Calibrated Precision Matrix Estimation for High-Dimensional Elliptical Distributions

Approaches to High-Dimensional Covariance and Precision Matrix Estimation

Tail Asymptotics and Estimation for Elliptical Distributions

Abstract. Let (X, Y ) be a bivariate elliptical random vector with associated random radius in the Gumbel maxdomain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability P{X > x, Y > y} for x, y large. Further, based on the asymptotic bounds we discuss some aspects of the statistical modelling of joint survival probabilities and the surviva...

Adaptive Estimation in Elliptical Distributions with Extensions to High Dimensions

The goal of this paper is to propose efficient and adaptive regularized estimators for the nonparametric component, mean and covariance matrix in both high and fixed dimensional situations. Although, semiparametric estimation of elliptical distribution has also been discussed in [8], we wish to expand the model in two ways. First, study adaptive estimation methods with a novel scheme of estimat...

Bayesian Statistical Inference on Elliptical Matrix Distributions

In this paper we are concerned with Bayesian statistical inference for a class of elliptical distributions with parameters + and 7. Under a noninformative prior distribution, we obtain the posterior distribution, posterior mean, and generalized maximim likelihood estimators of + and 7. Under the entropy loss and quadratic loss, the best Bayesian estimators of 7 are derived as well. Some applica...

An R Package flare for High Dimensional Linear Regression and Precision Matrix Estimation

This paper describes an R package named flare, which implements a family of new high dimensional regression methods (LAD Lasso, SQRT Lasso, `q Lasso, and Dantzig selector) and their extensions to sparse precision matrix estimation (TIGER and CLIME). These methods exploit different nonsmooth loss functions to gain modeling flexibility, estimation robustness, and tuning insensitiveness. The devel...