Nonparametric regression estimation with missing data. (English) Zbl 0897.62038
Summary: 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 of P. E. Cheng and L. J. Wei [Int. Stat. Symp. Vol. 1, Taipei, ROC, 97-112 (1986)], the effect of missing is precisely quantified through the asymptotic mean square error (AMSE) for the local linear smoother (LLS) of J. Fan [Ann. Stat. 21, No. 1, 196-216 (1993; Zbl 0773.62029)].
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.
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.
Keywords:
imputed local linear smoother; asymptotic mean square error; missing completely at random; missing at random; nonparametric regression; missing observations; kernel estimators; local linear smootherCitations:
Zbl 0773.62029References:
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