Nonparametric Mean Estimation with Missing Data

Abstract

Missing data occur in most applied statistical analysis. The need to estimate the conditional or unconditional mean of a variable when some of its observations are missing is very frequent. In this article we study the effect of missing observations on the response variable in the estimation of a multivariate regression function. This effect is also considered in the estimation of the marginal mean. Following the research of Chu and Cheng [Chu, C. K., Cheng, P. E. (1995). Nonparametric regression estimation with missing data. J. Statist. Planning Inference 48:85–99] for the univariate case, we propose three non-parametric estimators of the regression function based on the Multivariate Local Linear Smoother [see Ruppert, D., Wand, M. P. (1994). Multivariate locally weighted least squares regression. Ann. Statist. 22(3):1346–1370]. The first consists of using only complete observations; the other two use simple or multiple imputation techniques respectively to complete the sample. The behavior in function of the Asymptotic Mean Squared Error (AMSE) is studied for the estimators. A method for obtaining optimal estimated bandwidth matrices based on the Bootstrap resampling mechanism is proposed.

Key Words:

• Bandwidth matrix
• Bootstrap
• Missing data
• Missing at random
• Multiple imputation
• Nonparametric regression
• Simple imputation

Acknowledgment

Research supported in part by MCyT Grant BFM2002-03213 (European FEDER support included).