Nonparametric tests using a kernel estimation metho

This thesis proposes several diagnostic tests using a nonparametric kernel estimation method. Nonparametric estimates are known to have a slow rate of point-wise convergence to the true value. Averaging these non-parametric estimates will improve the rate of convergence. U-statistics theory is used to establish the $surd$N-consistency result.;A model specification test is constructed by comparing the normalized average sum of squared residuals from nonparametric kernel regression estimates with these of linear least squares regression estimates. Under the homoskedasticity assumption, these two average sum of squared residuals behave similarly in an asymptotic sense if the true mean regression function is linear.;A new heteroskedasticity test is proposed. Conventional heteroskedasticity tests assume a linear regression function to obtain the residual estimates. However, if the regression function is not linear, false inferences may be drawn even if the true disturbance terms are homoskedastic. The proposed test statistic obtains residual estimates from nonparametric kernel regression estimates and examines the asymptotic behavior of nonparametric residual estimates to determine the presence of heteroskedasticity.;Finally, a new derivative restriction test is introduced. If the mean regression function is misspecified, parametric tests of derivative restrictions can be misleading. The proposed test statistic uses a total differential technique to modify the raw data set according to the derivative restrictions. If the derivative restrictions are valid, the normalized average sum of squared residuals from the restricted and unrestricted mean regression functions should behave similarly in an asymptotic sense under the homoskedasticity assumption.