母體平均值比較的一致強韌分數統計量;A unified robust score statistic for population means comparison

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/71919

Title:	母體平均值比較的一致強韌分數統計量;A unified robust score statistic for population means comparison
Authors:	劉小篔;Liu,Hsiao-yun
Contributors:	統計研究所
Keywords:	強韌分數統計量;變異數分析;指數族的分配;Robust score statistic;Analysis of variance;Exponential family distribution
Date:	2016-07-18
Issue Date:	2016-10-13 14:06:21 (UTC+8)
Publisher:	國立中央大學
Abstract:	在母體分配未知的情形下，本文處理母體平均值的比較問題，探討的問題與變異數分析(analysis of variance)法類似，但我們不做母體分配的假設。我們藉由修正包括珈瑪、常態、卜阿松、負二項及逆高斯模型的分數統計量，導出這個強韌檢定統計量，這個統計量有熟悉的(觀察值-期望值)的型式。儘管這些分配不同，但產生唯一且一致的強韌分數統計量，且此強韌分數統計量可以推廣至指數族的分配。同時，我們提出強韌檢定優於目前其他的檢定方法的條件，並證明這些性質。再經由模擬和實際資料分析，我們呈現強韌分數檢定有限樣本的性質。;This dissertation deals with comparison of population means, similar to that of analysis of variance, in a way that the knowledge of the underlying distributions is absent. We develop a novel robust score test statistic that is akin to the familiar (observed-expected)/expected formula, with extra terms incorporating impact of the unspecified population moments. We derive the test by correcting the score statistics from models including gamma, normal, Poisson, negative-binomial and inverse-Gaussian. These models, in spite of their diversity, give rise to a single unified corrected robust score statistic which can be extended to exponential family distributions. Conditions under which our new robust test is more powerful than current competitors are provided. Finite sample performance is demonstrated via simulations and real data analysis.
Appears in Collections:	[Graduate Institute of Statistics] Electronic Thesis & Dissertation

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