Related papers: Robust and Resistant Regularized Covariance Matric…

Identification of multinomial choice models is often established by using special covariates that have full support. This paper shows how these identification results can be extended to a large class of multinomial choice models when all…

The Minimum Covariance Determinant (MCD) method is a highly robust estimator of multivariate location and scatter, for which a fast algorithm is available. Since estimating the covariance matrix is the cornerstone of many multivariate…

This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of…

There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust…

Spatial-sign covariance matrix (SSCM) is an important substitute of sample covariance matrix (SCM) in robust statistics. This paper investigates the SSCM on its asymptotic spectral behaviors under high-dimensional elliptical populations,…

Semi-supervised learning with manifold regularization is a classical framework for jointly learning from both labeled and unlabeled data, where the key requirement is that the support of the unknown marginal distribution has the geometric…

Recent advances in healthcare technologies have led to the availability of large amounts of biological samples across several techniques and applications. In particular, in the last few years, Raman spectroscopy analysis of biological…

Datasets containing both categorical and continuous variables are frequently encountered in many areas, and with the rapid development of modern measurement technologies, the dimensions of these variables can be very high. Despite the…

This chapter reviews methods for linear shrinkage of the sample covariance matrix (SCM) and matrices (SCM-s) under elliptical distributions in single and multiple populations settings, respectively. In the single sample setting a popular…

This paper proposes a family of weighted batch means variance estimators, which are computationally efficient and can be conveniently applied in practice. The focus is on Markov chain Monte Carlo simulations and estimation of the asymptotic…

There is a great need for robust techniques in data mining and machine learning contexts where many standard techniques such as principal component analysis and linear discriminant analysis are inherently susceptible to outliers.…

In this paper we propose a family of robust estimates for isotonic regression: isotonic M-estimators. We show that their asymptotic distribution is, up to an scalar factor, the same as that of Brunk's classical isotonic estimator. We also…

The matrix exponential spatial models exhibit similarities to the conventional spatial autoregressive model in spatial econometrics but offer analytical, computational, and interpretive advantages. This paper provides a comprehensive review…

This paper considers the problem of estimating a high-dimensional (HD) covariance matrix when the sample size is smaller, or not much larger, than the dimensionality of the data, which could potentially be very large. We develop a…

Modern computational advances have enabled easy parallel implementations of Markov chain Monte Carlo (MCMC). However, almost all work in estimating the variance of Monte Carlo averages, including the efficient batch means (BM) estimator,…

Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both…

We obtain the upper error bounds of robust estimators for mean vector, using the median-of-means (MOM) method. The method is designed to handle data with heavy tails and contamination, with only a finite second moment, which is weaker than…

This paper deals with the asymptotic statistical properties of a class of redescending M-estimators in linear models with increasing dimension. This class is wide enough to include popular high breakdown point estimators such as…

We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…

A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…