Doctoral Dissertation Defense: Ye Yang
Advisor: Dr. Thomas Mathew
Location
Mathematics/Psychology : 401
Date & Time
November 28, 2016, 10:00 am – 12:00 pm
Description
Title: The Simultaneous Assessment of Normality and Homoscedasticity in Some Linear Models
Abstract
The validity of statistical inference usually depends on the underlying assumptions. Thus it is important to check if the data are consistent with the assumptions. In the analysis of variance (ANOVA) methodology, linear models are typically used, and several assumptions are necessary for the ANOVA procedure to be valid. Two of the crucial assumptions are normality and homoscedasticity. The assessment of normality, based on graphical methods or formal tests, is usually carried out under the homoscedasticity assumption. On the other hand, most tests for homoscedasticity are sensitive to the normality assumption. Thus it is highly desirable to have a methodology that can be used for the simultaneous assessment of normality and homoscedasticity. In the thesis, such methodologies are developed under a general univariate fixed effects model, a bivariate fixed effects model, and the one-way random model with balanced or unbalanced data. This is accomplished by embedding the normal distribution within the class of the so called smooth alternatives due to Neyman (1937), and then deriving the score tests. Computational aspects are addressed, and the results are illustrated with examples.
Abstract
The validity of statistical inference usually depends on the underlying assumptions. Thus it is important to check if the data are consistent with the assumptions. In the analysis of variance (ANOVA) methodology, linear models are typically used, and several assumptions are necessary for the ANOVA procedure to be valid. Two of the crucial assumptions are normality and homoscedasticity. The assessment of normality, based on graphical methods or formal tests, is usually carried out under the homoscedasticity assumption. On the other hand, most tests for homoscedasticity are sensitive to the normality assumption. Thus it is highly desirable to have a methodology that can be used for the simultaneous assessment of normality and homoscedasticity. In the thesis, such methodologies are developed under a general univariate fixed effects model, a bivariate fixed effects model, and the one-way random model with balanced or unbalanced data. This is accomplished by embedding the normal distribution within the class of the so called smooth alternatives due to Neyman (1937), and then deriving the score tests. Computational aspects are addressed, and the results are illustrated with examples.
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