Three nonparametric specification tests for parametric regression models: The kernel estimation approac

The purpose of this dissertation is two-fold. The first is to derive a set of non-parametric specification tests for parametric regression models through the kernel estimation of density function. The second is to compare their practical performance with those of other specification tests suggested in the literature through a set of Monte Carlo simulation studies. The most attractive feature of the kernel estimation is that it estimates density and regression functions without making specific assumptions about stochastic distribution and a functional form. These properties of model-freeness and robustness guarantee that the nonparametric estimators of density and regression functions tend to mirror the characteristics of the true data generating process at least asymptotically. A comparison between the nonparametric and parametric estimates of a regression function provides theoretical basis to derive model misspecification tests for parametric models.;These tests are based on the nonparametric estimation of the orthogonality condition of the errors with a suitable weighting function. Depending on a choice of weighting function, three nonparametric specification tests are proposed, all of which can be put in the class of Newey's conditional moment tests. The asymptotic normality of these tests is established using an extension of the classical U-statistic theory. In order to evaluate their practical performance in finite samples, a set of limited Monte Carlo simulation experiments is conducted to investigate their power functions under various model/error specifications. The results from these simulation studies indicate that the proposed tests are powerful in detecting functional form misspecification, and robust to the presence of heteroskedastic errors in regression models.;The kernel estimation has wide application in the context of specification analysis. Since it estimates regression and density functions directly from the data, requiring no computational techniques for maximization or other types of equation solving, it can be easily applied in practice, and provides useful information about the true data generating process. Thus, a similar approach used in this dissertation can be employed to derive tests against specific model misspecification errors such as serial correlation, heteroskedasticity, and departure from normality, which are the next research subjects to be explored.