Relative performance of the grid, nearest neighbor, and OLS estimators

This article provides various paradigms for the grid estimator, the most useful being a representation of the grid estimator as a combination of the nonparametric nearest neighbor estimator and a parametric estimator. Hence, the grid estimator falls into the class of semiparametric estimators. The article used this representation to derive the relative efficiency of the nearest neighbor, grid, and OLS estimators. Under statistically perfect conditions, the OLS estimator dominated the grid estimator, which in turn dominated the nearest neighbor estimator. A Monte Carlo experiment verified the theoretical results. A second Monte Carlo experiment showed the fragility of the OLS superiority to misspecification. The results cast light upon appraisal practice.