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A Smoothed-Distribution Form of Nadaraya-Watson Estimation

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  • Ralph W. Bailey

    ()
    (University of Birmingham)

  • John T. Addison

    ()
    (University of South Carolina, Queen’s University Belfast, and 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 ).

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Bibliographic Info

Paper provided by GEMF - Faculdade de Economia, Universidade de Coimbra in its series GEMF Working Papers with number 2011-01.

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Length: 17 pages
Date of creation: Nov 2010
Date of revision:
Handle: RePEc:gmf:wpaper:2011-01

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Keywords: nonparametric regression; Nadaraya-Watson; kernel density; conditional expectation estimator; conditional variance estimator; local polynomial estimator;

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  1. Carlo V. Fiorio, 2004. "Confidence intervals for kernel density estimation," Stata Journal, StataCorp LP, StataCorp LP, vol. 4(2), pages 168-179, June.
  2. Christopher B. Barrett & Paul A. Dorosh, 1996. "Farmers' Welfare and Changing Food Prices: Nonparametric Evidence from Rice in Madagascar," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, Agricultural and Applied Economics Association, vol. 78(3), pages 656-669.
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