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Curve registration by Nonparametric goodness-of-fit Testing

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  • Olivier Collier

    ()
    (Université Marne la Vallée)

  • Arnak S, Dalalyan

    ()
    (CREST)

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    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

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    Bibliographic Info

    Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2013-33.

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    Length: 26
    Date of creation: Dec 2013
    Date of revision:
    Handle: RePEc:crs:wpaper:2013-33

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    Related research

    Keywords: nonparametric inference; hypotheses testing; Wilks’ phenomenon; keypoint matching;

    References

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    1. 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, Econometric Society, vol. 69(3), pages 599-631, May.
    2. 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, Springer, vol. 16(3), pages 409-444, December.
    3. 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.
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