Inversion Theorem Based Kernel Density Estimation for the Ordinary Least Squares Estimator of a Regression Coefficient

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 Graybill, F.A. (1961). Introduction to Linear Statistical Models. Vol. 1. New York: McGraw-Hill Book Company. Google Scholar]).