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Nearest neighbor smoothing in linear regression

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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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    References listed on IDEAS

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    1. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    2. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
    3. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-1453, November.
    4. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
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