Physical Sciences and Mathematics Commons^™

Mvgst: Tools For Multivariate And Directional Gene Set Testing, Dennis S. Mecham

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

There are many platforms available for simultaneously measuring the relative activity, or expression, levels of all genes in an organism. Genes that have systematically dier- ent expression levels between experimental factor levels are called \dierentially expressed". Because genes are annotated based on their known roles in biological processes (BP), molec- ular functions (MF) and cellular components (CC), gene expression levels can be used to determine relative activity levels of individual BP, MF, or CC between experimental fac- tor levels (this is called gene set testing). Often multiple experimental dierences are of interest simultaneously, which necessitates multivariate gene set testing. Only …

Curds And Whey: Little Miss Muffit's Contribution To Multivariate Linear Regression, John Cameron Kidd

Undergraduate Honors Capstone Projects

A common multivariate statistical problem is the prediction of two or more response variables using two or more predictor variables. The simplest model for this situation is the multivariate linear regression model. The standard least squares estimation for this model involves regressing each response variable separately on all the predictor variables. Breiman and Friedman [1] show how to take advantage of correlations among the response variables to increase the predictive accuracy for each of the response variable with an algorithm they call Curds and Whey. In this report, I describe an implementation of the Curds and Whey algorithm in …

Evaluation Of Multivariate Homogenous Arma Model, Lucy Chienhua Tseng

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis is to study a restricted multivariate AFRMA model, called the Homogeneous Model. This model is defined as one in which each univariate component of the multivariate model is of the same order in p and q as it is in the multivariate model.

From a mathematical respect, multivariate ARMA model is homogeneous if, and only if, its coefficient matrices are diagonal. From a physical respect, the present observation of a phenomenon can be modeled only by its own past observation and its present and past "errors."

The estimation procedures are developed based on maximum likelihood …

Linear Comparisons In Multivariate Analysis Of Variance, Hsin-Ming Tzeng

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The analysis of variance was created by Ronald Fisher in 1923. It is most widely used and basically useful approach to study differences among treatment averages.

Program For Missing Data In The Multivariate Normal Distribution, Chi-Ping Lu

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Missing data can often cause many problems in research work. Therefore for carrying out analysis, some procedure for obtaining estimates in the presence of missing data should be applied. Various theories and techniques have been developed for different types of problems.

Analysis of the Multivariate Normal Distribution with missing data is one of the areas studied. It has been discussed earlier by Wilkes (1932), Lord (1955), Edgett (1956) and Hartley (1958). They have established some basic concepts and an outline in the way of estimation.

In the last ten years, A. A. Afifi and R. M. Elasfoff also have contributed …