Nearest neighbor smoothing in linear regression
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.
Year of publication: |
1990
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Authors: | Stute, Winfried ; Manteiga, Wenceslao González |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 34.1990, 1, p. 61-74
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Publisher: |
Elsevier |
Keywords: | nearest neighbor smoothing linear regression nonparametric estimation |
Saved in:
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