Date of Award
Doctor of Philosophy
This thesis considers the problem of estimation in the presence of heteroskedasticity of unknown form in both single-equation and multi-equation (seemingly unrelated regression equation) settings.;Many existing parametric regression parameter and associated covariance estimators (e.g. ordinary least squares, generalized least squares) require estimates of the unknown covariance matrix of the disturbance terms. The term "semiparametric estimator" will denote any estimator which combines both parametric and nonparametric techniques; specifically, an estimator in which the functional form of the regression function is specified by the researcher, but the form of the heteroskedasticity function is not pre-specified, rather the function is estimated using density estimation techniques.;Semiparametric least-squares estimators of both regression parameters and their associated covariance matrices are examined. Specifically, a semiparametric estimator of the covariance matrix of the ordinary least squares regression parameters is examined, and a semiparametric generalized least squares regression parameter estimator for both single- and multi-equation (seemingly unrelated) regression models is derived.;The asymptotic properties of these estimators are derived, and the finite-sample behavior of these estimators is analyzed through the use of monte carlo simulation analysis. It is shown that these estimators can improve upon their parametric least-squares counterparts. In addition, it is found that the semiparametric estimators perform well when the true model is homoskedastic. This fact adds value to the estimators since the cost associated with using the estimator when in fact the disturbances are homoskedastic is low.
Racine, Jeffrey Scott, "Semiparametric Estimation Of Single- And Multiequation Models In The Presence Of Heteroskedasticity Of Unknown Form" (1989). Digitized Theses. 1849.