Measuring the Discrepancy of a Parametric Model via Local Polynomial Smoothing
(2012) , 33 pages
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- Authors
- 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 L2-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 Bahadurtype representation of the estimator from which √n-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.
- Affiliations
Texas A&M University, College Station, U.S.A. Department of Statistics Université de Sherbrooke, Québec, Canada Département de mathématiques
Citations
El Ghouch, A., Genton, M. G., & Bouezmarni, T. (2012). Measuring the Discrepancy of a Parametric Model via Local Polynomial Smoothing (ISBA Discussion Paper 2012/01). https://hdl.handle.net/2078.5/209140