This project develops nonparametric and semiparametric methods for estimation of econometric models. The research consists of three main parts: 1) additive interactive regression, 2) covariance matrix estimation in the presence of heteroskedasticity and autocorrelation of unknown forms, and 3) general methods for inference in semiparametric models. Additive Interactive Regression (AIR) models are econometric models which put more structure on the regression function than nonparametric models, and thus circumvent the problems of dimensionality that severely hinder the use of fully nonparametric techniques in applied econometrics. This project adds to that line of work by analyzing the statistical properties of AIR models, and developing efficient estimation techniques for them. The work on estimation of the covariance matric under varying distributional assumptions extends existing work on comparing different kernel estimators by determining suitable bandwidth/lag truncation parameters for use with these estimators, and comparing the properties of these estimators with those of other covariance estimators. In addition, computationally efficient estimation techniques are developed for obtaining consistency against arbitrary forms of heteroskedasticity. %%% This project investigates the properties of various estimation techniques used in econometric models. Such models are used widely in all areas of applied economics, including macroeconomics and government policy analysis, studies of the behavior of firms and industries, and the dynamics of the international economy. Until recently, all these types of econometric investigations started by postulating a mathematical function or system of functions simulating the economic relationships to be examined. Research has shown that in many cases the results of these studies can be dependent on the particular mathematical specification of the functions. During the last decade much econometric work has focused on developing statistical estimation techniques which do not require a specified mathematical function. These techniques, known generically as nonparametric techniques, have obvious advantages over the nonparametric ones in that fewer assumptions about the structure of the economy have to be made, and more information about the economy is derived from the data themselves. However, statistical problems arise with the use of nonparametric techniques. This project adds significantly to the existing work on nonparametric estimation by examining three of the most difficult problems, namely dimensionality, covariance estimation, and computational efficiency.
