Measuring the discrepancy of a parametric model via local polynomial smoothing

Anouar El Ghouch*, Marc G. Genton, Taoufik Bouezmarni

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 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.

Original languageEnglish (US)
Pages (from-to)455-470
Number of pages16
JournalScandinavian Journal of Statistics
Issue number3
StatePublished - Sep 2013


  • Explanatory power
  • Inadequacy index
  • Model misspecification
  • Multivariate local polynomial smoothing
  • Strong mixing sequence
  • Validation test

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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