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Full-Text Articles in Physical Sciences and Mathematics
Convolution Inequalities And Applications To Partial Differential Equations., Matthew Reynolds
Convolution Inequalities And Applications To Partial Differential Equations., Matthew Reynolds
Electronic Theses and Dissertations
In this dissertation we develop methods for obtaining the existence of mild solutions to certain partial differential equations with initial data in weighted L p spaces and apply them to some examples as well as improve the solutions to some known PDEs studied extensively in the literature. We begin by obtaining a version of a Stein-Weiss integral inequality which we will use to obtain general convolution inequalities in weighted L p spaces using the techniques of interpolation. We will then use these convolution inequalities to make estimates on PDEs that will help us obtain mild solutions as fixed points of …
Linear Methods For Regression With Small Sample Sizes Relative To The Number Of Variables., Rajesh Sikder
Linear Methods For Regression With Small Sample Sizes Relative To The Number Of Variables., Rajesh Sikder
Electronic Theses and Dissertations
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 …