NONPARAMETRIC REGRESSION ESTIMATION WITH MISSING DATA

For nonparametric regression, there might be a part of the design points on which the observations are missing. A fundamental issue of interest is to study the impact of the missing observations on the performance of kernel estimators. Utilizing the estimation idea in Cheng and Wei (Internat. Statistical Symposium, Taiwan, 1986), the effect of missing is precisely quantified through the asymptotic mean square error (AMSE) for the local linear smoother (LLS) in Fan (Ann. Statist. 20 (1993) 196-216). An imputed LLS which adjusts for the effect of missing by substituting the missing observations with the respective kernel estimates is also investigated. The imputed LLS is analyzed by its AMSE. This AMSE shows clearly how the kernel function and the value of bandwidth used in constructing the substitutes effect the performance of the imputed LLS. Simulations demonstrate that the derived asymptotic results hold for reasonable sample sizes.