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

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  • Dongliang Wang
  • Alan D. Hutson

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).

Suggested Citation

  • Dongliang Wang & Alan D. Hutson, 2015. "Inversion Theorem Based Kernel Density Estimation for the Ordinary Least Squares Estimator of a Regression Coefficient," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(8), pages 1571-1579, April.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:8:p:1571-1579
    DOI: 10.1080/03610926.2013.781633
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