Estimation in multiple regression model with elliptically contoured errors under MLINEX loss

This paper considers estimation of the regression vector of the multiple regression model with elliptically symmetric contoured errors. The generalized least square (GLS), restricted GLS and preliminary test (PT) estimators for regression parameter vector are obtained. The performances of the estimators are studied under multiparameter linear exponential loss function (MLINEX), and the dominance order of the estimators are given

Shrinkage estimation under multivariate elliptic models

The estimation of the location vector of a p-variate elliptically contoured distribution (ECD) is considered using independent random samples from two multivariate elliptically contoured populations when it is apriori suspected that the location vectors of the two populations are equal. For the setting where the covariance structure of the populations is the same, we define the maximum likelihood, Stein-type shrinkage and positive-rule shrinkage estimators. The exact expressions for the bias and quadratic risk functions of the estimators are derived. The comparison of the quadratic risk functions reveals the dominance of the Stein-type estimators if p ≥ 3. A graphical illustration of the risk functions under a 'typical' member of the elliptically contoured family of distributions is provided to confirm the analytical results

Estimation of the location parameter under LINEX loss function: multivariate case

Moment generating function, Empirical Bayes, LINEX loss function, Restricted model,

Estimation of parameters of parallelism model with elliptically distributed errors

Parallelism model, Elliptically contoured distribution, Inverse Laplace transform, Signed measure, Preliminary test estimator, Stein-type shrinkage estimator, Positive-rule shrinkage estimator, Weighted quadratic loss function,