Problems in Mathematical Statistics

Abstract

The primary goal of this project was to develop new statistical methods to meet the challenges of the evolving data analysis problems that the army encounters. These statistical methods also have numerous applications in biology, medicine and related sciences. Our research is focused on the following three important problems: (I) study mathematical details of the quasi-least squares method that we have developed for analyzing longitudinal and clustered data, (2) develop bivariate models for gene expression data to identify differentially expressed genes in microarrays, (3) study invariance properties of test statistics that occur in multivariate analysis of variance. For binary longitudinal data, we have studied the efficiency of generalized estimating equations with respect to a latent variable model and made some recommendations on how to choose the weight matrix. For continuous longitudinal data, we have studied theoretical properties of the quasi-least squares method. We have proved fairly general theorems establishing the asymptotic distributions of the quasi-least squares estimates. Using the asymptotic relative efficiency criterion we have shown that the quasi-least squares estimates are good competitors to the traditional maximum likelihood estimates obtained under the normality assumption for autoregressive time series regression models. In recent years, technology has made it possible to study gene expressions of thousands of genes simultaneously through the use of microarrays. We have developed novel statistical models to identify differentially expressed genes in microarray experiments. Next, for normal data we have obtained simplified versions of the Cochran's theorem for the independence and Wishartness of matrix quadratic forms for arbitrary covariance matrix. The results were used to characterize the class of covariance matrices such that the distributions of popular multivariate test statistics remain invariant except for a scale factor.

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Document Details

Document Type
Technical Report
Publication Date
Mar 10, 2005
Accession Number
ADA431200

Entities

People

  • N. R. Chaganty

Organizations

  • Old Dominion University

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Analysis Of Variance
  • Computational Science
  • Covariance
  • Data Analysis
  • Data Mining
  • Data Science
  • Efficiency
  • Equations
  • Gene Expression
  • Information Science
  • Knowledge Management
  • Least Squares Method
  • Multivariate Analysis
  • Normality
  • Statistical Analysis
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Oncology and Biomarker-Based Cancer Detection.
  • Statistical inference.