In random effect models, error variance (stage 1 variance) and scalar random effect variance components (stage 2 variances) are a priori modeled independently. Considering the intrinsic link between the stages 1 and 2 variance components and their interactive effect on the parameter draws in...

In this paper, from the estimating equation-based sufficient dimension reduction method in the literature, its robust version is proposed to alleviate the impact from outliers. To achieve this, a robust nonparametric regression estimator is suggested. The estimator is plugged in the estimating...

Reference intervals and regions are widely used to identify the measurement range expected from a reference population. Such regions capture the central part of the population, and have potential applications in the field of laboratory medicine. Furthermore, the uncertainty in an estimated...

A family of possibly asymmetric distributions on the unit hyper-disc with center at the origin is proposed. The paper presents a non-trivial multivariate generalization of the Möbius distribution on the unit disc. The family is obtained by applying a conformal mapping to the spherically...

We present a robust Generalized Empirical Likelihood estimator and confidence region for the parameters of an autoregression that may have a heavy tailed heteroscedastic error. The estimator exploits two transformations for heavy tail robustness: a redescending transformation of the error that...

Three-dimensional orientation data, with observations as 3×3 rotation matrices, have applications in areas such as computer science, kinematics and materials sciences, where it is often of interest to estimate a central orientation parameter S represented by a 3×3 rotation matrix. A well-known...

Heckman selection model is the most popular econometric model in analysis of data with sample selection. However, selection models with Normal errors cannot accommodate heavy tails in the error distribution. Recently, Marchenko and Genton proposed a selection-t model to perform frequentist’...

To deal with the compatibility issue of full conditional distributions of a (discrete) random vector, a graphical representation is introduced where a vertex corresponds to a configuration of the random vector and an edge connects two vertices if and only if the ratio of the probabilities of the...

The likelihood ratio (LR) for testing if the covariance matrix of the observation matrix X is R has some invariance properties that can be exploited for covariance matrix estimation purposes. More precisely, it was shown in Abramovich et al. (2004, 2007, 2007) that, in the Gaussian case,...

This paper deals with the problem of estimating the normal covariance matrix relative to the Stein loss. The main interest concerns a new class of estimators which are invariant under a commutator subgroup of lower triangular matrices. The minimaxity of a James–Stein type invariant estimator...