Smoothness: Bias and Efficiency of Nonparametric Kernel Estimators

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.

Citation

Kotlyarova, Y., Schafgans, M.M.A. and Zinde-Walsh, V. (2016), "Smoothness: Bias and Efficiency of Nonparametric Kernel Estimators", Essays in Honor of Aman Ullah (Advances in Econometrics, Vol. 36), Emerald Group Publishing Limited, Leeds, pp. 561-589. https://doi.org/10.1108/S0731-905320160000036025