Behrens-Fisher问题的正态逼近

统计研究 ›› 2009, Vol. 26 ›› Issue (11): 106-108.

Behrens-Fisher问题的正态逼近

金华郑圣听陈伟权

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2009-11-15 发布日期:2009-11-15

Normal Approximation to the Behrens-Fisher Problem

Jin Hua; Zheng Shengting; Chen Weiquan

Received:1900-01-01 Revised:1900-01-01 Online:2009-11-15 Published:2009-11-15

摘要/Abstract

摘要： 本文提出用基于得分检验的正态逼近方法来解决Behrens-Fisher问题，即比较方差比未知时两正态总体的均值。模拟结果显示：在所有的研究情况下，我们的方法都能很好地控制第一类错误，检验功效也不差；而最常用的Welch近似t检验在样本量不等时大多数情况都不能控制第一类错误。

关键词: Behrens-Fisher问题, Welch近似t检验, 得分检验, 正态逼近

Abstract: Normal approximation based on the score test is proposed to solve the Behrens-Fisher problem, that is to compare the means of two normal populations with the ratio of the population variances unknown. Simulation results suggest that our new approach can definitely control the type I error rates with reasonable powers under all studied conditions while the popular Welch’s approximate t-test cannot for most cases when the sizes of two samples are unequal.

Key words: Behrens-Fisher problem, Welch’s approximate t-test, Score test, Normal approximation

金华郑圣听陈伟权. Behrens-Fisher问题的正态逼近[J]. 统计研究, 2009, 26(11): 106-108.

Jin Hua, Zheng Shengting, Chen Weiquan. Normal Approximation to the Behrens-Fisher Problem[J]. Statistical Research, 2009, 26(11): 106-108.