多样本变异系数比较的似然比检验  

A Likelihood Ratio Test for Coefficient of Variations from Multiple Samples

作　　者：汪鹏[1] 周怡[1] 周基元[1] 

机构地区：[1]南方医科大学公共卫生与热带医学学院生物统计学系,510515

出　　处：《中国卫生统计》2013年第3期317-322,共6页Chinese Journal of Health Statistics

基　　金：国家自然科学基金资助(81072386);南方医科大学公共卫生与热带医学学院本科生课外科研活动重点资助立项资助项目(GWXS20110105)

摘　　要：目的通过求非中心t分布未知参数最大似然估计,由此提出一种比较多个样本变异系数差异的似然比检验(LRT)方法,并与现有的D'AD检验在第Ⅰ类错误率与检验效能两方面进行模拟比较。方法由于样本变异系数的似然函数跟非中心t分布有关,本文首先提出一种求非中心t分布未知参数最大似然估计的算法,然后由此构造出比较多个样本变异系数的似然比检验统计量,并求出其Bartlett校正系数,对似然比检验统计量进行Bartlett校正,以便该方法也能用于小样本的情形。计算机模拟时从正态分布总体中抽样,模拟LRT的第Ⅰ类错误率与检验效能,并与D'AD检验做比较。将LRT方法编写成R语言程序,输出校正后的统计量值和相应P值,以方便实际应用。结果校正的LRT方法能更好地控制第Ⅰ类错误率,并且其检验效能比D'AD检验更稳健。在小样本且样本量不均衡的情形下,其检验效能比D'AD方法高。结论校正的LRT方法适用范围更广,检验效能高,可为检验多样本变异系数间差异提供更加有效的方法。Objective To propose an algorithm to find the maximum likelihood estimate of the unknown parameter of the noncentral t- distribution, develop a likelihood ratio test（LRT） to compare the difference among coefficient of variations （CVs） from multiple samples, and conduct simulation studies to compare the performance of the proposed LRT with the existing DAD test in terms of the type I error rate and test power, Methods As noting that the likelihood function of the sample coefficient of variation is related to a noncentral t-distribution,we firstly propose an al- gorithm to find the maximum likelihood estimate of the unknown parameter of the noncentral t-distribution. Secondly, we develop a LRT to compare the difference among CVs from multiple samples. Thirdly, by calculating the Bartlett Correction Factor, we suggest an adjusted LRT, which is denoted by LRT ＊ in this paper, so that LRT ＊ can be suitable for samples of small size. Fourthly, by randomly choosing the samples from a normal distribu- tion, we simulate the size and power of the LRT ＊ and compare the per- formance of LRT ＊ with the DAD test. Finally, we develop the freely avail- able source code in R language based on the LRT＊ method, which outputs the value of LRT ＊ and the corresponding P value for easy use in practice. Results The LRT ＊ controls the type I error rate better and has steadier and higher power than the DAD test,especially under the situation of sam- ples of small and different sizes. Conclusion The LRT ＊ is an effective tool to test for the difference among CVs from multiple samples.

关 键 词：变异系数 似然比检验 非中心 T分布 多样本 

分 类 号：O212.1[理学—概率论与数理统计]