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Permutation Test for Location Parameters When Sample Size is Small

Author: HanYuGuo
Tutor: XuJin
School: East China Normal University
Course: Probability Theory and Mathematical Statistics
Keywords: Permutation test Significance level Efficacy Small sample Positional parameters
CLC: O211.3
Type: Master's thesis
Year: 2009
Downloads: 260
Quote: 1
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Abstract


The two parameters of the normal distribution hypothesis testing overall position has been more mature theories and methods. Targeted at non-normal two-sample location parameter hypothesis testing , Welch (1942) on the t-test amendments proposed Welch statistic T_w, and use the t-distribution approximation T_w distribution . Xu (2008) derived Welch statistic in a non -normal distribution under general approximation . For other distribution location parameter testing, the additional certain conditions can then make use of the central limit theorem normality progressive to be addressed. But in reality , especially in small samples , the central limit theorem conditions difficult to meet , Wilcoxon (1963) proposed a rank test. Efron (1979) proposed a self-help method, it can also be applied to hypothesis testing . Fisher (1935) and Pitman (19337,1938) proposed a permutation test and distribution -independent , but it was limited by the large amount of calculation , the development and application is limited. But with the high-speed development of computers , permutation test is widely used , to be welcomed. But recently Huang et al ( 2006 ) pointed out that the distribution of permutation test in two different cases, the test is too conservative . We focused on this issue , focusing on relatively small samples as well as in the overall distribution of unknown circumstances , Welch test, rank sum test. Bootstrap test and permutation test for position -parametric test of significance and efficacy . In order to improve the two-sample test of positional parameters permutation test efficacy , we propose a permutation test to the center of the amendment ; to improve the discrete case permutation test significance level of accuracy presents a discrete random variable permutation test for continuous correction . At the same time promote the comparison to a single overall position overall and multi- parametric test , and through a lot of theory and simulations confirmed case of small sample two parameters permutation test sample position and other inspection methods significance level or less, but the permutation test with greater efficacy testing ; larger sample size in case of permutation test and Welch t test test power less.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Distribution theory
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