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Nearest neighbor smoothing in linear regression


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  • Stute, Winfried
  • Manteiga, Wenceslao González
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 34 (1990)
    Issue (Month): 1 (July)
    Pages: 61-74

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    Handle: RePEc:eee:jmvana:v:34:y:1990:i:1:p:61-74

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    Keywords: nearest neighbor smoothing linear regression nonparametric estimation;


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