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A Smoothed-Distribution Form of Nadaraya-Watson Estimation

Author

Listed:
  • 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 ).

Suggested Citation

  • Ralph W. Bailey & John T. Addison, 2010. "A Smoothed-Distribution Form of Nadaraya-Watson Estimation," GEMF Working Papers 2011-01, GEMF, Faculty of Economics, University of Coimbra.
  • Handle: RePEc:gmf:wpaper:2011-01
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    References listed on IDEAS

    as
    1. 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, vol. 78(3), pages 656-669.
    2. Carlo V. Fiorio, 2004. "Confidence intervals for kernel density estimation," Stata Journal, StataCorp LP, vol. 4(2), pages 168-179, June.
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    Keywords

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

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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