A goodness-of-fit testing approach for normality based on the posterior predictive distribution

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• 作者：Daojiang He (1) (2)
  Xingzhong Xu (1)
  
• 关键词：Goodness ; of ; fit test ; Posterior predictive distribution ; Predictive sample ; Anderson鈥揇arling test ; Shapiro鈥揥ilk test ; 62G10 ; 62G09 ; 62F15
• 刊名：TEST
• 出版年：2013
• 出版时间：March 2013
• 年：2013
• 卷：22
• 期：1
• 页码：1-18
• 全文大小：560KB
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• 作者单位：Daojiang He (1) (2)
  Xingzhong Xu (1)
  
  1. Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, P.R. China
  2. Department of Mathematics, Anhui Normal University, Wuhu, 241000, P.R. China
  
• ISSN：1863-8260

文摘

In this paper, we propose several new goodness-of-fit tests for normality based on the distance between the observed sample and the predictive sample drawn from the posterior predictive distribution. Note that the predictive sample is stochastic for a set of given sample observations, the distance being consequently random. To circumvent the randomness, we choose the conditional expectation and qth quantile as the test statistics. Two statistics are related to the well-known Shapiro鈥揊rancia test, and their asymptotic distributions are derived. The simulation study shows that the new tests are able to better discriminate between the normal distribution and heavy-tailed distributions or mixed normal distributions. Against those alternatives, the new tests are more powerful than existing tests including the Anderson鈥揇arling test and the Shapiro鈥揥ilk test, which are two of the best tests of normality in the literature.