Date on Master's Thesis/Doctoral Dissertation

1-2020

Document Type

Master's Thesis

Degree Name

M.A.

Department

Mathematics

Degree Program

Mathematics, MA

Committee Chair

Gill, Ryan

Committee Co-Chair (if applicable)

Han, Dan

Committee Member

Han, Dan

Committee Member

Gaskins, Jeremy

Author's Keywords

linear methods; variables; regression

Abstract

In data sets where there are a small number of observations but a large number of variables observed for each observation, ordinary least squares estimation cannot be used for regression models. There are many alternative including stepwise regression, penalized methods such as ridge regression and the LASSO, and methods based on derived inputs such as principal components regression and partial least squares regression. In this thesis, these five methods are described. K-fold cross validation is also discussed as a way for determining regularization parameters for each method. The performance of these methods in estimation and prediction is also examined through simulation studies under various interesting scenarios. Finally, the methods will be applied to a real data set in which each method is applied to build a model for the weights of mice based on microarray expression data for a large number of genes.

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