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Nonparametric mean estimation with missing data. (English) Zbl 1102.62033
Summary: 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. 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 research of C. K. Chu and P. E. Cheng [Nonparametric regression estimation with missing data. J. Stat. Plann. Inference 48, 85–99 (1995; Zbl 0897.62038)] for the univariate case, we propose three nonparametric estimators of the regression function based on the multivariate local linear smoother [see D. Ruppert and M. P. Wand, Multivariate locally weighted least squares regression. Ann. Stat. 22, No. 3, 1346–1370] (1994; Zbl 0821.62020)]. The first consists of using only complete observations; the other two use simple or multiple imputation techniques, respectively, to complete the sample. The behavior 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.

MSC:
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
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