An Empirical Bayesian Approach for Testing Normality

  • 呂 易錦

Student thesis: Master's Thesis


Many fundamental statistical methods root in normal assumption Therefore a variety of normality tests are frequently applied to these methods to prevent normal assumption violation In this thesis we first review popular normality tests and then propose a new normality test The test statistic as motivated by information matrix test is the ratio of determinants of two variance matrices The numerator is the determinant of the sandwich variance formula often used in estimating equation approaches whereas the denominator is the determinant of the inverse of Fisher's information matrix When the sample size is large and the normal assumption is true the test statistic converges in probability to 1 Moreover the test statistic is also the Bayes factor of a particular empirical Bayesian model Furthermore the test statistic can be expressed as the weighted sum of the excess kurtosis and the skewness square Under the null hypothesis and for large sample the test statistic can be well-approximated by a normal distribution We simulated and studied the size and power of the proposed test and found that it is compatible with some popularly used normality tests when sample size is as large as 100 We also applied the proposed test to examine the normal assumption on the body fat percentage prediction and to examine the Brownian motion assumption on the log-returns of stock prices And we showed the consequences of the proposed test and popularly used normality tests
Date of Award2017 Sep 12
Original languageEnglish
SupervisorSheng-Mao Chang (Supervisor)

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