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dc.contributor.authorLee, Yew-Haur Jr.en_US
dc.description.abstractAn 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.

dc.publisherVirginia Techen_US
dc.rightsI hereby grant to Virginia Tech or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University Libraries in all forms of media, now or hereafter known. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation.en_US
dc.subjectNormality testingen_US
dc.subjectFisher Information for locationen_US
dc.subjectPower studyen_US
dc.subjectNonparametric density estimationen_US
dc.subjectCalculus of variationen_US
dc.titleFisher Information Test of Normalityen_US
dc.description.degreePh. D.en_US D.en_US Polytechnic Institute and State Universityen_US
dc.contributor.committeechairTerrell, George R.en_US
dc.contributor.committeememberCoakley, Clint W.en_US
dc.contributor.committeememberHinkelmann, Klaus H.en_US
dc.contributor.committeememberSmith, Eric P.en_US
dc.contributor.committeememberYe, Keyingen_US

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