Abstract
Robinson (1987) proposed to use a nearest neighbor approach to estimate the regression coefficient in a heteroskedastic linear model. While this estimator is asymptotically efficient, it has been said to be inefficient in small samples compared with other semiparametric estimators such as those using a kernel. Like other semiparametric methods, his estimators of variances, which are used to get the weighted least squares estimator of the regression coefficient, are constructed as a weighted sum of the squared ols residuals. As Robinson (1987) indicated himself, however, there exists a sample splitting problem in his estimator and this may cause the small-sample inefficiency. Therefore a slight modification improves the small sample property of the k-NN estimator. In this paper we report Monte Carlo experiments and show that the modified Nearest Neighbor estimator has a sufficient level of efficiency in small samples.
