Multivariate Local Polynomial Estimators: Uniform Boundary Properties and Asymptotic Linear Representation

Yangin Fan and Emmanuel Guerre

A chapter in Essays in Honor of Aman Ullah, 2016, vol. 36, pp 489-537 from Emerald Group Publishing Limited

Abstract: The asymptotic bias and variance of a general class of local polynomial estimators of M-regression functions are studied over the wholecompactsupport of themultivariatecovariate 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.

Keywords: Compact support; boundary effect; pseudo-true value; Newton–Kantorovich Theorem; regression discontinuity design; trimming; C12; C14; C21 (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://www.emerald.com/insight/content/doi/10.110 ... d&utm_campaign=repec (text/html)
https://www.emerald.com/insight/content/doi/10.110 ... 1-905320160000036023
https://www.emerald.com/insight/content/doi/10.110 ... d&utm_campaign=repec (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eme:aecozz:s0731-905320160000036023

DOI: 10.1108/S0731-905320160000036023

Access Statistics for this chapter

More chapters in Advances in Econometrics from Emerald Group Publishing Limited
Bibliographic data for series maintained by Emerald Support ().