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Dissertation Information for Jorge L. Romeu

NAME:
- Jorge L. Romeu

DEGREE:
- Ph.D.

DISCIPLINE:
- Operations Research

SCHOOL:
- Syracuse University (USA) (1990)

ADVISORS:
- None

COMMITTEE MEMBERS:
- None

MPACT Status: Incomplete - Not_Inspected

Title: Development and evaluation of a general procedure for assessing multivariate normality

Abstract: In this dissertation we develop a methodology for assessing distributional assumptions of multivariate data, with graphical applications. This methodology is a multivariate extension of the univariate graphical Goodness-of-Fit (GOF) procedure of Ozturk and Dudewicz (1990). Their univariate test is based on representing the sample ordered statistics by linked vectors in a two dimensional space. Our multivariate procedure transforms the p-variate sample into p independent univariate samples and then applies the multisample univariate test of Ozturk and Dudewicz to the transformed data.

We study the general properties of our new methodology, both theoretically and numerically. We develop two specific implementations. We classify the existing multivariate normality GOF competitor tests and select the "best" eight for a Monte Carlo power study. This study includes twelve non normal alternatives, four sample sizes, three different p-variates and two covariance structures. We classify the statistical alternatives by the shape of the distribution and the degree of non-normality. We rank the ten procedures compared by their performance under the different types of statistical alternatives. And we devise a strategy for testing multivariate normality based on these results.

Finally, all multivariate normality GOF competitor procedures either follow a known asymptotic distribution or are empirical in nature. Hence, their asymptotic critical values are not valid when treating small samples or simply are not available. We obtain, by simulation, empirical critical values for selected sample sizes, number of p-variates and correlations, as a working solution for this problem.

MPACT Scores for Jorge L. Romeu

A = 0
C = 1
A+C = 1
T = 0
G = 0
W = 0
TD = 0
TA = 0
calculated 2010-09-26 00:53:25

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