Multiparameter estimation in truncated power series distributions under the stein's loss

Abstract

LetX ₁,…,X _p be p(≥2)independent random variables, where each X.has a distribution belonging to a one parameter truncated power series

distribution. The problem is to estimate simultaneously the unknown parameters under asymmetric loss developed by James and Stein (Proc. Fourth Berkeley Symp. Math. Statist. Prob. 1, 361-380). Several new classes of dominating estimators are obtained by solving a certain difference inequality.

Keywords:

• Simultaneous estimation
• truncated power series
• unbiasedness
• trimmed estimator
• Stein’s loss