Titlebook: Robust and Multivariate Statistical Methods; Festschrift in Honor Mengxi Yi,Klaus Nordhausen Book 2023 The Editor(s) (if applicable) and Th

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Robust Forecasting of Multiple Time Series with One-Sided Dynamic Principal Componentsnts. Peña et al. (J Am Stat Assoc 114(528):1683–1694, 2019) defined one-sided dynamic principal components as linear combinations of the present and past values of the series with optimal reconstruction properties. In order to make the estimation of these components robust to outliers, we propose he

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Robustly Fitting Gaussian Graphical Models—the R Package robFitConGraphmodels. Its use is demonstrated at a data example on music performance anxiety, which also illustrates . one would want to fit a Gaussian graphical model—and why one should do so robustly. The underlying theory is briefly explained, much of which has been developed by David Tyler.

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Robust Estimation of General Linear Mixed Effects Modelsis leads to a generally applicable robust M-type estimator that we call robust scoring equations estimator. It requires only minor assumptions on the covariance matrices (block diagonal for the random effects and diagonal, known up to scale for the residual errors) additional to those of the classic

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Asymptotic Behaviour of Penalized Robust Estimators in Logistic Regression When Dimension Increasesnce have been previously studied for fixed dimension. In this chapter, we consider a wide class of .-estimators that involves some well-known robust proposals and study their asymptotic behaviour when the covariates dimension grows to infinity with the sample size. Among other results, we obtain con

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Conditional Distribution-Based Downweighting for Robust Estimation of Logistic Regression Modelsead of downweighting observations based on the marginal distribution often adopted in common approaches (e.g., the Mallows class), we propose using the conditional distributions that align with a case-control perspective of binary regression. We justify our proposed weighting scheme by showing that

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A Review of Tyler’s Shape Matrix and Its Extensionsbject of active research, e.g., in the signal processing literature, which discusses structured and regularized shape matrices. In this article, we review Tyler’s original shape matrix and some recent developments.

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On Minimax Shrinkage Estimation with Variable Selectionrically symmetric distributions with a residual vector. Certain subclasses of these estimators based on truncated order statistics are shown to be particularly effective when some information on the sparsity is known.