A nonparametric regression approach to prediction in finite populations

Abstract

Nonparametric regression provides an intuitive estimate of a regression function or conditional expectation without the restrictions imposed by parametric models. This is a particularly useful property since the rigidity of such parametric models is not always desirable. The application of nonparametric regression, in the univariate setting, is investigated in the context of predicting a finite population total. We propose, instead of parametric estimators of the finite population total, nonparametric regression estimators obtained by smoothing the data and interpolating the smooth to predict nonsample values. It is shown how such estimation can be more robust and efficient than inference tied to parametric regression models. The nonparametric regression estimators considered are classified as operational and model-based. They require the selection of a smoothing parameter which controls the smoothness of the resultant curve. Methods of choosing the smoothing parameter are discussed.

One important property that some of the estimators are shown to possess is `total preservation'. Suppose ^y = Sy, where S os a smoother matrix and ^y and y are vectors of estimated and observed y respectively. Then an estimator is said to be `total-preserving' if 1^T^y = 1^TSy = 1^Ty. It is shown how, under repeated sampling, `total preserving' nonparametric regression estimators are design-unbiased or approximately design-unbiased and how they remain more efficient than standard parametric methods, for a suitable choice of the smoothing parameter.

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