Date of Graduation

Spring 2014

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

George Mathew

Abstract

Analyzing large data sets is often time-consuming as many data sets depend on many variables, and multiple methods of analyzing such data sets are explored. In many practical situations such data sets can be modeled by the multivariate normal distribution. For statistical analysis of multivariate data sets, hypothesis testing and discriminant analysis are often used. These techniques require a strong background in univariate statistics and knowledge of the multivariate normal distribution. Specifically, the maximum likelihood estimators for the parameters of the multivariate normal population are often used in statistical inference settings. An approach to determining the maximum likelihood estimators is presented along with other important aspects of the multivariate normal distribution. Furthermore, both the likelihood ratio test and union intersection method of hypothesis testing are investigated in-depth. Discriminant analysis allows researchers to group data into pre-existing groups, and discriminant analysis is investigated here for two populations. Multiple discriminant rules are proved, including Fisher's linear discriminant function. In addition, the practical applications of discriminant analysis are demonstrated through the analysis of two data sets. In one application, thirteen variables are used to group homes based on median home cost. In another application, financial ratios are used to predict the bankruptcy status of banks.

Keywords

multivariate normal distribution, hypothesis testing, likelihood ratio test, union intersection test, discriminant analysis, Fisher's discriminant function, maximum likelihood allocation rule

Subject Categories

Mathematics

Copyright

© Katelin Lea Strand

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