Related papers: Robust estimators for non-decomposable elliptical …
Penalized $M-$estimators for logistic regression models have been previously study for fixed dimension in order to obtain sparse statistical models and automatic variable selection. In this paper, we derive asymptotic results for penalized…
A large dimensional characterization of robust M-estimators of covariance (or scatter) is provided under the assumption that the dataset comprises independent (essentially Gaussian) legitimate samples as well as arbitrary deterministic…
Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few…
We study the semiparametric efficient estimation of a class of linear functionals in settings where a complete multivariate dataset is supplemented by additional datasets recording subsets of the variables of interest. These datasets are…
Graphical models have found widespread applications in many areas of modern statistics and machine learning. Iterative Proportional Fitting (IPF) and its variants have become the default method for undirected graphical model estimation, and…
We show that the limiting variance of a sequence of estimators for a structured covariance matrix has a general form that appears as the variance of a scaled projection of a random matrix that is of radial type and a similar result is…
A new type of redescending M-estimators is constructed, based on data augmentation with an unspecified outlier model. Necessary and sufficient conditions for the convergence of the resulting estimators to the Hubertype skipped mean are…
This paper propose a novel decomposable graphical model to accommodate skew Gaussian graphical models. We encode conditional independence structure among the components of the multivariate closed skew normal random vector by means of a…
We introduce a class of hybrid M-estimators of multivariate scatter which, analogous to the popular spatial sign covariance matrix (SSCM), possess high breakdown points. We also show that the SSCM can be viewed as an extreme member of this…
M-estimators are ubiquitous in machine learning and statistical learning theory. They are used both for defining prediction strategies and for evaluating their precision. In this paper, we propose the first non-asymptotic "any-time"…
Penalized regression estimators are a popular tool for the analysis of sparse and high-dimensional data sets. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of…
We propose an approach to the estimation of infinite sets of random vectors. The problem addressed is as follows. Given two infinite sets of random vectors, find a single estimator that estimates vectors from with a controlled associated…
In this paper, we are basically discussing on a class of Baranchik type shrinkage estimators of the vector parameter in a location model, with errors belonging to a sub-class of elliptically contoured distributions. We derive conditions…
We establish asymptotic properties of $M$-estimators, defined in terms of a contrast function and observations from a continuous-time locally stationary process. Using the stationary approximation of the sequence, $\theta$-weak dependence,…
We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear…
We consider the problem of estimating the proportion $\theta$ of true null hypotheses in a multiple testing context. The setup is classically modeled through a semiparametric mixture with two components: a uniform distribution on interval…
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
We characterize the full classes of M-estimators for semiparametric models of general functionals by formally connecting the theory of consistent loss functions from forecast evaluation with the theory of M-estimation. This novel…
Surface integrals on density level sets often appear in asymptotic results in nonparametric level set estimation (such as for confidence regions and bandwidth selection). Also surface integrals can be used to describe the shape of level…