﻿ 纵向数据下线性指数分布参数的经验Bayes双边检验 The Empirical Bayes Two-Sided Tests for the Parameter of Linear Exponential Distribution under Longitudinal Data

Statistics and Application
Vol.05 No.03(2016), Article ID:18501,7 pages
10.12677/SA.2016.53022

The Empirical Bayes Two-Sided Tests for the Parameter of Linear Exponential Distribution under Longitudinal Data

Xiuhui Luo, Chengdong Wei*, Jinli Li

School of Mathematical and Statistics Sciences, Guangxi Teachers Education University, Nanning Guangxi

Received: Aug. 19th, 2016; accepted: Sep. 4th, 2016; published: Sep. 9th, 2016

ABSTRACT

In the case of longitudinal data, this paper studies two-side test problem of linear exponential distribution parameters under square loss function. By applying Markov inequality, the EB test rules for parameter of the linear exponential distribution are constructed and the asymptotically optimal property is obtained. Finally, we obtain the convergence rate of the proposed EB test under suitable conditions.

Keywords:Longitudinal Data, Linear Exponential Distribution, Empirical Bayes Test, Asymptotic Optimality, Convergence Rate

1. 引言

(1)

(2)

(3)

, (4)

(5)

(6)

，故有

(7)

(8)

(9)

2. EB检验函数的构造

(10)

(11)

(12)

(13)

3. 几个主要的引理

(I) 当关于连续，当时，则有

(II) 当，当取时，对于

4. EB检验函数的性质

(i)为正数序列，且满足,

(ii)

(iii)的连续函数。

(14)

(15)

，则有。又由式(6)和Fubini定理得

(16)

(iv)

(17)

(18)

(19)

(20)

(21)

(22)

The Empirical Bayes Two-Sided Tests for the Parameter of Linear Exponential Distribution under Longitudinal Data[J]. 统计学与应用, 2016, 05(03): 225-231. http://dx.doi.org/10.12677/SA.2016.53022

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