On the $$L_p$$ L p norms of kernel regression estimators for incomplete data with applications to classification

Timothy Reese () and Majid Mojirsheibani ()
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Timothy Reese: California State University
Majid Mojirsheibani: California State University

Statistical Methods & Applications, 2017, vol. 26, issue 1, No 4, 112 pages

Abstract: Abstract We consider kernel methods to construct nonparametric estimators of a regression function based on incomplete data. To tackle the presence of incomplete covariates, we employ Horvitz–Thompson-type inverse weighting techniques, where the weights are the selection probabilities. The unknown selection probabilities are themselves estimated using (1) kernel regression, when the functional form of these probabilities are completely unknown, and (2) the least-squares method, when the selection probabilities belong to a known class of candidate functions. To assess the overall performance of the proposed estimators, we establish exponential upper bounds on the $$L_p$$ L p norms, $$1\le p

Keywords: Kernel; Selection probability; Strong convergence; Incomplete covariates (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10260-016-0359-6

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