Title page for ETD etd-82198-9530

Type of Document Dissertation
Author Lee, Yew-Haur Jr.
Author's Email Address yhlee@vt.edu
URN etd-82198-9530
Title Fisher Information Test of Normality
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Terrell, George R. Committee Chair
Coakley, Clint W. Committee Member
Hinkelmann, Klaus H. Committee Member
Smith, Eric P. Committee Member
Ye, Keying Committee Member
  • Normality testing
  • Fisher Information for location
  • Power study
  • Residuals
  • Nonparametric density estimation
  • Calculus of variation
Date of Defense 1998-09-03
Availability unrestricted
An extremal property of normal distributions is that they have the smallest Fisher Information for location among all distributions with the same variance. A new test of normality proposed by Terrell (1995) utilizes the above property by finding that density of maximum likelihood constrained on having the expected Fisher Information under normality based on the sample variance. The test statistic is then constructed as a ratio of the resulting likelihood against that of normality.

Since the asymptotic distribution of this test statistic is not available, the critical values for n = 3 to 200 have been obtained by simulation and smoothed using polynomials. An extensive power study shows that the test has superior power against distributions that are symmetric and leptokurtic (long-tailed). Another advantage of the test over existing ones is the direct depiction of any deviation from normality in the form of a density estimate. This is evident when the test is applied to several real data sets.

Testing of normality in residuals is also investigated. Various approaches in dealing with residuals being possibly heteroscedastic and correlated suffer from a loss of power. The approach with the fewest undesirable features is to use the Ordinary Least Squares (OLS) residuals in place of independent observations. From simulations, it is shown that one has to be careful about the levels of the normality tests and also in generalizing the results.

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