IJPAM: Volume 27, No. 1 (2006)

EMPIRICAL BAYES TEST FOR ONE-SIDE TRUNCATION
PARAMETERS WITH ASYMMETRIC LOSS FUNCTIONS
USING NA SAMPLES

Jun-Feng Zhao$^1$, De-Qin Chen$^2$, Yong Xu$^1$, Yi-Min Shi$^1$
$^{1,3,4}$Department of Applied Mathematics
Northwestern Polytechnical University
Xi'an, 710072, P.R. CHINA
$^1$e-mall: zhaojf@nwpu.edu.cn
$^3$e-mail: hsux3@263.net
$^4$e-mail: ymshi@nwpu.edu.cn
$^2$Department of Mathematics
Sichuan University of Science and Engineering
Zigong, Sichuan, 643000, P.R. CHINA
e-mail: chendeqin-66@163.com


Abstract.In the case of negatively associated (NA) samples, this paper is to investigate empirical Bayes test of parameters in one-side truncated distribution family under the asymmetric loss function of the form $L(\theta ,\theta _0 ) = k_1 (\theta - \theta _0 )^2I_{(\theta < \theta _0 )} + ...
... + k_2 (\theta - \theta _0 )]{\kern 1pt} I_{(\theta \ge \theta _0 )}, k_i \ge 0$, $i = 1,2$. The kernel estimation of probability density function is used to construct EB test function, and its asymptotical optimality is obtained.

Received: December 16, 2005

AMS Subject Classification: 62C12

Key Words and Phrases: negatively associated (NA), asymmetric loss functions, empirical Bayes (EB) test, asymptotical optimality

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