title: Inversion Theorem Based Kernel Density Estimation for the Ordinary Least Squares Estimator of a Regression Coefficient.
abstract: The traditional confidence interval associated with the ordinary least squares estimator of linear regression coefficient is sensitive to non-normality of the underlying distribution. In this article, we develop a novel kernel density estimator for the ordinary least squares estimator via utilizing well-defined inversion based kernel smoothing techniques in order to estimate the conditional probability density distribution of the dependent random variable. Simulation results show that given a small sample size, our method significantly increases the power as compared with Wald-type CIs. The proposed approach is illustrated via an application to a classic small data set originally from Graybill (1961).
authors.affiliation: Department of Public Health and Preventive Medicine, State University of New York Upstate Medical University, Syracuse, New York, USA.
authors.forename: Dongliang
authors.initials: D
authors.lastname: Wang
authors.affiliation: Department of Biostatistics, University at Buffalo, Buffalo, New York, USA.
authors.forename: Alan D
authors.initials: AD
authors.lastname: Hutson
keywords: Characteristic function; Inversion theorem; Kernel density estimation