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Multivariate local polynomial estimators: uniform boundary properties and asymptotic linear representation

Fan, Yanqin and Guerre, Emmanuel (2016) Multivariate local polynomial estimators: uniform boundary properties and asymptotic linear representation. In: Essays in Honor of Aman Ullah. Advances in Econometrics . Emerald, pp. 489-537. ISBN 978-1-78560-787-5. E-ISBN 978-1-78560-786-8. (doi:10.1108/S0731-905320160000036023) (KAR id:76313)

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http://dx.doi.org/10.1108/S0731-905320160000036023

Abstract

The asymptotic bias and variance of a general class of local polynomial estimators of M-regression functions are studied over the whole compact support of the multivariate covariate under a minimal assumption on the support. The support assumption ensures that the vicinity of the boundary of the support will be visited by the multivariate covariate. The results show that like in the univariate case, multivariate local polynomial estimators have good bias and variance properties near the boundary. For the local polynomial regression estimator, we establish its asymptotic normality near the boundary and the usual optimal uniform convergence rate over the whole support. For local polynomial quantile regression, we establish a uniform linearization result which allows us to obtain similar results to the local polynomial regression. We demonstrate both theoretically and numerically that with our uniform results, the common practice of trimming local polynomial regression or quantile estimators to avoid “the boundary effect” is not needed.

Item Type: Book section
DOI/Identification number: 10.1108/S0731-905320160000036023
Uncontrolled keywords: Compact support; boundary effect; pseudo-true value; Newton–Kantorovich Theorem; regression discontinuity design; trimming
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HB Economic Theory
Divisions: Faculties > Social Sciences > School of Economics
Depositing User: Emmanuel Guerre
Date Deposited: 10 Sep 2019 10:52 UTC
Last Modified: 30 Oct 2019 13:16 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/76313 (The current URI for this page, for reference purposes)
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