A general model specification testing framework for nonparametric estimation of the regression functio

Since the initial work by Rosenblatt (1956) and Parzen (1962) on nonparametric smoothing estimation, a considerable amount of research has been done in this area, in particular in the study of the consistency and asymptotic normality properties of these estimators. The application of these results to hypothesis testing on the other hand, has been quite small by comparison. Some test statistics have been proposed in a few cases to test a particular hypothesis. In most cases, however, all we find is a brief mention to the possibility of applying the Central Limit Theorem results to hypothesis testing.;This dissertation proposed a general framework for specification testing of the regression function in a nonparametric smoothing estimation context. The same analysis can be applied to cases as varied as testing for omission of variables, testing certain nonlinear restrictions in the parameters and, testing the correct specification of some parametric or semiparamentric model of interest, e.g. to test certain kinds of nonlinearity.;Furthermore, the test can be applied to iid and time series data, and when some or all of the regressors are allowed to be discrete.;Chapter 1 addresses the theoretical considerations of this research. It develops our test statistic and studies its properties.;Chapter 2 studies the small sample properties of our test. We consider the case of testing for the exclusion of a subset of the original set of regressors used in a regression function. We find the test to have reasonably good behaviour under the null hypothesis in some cases, and to have good power in most instances.;Finally, Chapter 3 applies these nonparametric kernel estimation techniques to the analysis of cross-section Engel curves. Based on the estimation results, we apply the methodology developed in the first two chapters to test the specification of certain hypothesis. In particular, we test for the significance of age as an explanatory variable. We also test the specification of the Engel curves in per capita terms, and lastly, we test the correct specification of the now popular parametric third order polynomial model for the Engel curve for food in share form.