IJPAM: Volume 27, No. 1 (2006)

CONVERGENCE RATES OF EMPIRICAL BAYES TEST FOR
ONE-SIDE TRUNCATION PARAMETERS WITH
ASYMMETRIC LOSS FUNCTIONS

Yu-Sheng Xu$^1$, Yong Xu$^2$ , Yi-Min Shi$^3$
$^1$College of Science
Xi'an University of Architecture and Technology
Xi'an, 710055, P.R. CHINA
$^{2,3}$Department of Applied Mathematics
Northwestern Polytechnical University
Xi'an, 710072, P.R. CHINA
$^2$e-mail: hsux3@263.net
$^3$e-mail: ymshi@nwpu.edu.cn


Abstract.This paper is to investigate the convergence rates of empirical Bayes test of parameters in one-side truncated distribution family under the asymmetric loss function of the form $L(\theta ,\theta _0 ) = k_1
(\theta - \theta _0 )^2I_{(\theta < \theta _0 )} + ...
...2 + k_3 (\theta - \theta _0 )]{\kern 1pt} I_{(\theta
\ge \theta _0 )} k_i \ge 0$, $i = 1,2,3$. The kernel estimation is used to construct the empirical Bayes decision function and its convergence rates $O(n^{-\lambda /2})$ is presented. Finally an illustrative example is given to verify the conditions in theorem.

Received: December 16, 2005

AMS Subject Classification: 62C12

Key Words and Phrases: asymmetric loss functions, empirical Bayes (EB) test, convergence rates

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 27
Issue: 1