This project investigates the construction and asymptotic theory of semiparametric estimators using moment conditions or minimization problems based upon a pairwise differencing approach. This research should make valuable contributions both to applied statistics and econometrics. The data-differencing approach taken in the project permits the development of semiparametric estimators for important economic models that have not previously been considered in the nonparametric literature. The approach taken exploits the fact that the difference of independent and identically-distributed random variables will be symmetrically distributed around zero; by choosing transformations of pairs of observations which satisfy this condition, moment conditions can be constructed to estimate the parameters of interest. The research on this subject proceeds along four lines: (1) Existing results on minimizers of U-processes will be extended to permit the kernel of the U-statistic to depend on the sample size, as required for "smoothed" variants of pairwise difference estimators. Also, these theoretical results will be applied to a number of potential semiparametric estimators, based on pairwise differences for semilinear, selection, and index models, and efficient construction of pairwise difference estimators will also be considered. (2) For the "smoothed" pairwise difference estimators, the form of the optimal bandwiths will be derived, and "plug in" estimators of these optimal bandwidths will be proposed. (3) A large-sample theory for pairwise difference estimators which rely on preliminary nonparametric estimators of regression functions will be developed. (4) The proposed estimators will be evaluated using an empirically-based simulation study.
