Nearest neighbor smoothing in linear regression

AbstractA new class of estimators is introduced for estimating the parameter (θ10, θ20) in the linear regression model y = E[Y|X = x] = θ10 + θ20x. Given independent copies {(X1, Y1),…, (Xn, Yn)} of the two-dimensional random vector (X, Y), these estimators are derived from minimizing the functional ψn(θ) = ∫ (mn(x) − θ1 − θ2x)2νn(dx), where mn(x) is a nearest neighbor type estimator of m(x) = E[Y|X = x] and νn 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