Author： Wang Dongliang Hutson Alan D.
Publisher： Taylor & Francis Ltd
E-ISSN： 1532-415X|44|8|1571-1579
ISSN： 0361-0926
Source： Communications in Statistics: Theory and Methods, Vol.44, Iss.8, 2015-04, pp. : 1571-1579
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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).
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