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Adapting Kernel Estimation to Uncertain Smoothness

37 Pages Posted: 30 Sep 2011  

Yulia Kotlyarova

affiliation not provided to SSRN

Marcia Schafgans

London School of Economics & Political Science (LSE)

Victoria Zinde‐Walsh

McGill University - Department of Economics

Date Written: April 2011

Abstract

For local and average kernel based estimators, smoothness conditions ensure that the kernel order determines the rate at which the bias of the estimator goes to zero and thus allows the econometrician to control the rate of convergence. In practice, even with smoothness the estimation errors may be substantial and sensitive to the choice of the bandwidth and kernel. For distributions that do not have sufficient smoothness asymptotic theory may importantly differ from standard; for example, there may be no bandwidth for which average estimators attain root-n consistency. We demonstrate that non-convex combinations of estimators computed for different kernel/bandwidth pairs can reduce the trace of asymptotic mean square error relative even to the optimal kernel/bandwidth pair. Our combined estimator builds on these results. To construct it we provide new general estimators for degree of smoothness, optimal rate and for the biases and covariances of estimators. We show that a bootstrap estimator is consistent for the variance of local estimators but exhibits a large bias for the average estimators; a suitable adjustment is provided.

JEL Classification: C14

Suggested Citation

Kotlyarova, Yulia and Schafgans, Marcia and Zinde‐Walsh, Victoria, Adapting Kernel Estimation to Uncertain Smoothness (April 2011). LSE STICERD Research Paper No. EM557. Available at SSRN: https://ssrn.com/abstract=1935767

Yulia Kotlyarova (Contact Author)

affiliation not provided to SSRN

Marcia Schafgans

London School of Economics & Political Science (LSE) ( email )

Houghton Street
London, WC2A 2AE
United Kingdom

Victoria Zinde-Walsh

McGill University - Department of Economics ( email )

855 Sherbrooke Street West
Montreal, QC H3A 2T7
CANADA
514-398-4834 (Phone)
514-398-4938 (Fax)

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