A Smoothed- Distribution Form of Nadaraya- Watson Estimation
AbstractGiven 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 InfoPaper provided by Department of Economics, University of Birmingham in its series Discussion Papers with number 10-30.
Length: 11 pages
Date of creation: Nov 2010
Date of revision:
nonparametric regression; Nadaraya- Watson; kernel density; conditional expectation estimator; conditional variance estimator; local polynomial estimator;
Other versions of this item:
- Ralph W. Bailey & John T. Addison, 2010. "A Smoothed-Distribution Form of Nadaraya-Watson Estimation," GEMF Working Papers 2011-01, GEMF - Faculdade de Economia, Universidade de Coimbra.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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