Smoothness: bias and effciency of nonparametric kernel estimators

Kotlyarova, Yulia, Schafgans, Marcia M. A. and Zinde-Walsh, Victoria (2016) Smoothness: bias and effciency of nonparametric kernel estimators. In: Gonzalez-Rivera, Gloria, Hill, Carter R. and Lee, Tae-Hwy, (eds.) Essays in Honor of Aman Ullah. Advances in Econometrics,36. Emerald Group Publishing Limited. ISBN 9781785607875

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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.

Item Type:	Book Section
Official URL:	http://faculty.smu.edu/millimet/AiE.html#PVols
Additional Information:	© 2016 Emerald Group Publishing Limited
Library of Congress subject classification:	H Social Sciences > HA Statistics
Journal of Economic Literature Classification System:	C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C14 - Semiparametric and Nonparametric Methods
Sets:	Departments > Economics
Date Deposited:	19 May 2016 10:49
URL:	http://eprints.lse.ac.uk/66561/

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