| This dissertation treats a number of related issues involved in the practical implementation of some popular semiparametric estimation techniques in econometrics. It is generally recognized that many problems of statistical inference in economics have a semiparametric form in the sense that they are characterized by the presence of both unknown finite-dimensional parameters as well as unknown functions (cf. e.g., Powell, 1994; Horowitz, 1998b; Pagan and Ullah, 1999; Yatchew, 2003, for surveys). In most cases estimators for the finite-dimensional parameter in semiparametric models are well-established and can be shown to be n-1/2-consistent and asymptotically normal, with asymptotic covariance matrices attaining a semiparametric efficiency bound (cf. e.g., Robinson, 1988; Newey, 1994). In this dissertation it is argued that the problems of estimation of the unknown functions and approximation of the actual sampling variability of estimators of the finite-dimensional parameters are both important and interrelated, particularly when considering the reduction of discrepancies between the actual and nominal rejection probabilities of associated hypothesis tests. One of the chapters that follow presents an approach to the problem of implementing estimators of unknown functions in a popular class of semiparametric regression estimator. This is followed by a presentation of a method of size correction for tests based on regression quantile estimators as developed by Koenker and Bassett (1978). |
