Asymptotic normality and consistency of semi-nonparametric regression estimators using an upwards F test truncation rule

Abstract The consistency and asymptotic normality of semi-nonparametric regression estimators are shown when the truncation parameter is selected by an upwards F test. Moreover, the same statements are also shown to apply to a large class of linear estimators. The article concludes with a discussion of F test critical value settings, and includes results from a simulation study which demonstrates that confidence interval coverage can be increased by varying the critical values in a nonstandard way.