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Nearest neighbor smoothing in linear regression

Author

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  • Stute, Winfried
  • Manteiga, Wenceslao González

Abstract

A new class of estimators is introduced for estimating the parameter ([theta]10, [theta]20) in the linear regression model y = E[YX = x] = [theta]10 + [theta]20x. Given independent copies {(X1, Y1),..., (Xn, Yn)} of the two-dimensional random vector (X, Y), these estimators are derived from minimizing the functional [psi]n([theta]) = [integral operator] (mn(x) - [theta]1 - [theta]2x)2[nu]n(dx), where mn(x) is a nearest neighbor type estimator of m(x) = E[YX = x] and [nu]n is an empirical measure. Strong consistency and asymptotic normality are proved under weak assumptions on (X, Y). Also a small sample comparison with LSE is incluced.

Suggested Citation

  • Stute, Winfried & Manteiga, Wenceslao González, 1990. "Nearest neighbor smoothing in linear regression," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 61-74, July.
  • Handle: RePEc:eee:jmvana:v:34:y:1990:i:1:p:61-74
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