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Curve registration by Nonparametric goodness-of-fit Testing

Author

Listed:
  • Olivier Collier

    (Université Marne la Vallée)

  • Arnak S, Dalalyan

    (CREST)

Abstract

The problem of curve registration appears in many different areas of applications ranging from neuroscience to road traffic modeling. In the present work, we propose a nonparametric testing framework in which we develop a generalized likelihood ratio test to perform curve registration. We first prove that, under the null hypothesis, the resulting test statistic is asymptotically distributed as a chi-squared random variable. This result, often referred to as Wilks’ phenomenon, provides a natural threshold for the test of a prescribed asymptotic significance level and a natural measure of lack-of-fit in terms of the p-value of the x2-test. We also prove that the proposed test is consistent, i.e., its power is asymptotically equal to 1. Finite sample properties of the proposed methodology are demonstrated by numerical simulations. As an application, a new local descriptor for digital images is introduced and an experimental evaluation of its discriminative power is conducted

Suggested Citation

  • Olivier Collier & Arnak S, Dalalyan, 2013. "Curve registration by Nonparametric goodness-of-fit Testing," Working Papers 2013-33, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2013-33
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    References listed on IDEAS

    as
    1. C. A. Glasbey & K. V. Mardia, 2001. "A penalized likelihood approach to image warping," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 465-492.
    2. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
    3. Jianqing Fan & Jiancheng Jiang, 2007. "Nonparametric inference with generalized likelihood ratio tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(3), pages 409-444, December.
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    Cited by:

    1. Holger Dette & Subhra Sankar Dhar & Weichi Wu, 2021. "Identifying shifts between two regression curves," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 855-889, October.
    2. Olivier Collier & Arnak Dalalyan, 2017. "Estimating linear functionals of a sparse family of Poisson means Price Discrimination," Working Papers 2017-19, Center for Research in Economics and Statistics.
    3. del Barrio, Eustasio & Gordaliza, Paula & Lescornel, Hélène & Loubes, Jean-Michel, 2019. "Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 341-362.

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