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Measuring the Discrepancy of a Parametric Model via Local Polynomial Smoothing
Author(s) -
GHOUCH ANOUAR EL,
GENTON MARC G.,
BOUEZMARNI TAOUFIK
Publication year - 2013
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2012.00821.x
Subject(s) - mathematics , estimator , polynomial regression , asymptotic distribution , parametric statistics , context (archaeology) , covariate , statistics , polynomial , smoothing , consistency (knowledge bases) , parametric model , measure (data warehouse) , regression analysis , discrete mathematics , mathematical analysis , paleontology , database , computer science , biology
. 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.