A Smoothed-Distribution Form of Nadaraya-Watson Estimation

Ralph Bailey () and John Addison

No 2011-01, GEMF Working Papers from GEMF, Faculty of Economics, University of Coimbra

Abstract: Given observation-pairs (xi ,yi ), i = 1,...,n , taken to be independent observations of the random pair (X ,Y), we sometimes want to form a nonparametric estimate of m(x) = E(Y/ X = x). Let YE have the empirical distribution of the yi , and let (XS ,YS ) have the kernel-smoothed distribution of the (xi ,yi ). Then the standard estimator, the Nadaraya-Watson form mNW(x) can be interpreted as E(YE?XS = x). The smoothed-distribution estimator ms (x)=E(YS/XS = x) is a more general form than mNW (x) and often has better properties. Similar considerations apply to estimating Var(Y/X = x), and to local polynomial estimation. The discussion generalizes to vector (xi ,yi ).

Keywords: nonparametric regression; Nadaraya-Watson; kernel density; conditional expectation estimator; conditional variance estimator; local polynomial estimator (search for similar items in EconPapers)
JEL-codes: C14 (search for similar items in EconPapers)
Pages: 17 pages
Date: 2011-01
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Related works:
Working Paper: A Smoothed- Distribution Form of Nadaraya- Watson Estimation (2010)
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