Physical Sciences and Mathematics Commons^™

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 …

A Comparison Of Two Linear Nonparametric Regression Techniques, Sylvain Sardy

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis presented a useful tool in regression. Nonparametric linear regression techniques were described in the general context of regression. A comparison of two of these techniques, kernel regression and iterative regression, showed various aspects of nonparametric linear regressors.

Disconjugacy And Oscillation Theory Of Linear Differential And Difference Equations, Yuhua Xu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This dissertation is both a literature survey and a presentation of new and independent results.

The survey gives an overview of disconjugacy and oscillation theory for linear differential and difference equations with an emphasis on comparing the theory of difference equations to the theory of differential equations. Second order scalar equations, higher order scalar equations, matrix equations (systems) and Hamiltonian systems are discussed. A chapter on three-term recurrences of systems is also included. Both similarities and differences between differential and difference equations are described.

The new and independent results are for Hamiltonian systems of difference equations. Those results include the …

Linear Regression Of The Poisson Mean, Duane Steven Brown

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis was to compare two estimation procedures, the method of least squares and the method of maximum likelihood, on sample data obtained from a Poisson distribution. Point estimates of the slope and intercept of the regression line and point estimates of the mean squared error for both the slope and intercept were obtained. It is shown that least squares, the preferred method due to its simplicity, does yield results as good as maximum likelihood.

Also, confidence intervals were computed by Monte Carlo techniques and then were tested for accuracy. For the method of least squares, confidence …

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.