Statistics and Its Interface

Volume 4 (2011)

Number 4

Nonparametric regression with discrete covariate and missing values

Pages: 463 – 474



Song Xi Chen (Department of Business Statistics and Econometrics, Guanghua School of Management, Peking University, Beijing, China)

Cheng Yong Tang (Department of Statistics and Applied Probability, National University of Singapore, Singapore)


We consider nonparametric regression with a mixture of continuous and discrete explanatory variables where realizations of the response variable may be missing. An imputation based nonparametric regression estimator is proposed. We show that the proposed approach leads to a leading order variance benefit, whereas smoothing the categorical variables gives a second order variance improvement. We also demonstrate the applications of the proposed approach through numerical simulations and two practical examples.


nonparametric regression, discrete kernel smoothing, imputation, missing values, variance reduction

2010 Mathematics Subject Classification

Primary 62G08. Secondary 62G20.

Published 17 November 2011