Large sample results for varying kernel regression estimates

Hira L. Koul and Weixing Song

Journal of Nonparametric Statistics, 2013, vol. 25, issue 4, 829-853

Abstract: The varying kernel density estimates are particularly designed for positive random variables. Unlike the commonly used symmetric kernel density estimates, the varying kernel density estimates do not suffer from the boundary problem. This paper establishes asymptotic normality and uniform almost sure convergence results for a varying kernel density estimate when the underlying random variable is positive. Similar results are also obtained for a varying kernel nonparametric estimate of the regression function when the covariate is positive. Pros and cons of the varying kernel regression estimate are also discussed via a simulation study.

Date: 2013
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DOI: 10.1080/10485252.2013.810742

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