Date of Award

8-2009

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mathematical Science

Advisor

Kulasekera, Karunarathna B

Committee Member

Park , Chanseok

Abstract

We consider nonparametric estimation of a smooth regression function of one variable. In practice it is quite popular to use the data to select one global smoothing parameter. Such global selection procedures cannot sufficiently account for local sparseness of the covariate nor can they adapt to local curvature of the regression function. We propose a new method to select local smoothing parameters which takes into account sparseness and adapts to local curvature of the regression function. A Bayesian method allows the smoothing parameter to adapt to the local sparseness of the covariate and provides the basis for a local cross validation procedure which adjusts smoothing according to local curvature of the regression function. Simulation evidence indicates that the method can result in significant reduction of both point-wise mean squared error and integrated mean squared error of the estimators.

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.