Measuring the Discrepancy of a Parametric Model via Local Polynomial Smoothing |
| |
Authors: | ANOUAR EL GHOUCH MARC G. GENTON TAOUFIK BOUEZMARNI |
| |
Affiliation: | 1. Université catholique de Louvain;2. Texas A&M University;3. Université de Sherbrooke |
| |
Abstract: | Abstract. In the context of multivariate mean regression, we propose a new method to measure and estimate the inadequacy of a given parametric model. The measure is basically the missed fraction of variation after adjusting the best possible parametric model from a given family. The proposed approach is based on the minimum L 2 ‐distance between the true but unknown regression curve and a given model. The estimation method is based on local polynomial averaging of residuals with a polynomial degree that increases with the dimension d of the covariate. For any d ≥ 1 and under some weak assumptions we give a Bahadur‐type representation of the estimator from which ‐consistency and asymptotic normality are derived for strongly mixing variables. We report the outcomes of a simulation study that aims at checking the finite sample properties of these techniques. We present the analysis of a dataset on ultrasonic calibration for illustration. |
| |
Keywords: | explanatory power inadequacy index model misspecification multivariate local polynomial smoothing strong mixing sequence validation test |
|