Smoothness: Bias and Efficiency of Nonparametric Kernel Estimators

Yulia Kotlyarova, Marcia M. A. Schafgans and Victoria Zinde-Walsh

A chapter in Essays in Honor of Aman Ullah, 2016, vol. 36, pp 561-589 from Emerald Group Publishing Limited

Abstract: For kernel-based estimators, smoothness conditions ensure that the asymptotic rate at which the bias goes to zero is determined by the kernel order. In a finite sample, the leading term in the expansion of the bias may provide a poor approximation. We explore the relation between smoothness and bias and provide estimators for the degree of the smoothness and the bias. We demonstrate the existence of a linear combination of estimators whose trace of the asymptotic mean-squared error is reduced relative to the individual estimator at the optimal bandwidth. We examine the finite-sample performance of a combined estimator that minimizes the trace of the MSE of a linear combination of individual kernel estimators for a multimodal density. The combined estimator provides a robust alternative to individual estimators that protects against uncertainty about the degree of smoothness.

Keywords: Nonparametric estimation; kernel-based estimator; combined estimator; C14 (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eme:aecozz:s0731-905320160000036025

DOI: 10.1108/S0731-905320160000036025

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