On kernel nonparametric regression designed for complex survey data |
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Authors: | Torsten Harms Pierre Duchesne |
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Institution: | (1) Institute of Mathematics and Informatics, Vilnius, Lithuania |
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Abstract: | In this article, we consider nonparametric regression analysis between two variables when data are sampled through a complex
survey. While nonparametric regression analysis has been widely used with data that may be assumed to be generated from independently
and identically distributed (iid) random variables, the methods and asymptotic analyses established for iid data need to be
extended in the framework of complex survey designs. Local polynomial regression estimators are studied, which include as
particular cases design-based versions of the Nadaraya–Watson estimator and of the local linear regression estimator. In this
paper, special emphasis is given to the local linear regression estimator. Our estimators incorporate both the sampling weights
and the kernel weights. We derive the asymptotic mean squared error (MSE) of the kernel estimators using a combined inference
framework, and as a corollary consistency of the estimators is deduced. Selection of a bandwidth is necessary for the resulting
estimators; an optimal bandwidth can be determined, according to the MSE criterion in the combined mode of inference. Simulation
experiments are conducted to illustrate the proposed methodology and an application with the Canadian survey of labour and
income dynamics is presented. |
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Keywords: | |
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