The current note discusses the consistency proof for the penalized maximum likelihood estimator of a Gaussian mixture from the paper ‘Inference for multivariate normal mixtures’ by J. Chen and X. Tan. A soft spot in that proof is identified and a rigorous alternative proof based on a uniform...

In this paper, a new robust and efficient estimation approach based on local modal regression is proposed for partially linear single-index models, of which the univariate nonparametric link function is approximated by local polynomial regression. The asymptotic normality of proposed estimators...

We provide a feasible generalized least squares estimator for (unrestricted) multivariate GARCH(1, 1) models. We show that the estimator is consistent and asymptotically normally distributed under mild assumptions. Unlike the (quasi) maximum likelihood method, the feasible GLS is considerably...

We obtain random vectors with null third-order cumulants by projecting the data onto appropriate subspaces. Statistical applications include, but are not limited to, the robustification of Hotelling’s T2 test against nonnormality. Our approach only requires the existence of the third-order...

We propose jackknife empirical likelihood (EL) methods for constructing confidence intervals of mean with regression imputation that allows ignorable or nonignorable missingness. The confidence interval is constructed based on the adjusted jackknife pseudo-values (Rao and Shao, 1992). The...

In linear mixed models, the conditional Akaike Information Criterion (cAIC) is a procedure for variable selection in light of the prediction of specific clusters or random effects. This is useful in problems involving prediction of random effects such as small area estimation, and much attention...

The selection of a copula that appropriately describes the dependence structure of a bivariate distribution function is an issue of a prime interest in multivariate statistical analysis. The most popular methods of testing are those based on the empirical copula and on Kendall’s process; these...

For a class of skew-normal matrix distributions, the density function, moment generating function and independence conditions are obtained. The noncentral skew Wishart distribution is defined, and the necessary and sufficient conditions under which a quadratic form is noncentral skew Wishart...

In this paper, we describe and study a class of linear shrinkage estimators of the covariance matrix that is well-suited for high dimensional matrices, has a rather wide domain of applicability, and is rooted into the Gaussian conjugate framework of Chen (1979). We propose here a new look at...

Item nonresponse is often dealt with through imputation. Marginal imputation, which consists of treating separately each variable requiring imputation, generally leads to biased estimators of parameters (e.g., coefficients of correlation) measuring relationships between variables. Shao and Wang...