Local modal regression

Weixin Yao, Bruce G. Lindsay, Runze Li

Research output: Contribution to journalArticle

40 Citations (Scopus)

Abstract

A local modal estimation procedure is proposed for the regression function in a nonparametric regression model. A distinguishing characteristic of the proposed procedure is that it introduces an additional tuning parameter that is automatically selected using the observed data in order to achieve both robustness and efficiency of the resulting estimate. We demonstrate both theoretically and empirically that the resulting estimator is more efficient than the ordinary local polynomial regression (LPR) estimator in the presence of outliers or heavy-tail error distribution (such as t-distribution). Furthermore, we show that the proposed procedure is as asymptotically efficient as the LPR estimator when there are no outliers and the error distribution is a Gaussian distribution. We propose an expectation-maximisation-type algorithm for the proposed estimation procedure. A Monte Carlo simulation study is conducted to examine the finite sample performance of the proposed method. The simulation results confirm the theoretical findings. The proposed methodology is further illustrated via an analysis of a real data example.

Original languageEnglish (US)
Pages (from-to)647-663
Number of pages17
JournalJournal of Nonparametric Statistics
Volume24
Issue number3
DOIs
StatePublished - Sep 1 2012

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Regression
Local Polynomial Regression
Regression Estimator
Outlier
Heavy Tails
t-distribution
Expectation Maximization
Nonparametric Model
Parameter Tuning
Nonparametric Regression
Regression Function
Gaussian distribution
Regression Model
Monte Carlo Simulation
Simulation Study
Robustness
Estimator
Methodology
Estimate
Demonstrate

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Yao, Weixin ; Lindsay, Bruce G. ; Li, Runze. / Local modal regression. In: Journal of Nonparametric Statistics. 2012 ; Vol. 24, No. 3. pp. 647-663.
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Local modal regression. / Yao, Weixin; Lindsay, Bruce G.; Li, Runze.

In: Journal of Nonparametric Statistics, Vol. 24, No. 3, 01.09.2012, p. 647-663.

Research output: Contribution to journalArticle

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