideas Annotated Readings on Concepts and Methods, ed. S. Greenland, pp. 108-110. Newton Lower Falls, MA Epidemiology Resources. Gilles Desve & Peter Makary, 2007. CSTABLE Stata module to calculate summary table for cohort study Statistical Software Components S456879, Boston College Department of Economics. Gilles Desve & Peter Makary, 2007. CCTABLE Stata module to calculate summary table for case-control study Statistical Software Components S456878, Boston College Department of Economics.

This package implements the Arvind distribution and five novel stochastic regression models that replace the traditional Gaussian error assumption with Arvind'-distributed errors. The Arvind distribution is a flexible single-parameter continuous distribution on the positive real line characterised by a polynomial numerator with Gaussian-type decay. The package provides complete distribution functions (darvind(), parvind(), qarvind(), rarvind()), maximum likelihood estimation via fit_arvind_mle(), and five model-fitting routines: Random Walk on Coefficients via fit_rw1(), Time-Varying Coefficient Linear Model via fit_tvlm(), Simulation-Extrapolation via fit_simex(), Mixed-Effects Regression via fit_mixed(), and Regime-Switching Hidden Markov Model via fit_hmm(). Additionally provides Monte Carlo forecasting with prediction intervals via forecast_arvind(), comprehensive goodness-of-fit diagnostics (21 metrics and 25 plots) via diagnostics_arvind() and plot_arvind(), k-fold and rolling-window cross-validation via cv_arvind(), and unified model comparison via summary_arvind(). For more details see Pandey, Singh, Tyagi, and Tyagi (2024), "Modelling climate, COVID-19, and reliability data: A new continuous lifetime model under different methods of estimation", Statistics and Applications', 22(2).

Fits and compares representations of time-varying data against a prediction target. Given a table of targets and a table of time-stamped series belonging to them, it builds each candidate representation, from the record unreduced through a calendar grain such as a week or a month to a lookback anchored on each target, fits the requested learners on each, scores every candidate on one set of held-out folds, and stacks the out-of-fold predictions into an ensemble. Calendar-aware binning keeps a bin a real week or month rather than a fixed block of hours. Learners, response heads and metrics are registered rather than hard-coded, so adding one is a registration and not a fork of the fitting code. The penalised baseline is an elastic net fitted by cyclic coordinate descent along a warm-started path, following Friedman, Hastie and Tibshirani (2010) <doi:10.18637/jss.v033.i01>. The shipped default is presence-absence with a joint multi-label head scored by the true skill statistic of Allouche, Tsoar and Kadmon (2006) <doi:10.1111/j.1365-2664.2006.01214.x>, the setting used for species distribution modelling from microclimate loggers.

Bayesian regularized quantile regression utilizing two major classes of shrinkage priors (the spike-and-slab priors and the horseshoe family of priors) leads to efficient Bayesian shrinkage estimation, variable selection and valid statistical inference. In this package, we have implemented robust Bayesian variable selection with spike-and-slab priors under high-dimensional linear regression models (Fan et al. (2024) <doi:10.3390/e26090794> and Ren et al. (2023) <doi:10.1111/biom.13670>), and regularized quantile varying coefficient models (Zhou et al.(2023) <doi:10.1016/j.csda.2023.107808>). In particular, valid robust Bayesian inferences under both models in the presence of heavy-tailed errors can be validated on finite samples. Additional models with spike-and-slab priors include robust Bayesian group LASSO and robust binary Bayesian LASSO (Fan and Wu (2025) <doi:10.1002/sta4.70078>). Besides, robust sparse Bayesian regression with the horseshoe family of (horseshoe, horseshoe+ and regularized horseshoe) priors has also been implemented and yielded valid inference results under heavy-tailed model errors (Fan et al.(2026) <doi:10.1016/j.csda.2026.108358>). The Markov chain Monte Carlo (MCMC) algorithms of the proposed and alternative models are implemented in C++.

In agricultural, post-harvest and processing, engineering and industrial experiments factors are often differentiated with ease with which they can change from experimental run to experimental run. This is due to the fact that one or more factors may be expensive or time consuming to change i.e. hard-to-change factors. These factors restrict the use of complete randomization as it may make the experiment expensive and time consuming. Split plot designs can be used for such situations. In general model estimation of split plot designs require the use of generalized least squares (GLS). However for some split-plot designs ordinary least squares (OLS) estimates are equivalent to generalized least squares (GLS) estimates. These types of designs are known in literature as equivalent-estimation split-plot design. For method details see, Macharia, H. and Goos, P.(2010) <doi:10.1080/00224065.2010.11917833>.Balanced split plot designs are designs which have an equal number of subplots within every whole plot. This package used to construct equivalent estimation balanced split plot designs for different experimental set ups along with different statistical criteria to measure the performance of these designs. It consist of the function equivalent_BSPD().

This package provides easy access to Brazilian public health data from multiple sources including VIGITEL (Surveillance of Risk Factors for Chronic Diseases by Telephone Survey), PNS (National Health Survey), PNAD Continua (Continuous National Household Sample Survey), POF (Household Budget Survey with food security and consumption data), Censo Demografico (population denominators via SIDRA API), SIM (Mortality Information System), SINASC (Live Birth Information System), SIH (Hospital Information System), SIA (Outpatient Information System), SINAN (Notifiable Diseases Surveillance), CNES (National Health Facility Registry), SI-PNI (National Immunization Program - aggregated 1994-2019 via FTP, individual-level microdata 2020+ via OpenDataSUS API), SISAB (Primary Care Health Information System - coverage indicators via REST API), ANS ('Agencia Nacional de Saude Suplementar - supplementary health beneficiaries, consumer complaints, and financial statements), ANVISA ('Agencia Nacional de Vigilancia Sanitaria - product registrations, pharmacovigilance', hemovigilance', technovigilance', and controlled substance sales via SNGPC'), and other health information systems. Data is downloaded from DATASUS (the Ministry of Health's informatics department: compressed .dbc microdata read natively, or the healthbr-data Parquet mirror with per-file provenance) and from IBGE repositories, and is returned in tidy format following tidyverse conventions. A vignette compares the package with microdatasus on the DATASUS systems both read.

Obtaining accurate and stable estimates of regression coefficients can be challenging when the suggested statistical model has issues related to multicollinearity, convergence, or overfitting. One solution is to use principal component analysis (PCA) results in the regression, as discussed in Chan and Park (2005) <doi:10.1080/01446190500039812>. The swaprinc() package streamlines comparisons between a raw regression model with the full set of raw independent variables and a principal component regression model where principal components are estimated on a subset of the independent variables, then swapped into the regression model in place of those variables. The swaprinc() function compares one raw regression model to one principal component regression model, while the compswap() function compares one raw regression model to many principal component regression models. Package functions include parameters to center, scale, and undo centering and scaling, as described by Harvey and Hansen (2022) <https://cran.r-project.org/package=LearnPCA/vignettes/Vig_03_Step_By_Step_PCA.pdf>. Additionally, the package supports using Gifi methods to extract principal components from categorical variables, as outlined by Rossiter (2021) <https://www.css.cornell.edu/faculty/dgr2/_static/files/R_html/NonlinearPCA.html#2_Package>.

We provide functions to fit finite mixtures of multivariate normal or t-distributions to data with various factor analytic structures adopted for the covariance/scale matrices. The factor analytic structures available include mixtures of factor analyzers and mixtures of common factor analyzers. The latter approach is so termed because the matrix of factor loadings is common to components before the component-specific rotation of the component factors to make them white noise. Note that the component-factor loadings are not common after this rotation. Maximum likelihood estimators of model parameters are obtained via the Expectation-Maximization algorithm. See descriptions of the algorithms used in McLachlan GJ, Peel D (2000) <doi:10.1002/0471721182.ch8> McLachlan GJ, Peel D (2000) <ISBN:1-55860-707-2> McLachlan GJ, Peel D, Bean RW (2003) <doi:10.1016/S0167-9473(02)00183-4> McLachlan GJ, Bean RW, Ben-Tovim Jones L (2007) <doi:10.1016/j.csda.2006.09.015> Baek J, McLachlan GJ, Flack LK (2010) <doi:10.1109/TPAMI.2009.149> Baek J, McLachlan GJ (2011) <doi:10.1093/bioinformatics/btr112> McLachlan GJ, Baek J, Rathnayake SI (2011) <doi:10.1002/9781119995678.ch9>.

Method and tool for generating hybrid time series forecasts using an error remodeling approach. These forecasting approaches utilize a recursive technique for modeling the linearity of the series using a linear method (e.g., ARIMA, Theta, etc.) and then models (forecasts) the residuals of the linear forecaster using non-linear neural networks (e.g., ANN, ARNN, etc.). The hybrid architectures comprise three steps: firstly, the linear patterns of the series are forecasted which are followed by an error re-modeling step, and finally, the forecasts from both the steps are combined to produce the final output. This method additionally provides the confidence intervals as needed. Ten different models can be implemented using this package. This package generates different types of hybrid error correction models for time series forecasting based on the algorithms by Zhang. (2003), Chakraborty et al. (2019), Chakraborty et al. (2020), Bhattacharyya et al. (2021), Chakraborty et al. (2022), and Bhattacharyya et al. (2022) <doi:10.1016/S0925-2312(01)00702-0> <doi:10.1016/j.physa.2019.121266> <doi:10.1016/j.chaos.2020.109850> <doi:10.1109/IJCNN52387.2021.9533747> <doi:10.1007/978-3-030-72834-2_29> <doi:10.1007/s11071-021-07099-3>.

The merits of TIMESAT and phenopix are adopted. Besides, a simple and growing season dividing method and a practical snow elimination method based on Whittaker were proposed. 7 curve fitting methods and 4 phenology extraction methods were provided. Parameters boundary are considered for every curve fitting methods according to their ecological meaning. And optimx is used to select best optimization method for different curve fitting methods. Reference: Kong, D., (2020). R package: A state-of-the-art Vegetation Phenology extraction package, phenofit version 0.3.1, <doi:10.5281/zenodo.5150204>; Kong, D., Zhang, Y., Wang, D., Chen, J., & Gu, X. (2020). Photoperiod Explains the Asynchronization Between Vegetation Carbon Phenology and Vegetation Greenness Phenology. Journal of Geophysical Research: Biogeosciences, 125(8), e2020JG005636. <doi:10.1029/2020JG005636>; Kong, D., Zhang, Y., Gu, X., & Wang, D. (2019). A robust method for reconstructing global MODIS EVI time series on the Google Earth Engine. ISPRS Journal of Photogrammetry and Remote Sensing, 155, 13â 24; Zhang, Q., Kong, D., Shi, P., Singh, V.P., Sun, P., 2018. Vegetation phenology on the Qinghai-Tibetan Plateau and its response to climate change (1982â 2013). Agric. For. Meteorol. 248, 408â 417. <doi:10.1016/j.agrformet.2017.10.026>.

The name of the package is derived from the French, pour ridge, and provides functionality for ridge-type estimation of a potpourri of models. Currently, this estimation concerns that of various Gaussian graphical models from different study designs. Among others it considers the regular Gaussian graphical model and a mixture of such models. The porridge-package implements the estimation of the former either from i) data with replicated observations by penalized loglikelihood maximization using the regular ridge penalty on the parameters (van Wieringen, Chen, 2021) or ii) from non-replicated data by means of either a ridge estimator with multiple shrinkage targets (as presented in van Wieringen et al. 2020, <doi:10.1016/j.jmva.2020.104621>) or the generalized ridge estimator that allows for both the inclusion of quantitative and qualitative prior information on the precision matrix via element-wise penalization and shrinkage (van Wieringen, 2019, <doi:10.1080/10618600.2019.1604374>). Additionally, the porridge-package facilitates the ridge penalized estimation of a mixture of Gaussian graphical models (Aflakparast et al., 2018). On another note, the package also includes functionality for ridge-type estimation of the generalized linear model (as presented in van Wieringen, Binder, 2022, <doi:10.1080/10618600.2022.2035231>).

This package provides a tool for producing synthetic versions of microdata containing confidential information so that they are safe to be released to users for exploratory analysis. The key objective of generating synthetic data is to replace sensitive original values with synthetic ones causing minimal distortion of the statistical information contained in the data set. Most synthesising methods available in the package synthesise from conditional distributions where variables, which can be categorical or continuous, are synthesised one-by-one using sequential modelling. Replacements are generated by drawing from conditional distributions fitted to the original data using parametric or classification and regression trees models. Methods that are not sequential, but synthesise all variables at once, are sample', ipf', and catall'. Data are synthesised via the function syn() which can be largely automated, if default settings are used, or with methods defined by the user. Optional parameters can be used to influence the disclosure risk and the analytical quality of the synthesised data. The package also includes functions to assess the utility and disclosure risk of the synthetic data compared to the original. These are described in vignettes (Utility - Assessing, Visualizing and Improving the Utility of Synthetic Data) and (Disclosure - Practical Privacy Metrics for Synthetic Data).

Fits right-truncated meta-analysis (RTMA), a bias correction for the joint effects of p-hacking (i.e., manipulation of results within studies to obtain significant, positive estimates) and traditional publication bias (i.e., the selective publication of studies with significant, positive results) in meta-analyses [see Mathur MB (2022). "Sensitivity analysis for p-hacking in meta-analyses." <doi:10.31219/osf.io/ezjsx>.]. Unlike publication bias alone, p-hacking that favors significant, positive results (termed "affirmative") can distort the distribution of affirmative results. To bias-correct results from affirmative studies would require strong assumptions on the exact nature of p-hacking. In contrast, joint p-hacking and publication bias do not distort the distribution of published nonaffirmative results when there is stringent p-hacking (e.g., investigators who hack always eventually obtain an affirmative result) or when there is stringent publication bias (e.g., nonaffirmative results from hacked studies are never published). This means that any published nonaffirmative results are from unhacked studies. Under these assumptions, RTMA involves analyzing only the published nonaffirmative results to essentially impute the full underlying distribution of all results prior to selection due to p-hacking and/or publication bias. The package also provides diagnostic plots described in Mathur (2022).

This package provides a collection of tools that allow users to perform critical steps in the process of assessing ecological niche evolution over phylogenies, with uncertainty incorporated explicitly in reconstructions. The method proposed here for ancestral reconstruction of ecological niches characterizes species niches using a bin-based approach that incorporates uncertainty in estimations. Compared to other existing methods, the approaches presented here reduce risk of overestimation of amounts and rates of ecological niche evolution. The main analyses include: initial exploration of environmental data in occurrence records and accessible areas, preparation of data for phylogenetic analyses, executing comparative phylogenetic analyses of ecological niches, and plotting for interpretations. Details on the theoretical background and methods used can be found in: Owens et al. (2020) <doi:10.1002/ece3.6359>, Peterson et al. (1999) <doi:10.1126/science.285.5431.1265>, Soberón and Peterson (2005) <doi:10.17161/bi.v2i0.4>, Peterson (2011) <doi:10.1111/j.1365-2699.2010.02456.x>, Barve et al. (2011) <doi:10.1111/ecog.02671>, Machado-Stredel et al. (2021) <doi:10.21425/F5FBG48814>, Owens et al. (2013) <doi:10.1016/j.ecolmodel.2013.04.011>, Saupe et al. (2018) <doi:10.1093/sysbio/syx084>, and Cobos et al. (2021) <doi:10.1111/jav.02868>.

In order to facilitate the adjustment of the sample selection models existing in the literature, we created the ssmodels package. Our package allows the adjustment of the classic Heckman model (Heckman (1976), Heckman (1979) <doi:10.2307/1912352>), and the estimation of the parameters of this model via the maximum likelihood method and two-step method, in addition to the adjustment of the Heckman-t models introduced in the literature by Marchenko and Genton (2012) <doi:10.1080/01621459.2012.656011> and the Heckman-Skew model introduced in the literature by Ogundimu and Hutton (2016) <doi:10.1111/sjos.12171>. We also implemented functions to adjust the generalized version of the Heckman model, introduced by Bastos, Barreto-Souza, and Genton (2021) <doi:10.5705/ss.202021.0068>, that allows the inclusion of covariables to the dispersion and correlation parameters, and a function to adjust the Heckman-BS model introduced by Bastos and Barreto-Souza (2020) <doi:10.1080/02664763.2020.1780570> that uses the Birnbaum-Saunders distribution as a joint distribution of the selection and primary regression variables. This package extends and complements existing R packages such as sampleSelection (Toomet and Henningsen, 2008) and ssmrob (Zhelonkin et al., 2016), providing additional robust and flexible sample selection models.

This package creates interactive draggable plots from grouped projected sf geometry. The primary deliverable is a browser-based D3 helper where regions and labels can be moved freely; users drag, then copy or download the resulting offset tables. Labels can be derived automatically with make_region_labels(), supplied directly with as_drag_labels(), and their moved positions saved and restored with read_label_state() and apply_label_state(). Hierarchical spatial datasets are supported via hierarchy detection, upload profiling, make_hierarchy_key(), and inherit_layout(), which recommend parent-child groupings and propagate parent-level drag offsets to finer child groupings. Automatic starting layouts are provided by suggest_offsets() using radial, grid, or directional algorithms. Spatial file diagnostics are available through dragmapr_diagnostics(). When a reproducible static image is also needed, render_dragged_map() reconstructs the layout as a ggplot2 plot from the source geometry plus the exported offset tables. Project bundles can be written with write_dragmapr_project() and rendered with render_dragmapr_project(). The interactive layer is built on the D3 library: Bostock, Ogievetsky and Heer (2011) <doi:10.1109/TVCG.2011.185>. Spatial data handling uses the sf package: Pebesma (2018) <doi:10.32614/RJ-2018-009>.

Double constrained correspondence analysis (dc-CA) analyzes (multi-)trait (multi-)environment ecological data by using the vegan package and native R code. Throughout the two step algorithm of ter Braak et al. (2018) is used. This algorithm combines and extends community- (sample-) and species-level analyses, i.e. the usual community weighted means (CWM)-based regression analysis and the species-level analysis of species-niche centroids (SNC)-based regression analysis. The two steps use canonical correspondence analysis to regress the abundance data on to the traits and (weighted) redundancy analysis to regress the CWM of the orthonormalized traits on to the environmental predictors. The function dc_CA() has an option to divide the abundance data of a site by the site total, giving equal site weights. This division has the advantage that the multivariate analysis corresponds with an unweighted (multi-trait) community-level analysis, instead of being weighted. The first step of the algorithm uses vegan::cca(). The second step uses wrda() but vegan::rda() if the site weights are equal. This version has a predict() function. For details see ter Braak et al. 2018 <doi:10.1007/s10651-017-0395-x>. and ter Braak & van Rossum 2025 <doi:10.1016/j.ecoinf.2025.103143>.

Assessing predictive models of spatial data can be challenging, both because these models are typically built for extrapolating outside the original region represented by training data and due to potential spatially structured errors, with "hot spots" of higher than expected error clustered geographically due to spatial structure in the underlying data. Methods are provided for assessing models fit to spatial data, including approaches for measuring the spatial structure of model errors, assessing model predictions at multiple spatial scales, and evaluating where predictions can be made safely. Methods are particularly useful for models fit using the tidymodels framework. Methods include Moran's I ('Moran (1950) <doi:10.2307/2332142>), Geary's C ('Geary (1954) <doi:10.2307/2986645>), Getis-Ord's G ('Ord and Getis (1995) <doi:10.1111/j.1538-4632.1995.tb00912.x>), agreement coefficients from Ji and Gallo (2006) (<doi: 10.14358/PERS.72.7.823>), agreement metrics from Willmott (1981) (<doi: 10.1080/02723646.1981.10642213>) and Willmott et al'. (2012) (<doi: 10.1002/joc.2419>), an implementation of the area of applicability methodology from Meyer and Pebesma (2021) (<doi:10.1111/2041-210X.13650>), and an implementation of multi-scale assessment as described in Riemann et al'. (2010) (<doi:10.1016/j.rse.2010.05.010>).

Functionalities for facilitating systematic reviews, data extractions, and meta-analyses. It includes a GUI (graphical user interface) to help screen the abstracts and titles of bibliographic data; tools to assign screening effort across multiple collaborators/reviewers and to assess inter- reviewer reliability; tools to help automate the download and retrieval of journal PDF articles from online databases; figure and image extractions from PDFs; web scraping of citations; automated and manual data extraction from scatter-plot and bar-plot images; PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) flow diagrams; simple imputation tools to fill gaps in incomplete or missing study parameters; generation of random effects sizes for Hedges d, log response ratio, odds ratio, and correlation coefficients for Monte Carlo experiments; covariance equations for modelling dependencies among multiple effect sizes (e.g., effect sizes with a common control); and finally summaries that replicate analyses and outputs from widely used but no longer updated meta-analysis software (i.e., metawin). Funding for this package was supported by National Science Foundation (NSF) grants DBI-1262545 and DEB-1451031. CITE: Lajeunesse, M.J. (2016) Facilitating systematic reviews, data extraction and meta-analysis with the metagear package for R. Methods in Ecology and Evolution 7, 323-330 <doi:10.1111/2041-210X.12472>.

Implement different Item Response Theory (IRT) based procedures for the development of tests from item bank. The procedures are flexible enough to be adopted for the development of short forms of full-length tests. Different procedures are considered (Epifania, Anselmi & Robusto, 2022 <doi:10.1007/978-3-031-27781-8_7> and Epifania & Finos, 2025 <doi:10.1007/978-3-031-95995-0_32>). The main difference between the presented procedures refers to the degree of control that they allow for targeting specific latent trait levels. The simplest procedure, denoted as benchmark procedure, does not allow for any control on the latent trait levels of interest, while the other procedures allow for specifying either discrete latent trait levels for which the information needs to be maximized (theta-target procedure, <doi:10.1007/978-3-031-27781-8_7>) or a target information function that needs to be recreated with the selected items (item selection algorithm -ISA- denoted as Frank in <doi:10.1007/978-3-031-95995-0_32>). Another difference concerns the definition of the number of items to be selected. In the benchmark and theta-target procedures, the number of items must be defined a priori, while in ISA the number of items is determined automatically by the algorithm.

The kallisto | bustools pipeline is a fast and modular set of tools to convert single cell RNA-seq reads in fastq files into gene count or transcript compatibility counts (TCC) matrices for downstream analysis. Central to this pipeline is the barcode, UMI, and set (BUS) file format. This package serves the following purposes: First, this package allows users to manipulate BUS format files as data frames in R and then convert them into gene count or TCC matrices. Furthermore, since R and Rcpp code is easier to handle than pure C++ code, users are encouraged to tweak the source code of this package to experiment with new uses of BUS format and different ways to convert the BUS file into gene count matrix. Second, this package can conveniently generate files required to generate gene count matrices for spliced and unspliced transcripts for RNA velocity. Here biotypes can be filtered and scaffolds and haplotypes can be removed, and the filtered transcriptome can be extracted and written to disk. Third, this package implements utility functions to get transcripts and associated genes required to convert BUS files to gene count matrices, to write the transcript to gene information in the format required by bustools, and to read output of bustools into R as sparses matrices.

Online, Semi-online, and Offline K-medians algorithms are given. For both methods, the algorithms can be initialized randomly or with the help of a robust hierarchical clustering. The number of clusters can be selected with the help of a penalized criterion. We provide functions to provide robust clustering. Function gen_K() enables to generate a sample of data following a contaminated Gaussian mixture. Functions Kmedians() and Kmeans() consists in a K-median and a K-means algorithms while Kplot() enables to produce graph for both methods. Cardot, H., Cenac, P. and Zitt, P-A. (2013). "Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm". Bernoulli, 19, 18-43. <doi:10.3150/11-BEJ390>. Cardot, H. and Godichon-Baggioni, A. (2017). "Fast Estimation of the Median Covariation Matrix with Application to Online Robust Principal Components Analysis". Test, 26(3), 461-480 <doi:10.1007/s11749-016-0519-x>. Godichon-Baggioni, A. and Surendran, S. "A penalized criterion for selecting the number of clusters for K-medians" <arXiv:2209.03597> Vardi, Y. and Zhang, C.-H. (2000). "The multivariate L1-median and associated data depth". Proc. Natl. Acad. Sci. USA, 97(4):1423-1426. <doi:10.1073/pnas.97.4.1423>.

This package provides a gradient descent algorithm to find a geodesic relationship between real-valued independent variables and a manifold-valued dependent variable (i.e. geodesic regression). Available manifolds are Euclidean space, the sphere, hyperbolic space, and Kendall's 2-dimensional shape space. Besides the standard least-squares loss, the least absolute deviations, Huber, and Tukey biweight loss functions can also be used to perform robust geodesic regression. Functions to help choose appropriate cutoff parameters to maintain high efficiency for the Huber and Tukey biweight estimators are included, as are functions for generating random tangent vectors from the Riemannian normal distributions on the sphere and hyperbolic space. The n-sphere is a n-dimensional manifold: we represent it as a sphere of radius 1 and center 0 embedded in (n+1)-dimensional space. Using the hyperboloid model of hyperbolic space, n-dimensional hyperbolic space is embedded in (n+1)-dimensional Minkowski space as the upper sheet of a hyperboloid of two sheets. Kendall's 2D shape space with K landmarks is of real dimension 2K-4; preshapes are represented as complex K-vectors with mean 0 and magnitude 1. Details are described in Shin, H.-Y. and Oh, H.-S. (2020) <arXiv:2007.04518>. Also see Fletcher, P. T. (2013) <doi:10.1007/s11263-012-0591-y>.