Robust tests (RW, RPB and RGF) are provided for testing the equality of several long-tailed symmetric (LTS) means when the variances are unknown and arbitrary. RW, RPB and RGF tests are robust versions of Welch's F test proposed by Welch (1951) <doi:10.2307/2332579>, parametric bootstrap test proposed by Krishnamoorthy et. al (2007) <doi:10.1016/j.csda.2006.09.039>; and generalized F test proposed by Weerahandi (1995) <doi:10.2307/2532947>;, respectively. These tests are based on the modified maximum likelihood (MML) estimators proposed by Tiku(1967, 1968) <doi:10.2307/2333859>, <doi:10.1080/01621459.1968.11009228>.

Robust covariance estimation for matrix-valued data and data with Kronecker-covariance structure using the Matrix Minimum Covariance Determinant (MMCD) estimators and outlier explanation using and Shapley values.

Robust Estimation of Variance Component Models by classic and composite robust procedures. The composite procedures are robust against outliers generated by the Independent Contamination Model.

Robust estimators for the beta regression, useful for modeling bounded continuous data. Currently, four types of robust estimators are supported. They depend on a tuning constant which may be fixed or selected by a data-driven algorithm also implemented in the package. Diagnostic tools associated with the fitted model, such as the residuals and goodness-of-fit statistics, are implemented. Robust Wald-type tests are available. More details about robust beta regression are described in Maluf et al. (2022) <arXiv:2209.11315>.

This package provides an easy way to compute the Theil Sehn Regression method and also the Siegel Regression Method which are both robust methods base on the median of slopes between all pairs of data. In contrast with the least squared linear regression, these methods are not sensitive to outliers. Theil, H. (1992) <doi:10.1007/978-94-011-2546-8_20>, Sen, P. K. (1968) <doi:10.1080/01621459.1968.10480934>.

This package provides robust parameter tuning and model training for predictive models applied across data sources where the data distribution varies slightly from source to source. This package implements three primary tuning methods: cross-validation-based internal tuning, external tuning, and the RobustTuneC method. External tuning includes a conservative option where parameters are tuned internally on the training data and validating on an external dataset, providing a slightly pessimistic estimate. It supports Lasso, Ridge, Random Forest, Boosting, and Support Vector Machine classifiers. Currently, only binary classification is supported. The response variable must be the first column of the dataset and a factor with exactly two levels. The tuning methods are based on the paper by Nicole Ellenbach, Anne-Laure Boulesteix, Bernd Bischl, Kristian Unger, and Roman Hornung (2021) "Improved Outcome Prediction Across Data Sources Through Robust Parameter Tuning" <doi:10.1007/s00357-020-09368-z>.

This package implements full Bayesian analysis for calibrating mathematical models with new methodology for modeling the discrepancy function. It allows for emulation, calibration and prediction using complex mathematical model outputs and experimental data. See the reference: Mengyang Gu and Long Wang, 2018, Journal of Uncertainty Quantification; Mengyang Gu, Fangzheng Xie and Long Wang, 2022, Journal of Uncertainty Quantification; Mengyang Gu, Kyle Anderson and Erika McPhillips, 2023, Technometrics.

Fits the robust Bayesian Copas (RBC) selection model of Bai et al. (2020) <arXiv:2005.02930> for correcting and quantifying publication bias in univariate meta-analysis. Also fits standard random effects meta-analysis and the Copas-like selection model of Ning et al. (2017) <doi:10.1093/biostatistics/kxx004>.