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Based on the median and the median absolute deviation estimators, and the Hodges-Lehmann and Shamos estimators, robustified analogues of the conventional $t$-test statistic are proposed. The asymptotic distributions of these statistics are…
We present an estimator of the covariance matrix $\Sigma$ of random $d$-dimensional vector from an i.i.d. sample of size $n$. Our sole assumption is that this vector satisfies a bounded $L^p-L^2$ moment assumption over its one-dimensional…
We deal with the equivariant estimation of scatter and location for p-dimensional data, giving emphasis to scatter. It it important that the estimators possess both a high efficiency for normal data and a high resistance to outliers, that…
M-estimators offer simple robust alternatives to the maximum likelihood estimator. Much of the robustness literature, however, has focused on the problems of location, location-scale and regression estimation rather than on estimation of…
The Minimum Covariance Determinant (MCD) method is a widely adopted tool for robust estimation and outlier detection. In this paper, we introduce MCD model selection based on the notion of stability. Our best subset method leverages prior…
As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
Cellwise outliers are widespread in data and traditional robust methods may fail when applied to datasets under such contamination. We propose a variable selection procedure, that uses a pairwise robust estimator to obtain an initial…
This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those…
Multivariate analysis-of-variance (MANOVA) is a well established tool to examine multivariate endpoints. While classical approaches depend on restrictive assumptions like normality and homogeneity, there is a recent trend to more general…
G-computation has become a widely used robust method for estimating unconditional (marginal) treatment effects with covariate adjustment in the analysis of randomized clinical trials. Statistical inference in this context typically relies…
Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…
Standard Monte Carlo computation is widely known to exhibit a canonical square-root convergence speed in terms of sample size. Two recent techniques, one based on control variate and one on importance sampling, both derived from an…
This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the…
Mendelian randomization uses genetic variants as instrumental variables to make causal inferences about the effects of modifiable risk factors on diseases from observational data. One of the major challenges in Mendelian randomization is…
This article studies the limiting behavior of a class of robust population covariance matrix estimators, originally due to Maronna in 1976, in the regime where both the number of available samples and the population size grow large. Using…
Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…
Quadratic discriminant analysis (QDA) is a widely used statistical tool to classify observations from different multivariate Normal populations. The generalized quadratic discriminant analysis (GQDA) classification rule/classifier, which…
Mendelian randomization (MR) has become a popular approach to study the effect of a modifiable exposure on an outcome by using genetic variants as instrumental variables. A challenge in MR is that each genetic variant explains a relatively…
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential…