A Note on Double K-Class Estimators under Elliptical Symmetry

 

S.M.M. Tabatabaey and M. Arashi (2008). A Note on Double K-Class Estimators under Elliptical Symmetry . Journal of Statistical Research, Vol. 42, No. 1, pp.  75-83.

 

Abstract

In this paper, estimation of the regression vector parameter in the multiple regression model \mathbf{y} = \mathbf{X} \beta+ \epsilon is considered, when the error term belongs to the class of elliptically contoured distributions (ECD), say, \epsilon\sim EC_n(0; \sigma^2\mathbf{V},\psi), where \sigma^2 is unknown and \mathbf{V} is a symmetric p.d known matrix with the characteristic generator \psi. It is well-known that UMVU estimator of  has the form (\mathbf{X}'\mathbf{V}^{-1}\mathbf{X})^{-1}\mathbf{X}'\mathbf{V}^{-1}y. In this paper using integral series representation of ECDs, the dominance conditions of double k-class estimators given by \hat\beta_{ k1,k2} =  [1-\frac{k_1\hat\epsilon'\mathbf{V}^{-1}\hat\epsilon}{y'y-k_2\hat\epsilon\mathbf{V}^{-1}\hat\epsilon}]\hat\beta  over UMVUE, have been derived under weighted quadratic loss function.

 

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