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Huberian function applied to neurodegenerative disorder gait rhythm

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  • Christophe Corbier

Abstract

Huberian statistical approach is applied to differentiate three neurodegenerative disorder gait rhythm and presents a method reducing the number of parameters of an autoregressive moving average (ARMA) modeling of the walking signal. Gait rhythm dynamics differ between healthy control, Parkinson's disease, Huntington's disease and amyotrophic lateral sclerosis. Random variables such as the stride interval and its two sub-phases (i.e. swing and stance) present a great variability with natural outliers. Huberian function as a mixture of $ L_2 $ L2 and $ L_1 $ L1 norms with low threshold γ is used to present new statistical indicators by deducing the corresponding skewness and kurtosis. The choice of γ is discussed to ensure consistency and convergence of a low-order ARMA estimator of the gait rhythm signal. A mathematical point of view is developed and experimental results are presented.

Suggested Citation

  • Christophe Corbier, 2016. "Huberian function applied to neurodegenerative disorder gait rhythm," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 2065-2084, August.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:11:p:2065-2084
    DOI: 10.1080/02664763.2015.1126811
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    References listed on IDEAS

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    1. J. Liao & Yujun Wu & Yong Lin, 2010. "Improving Sheather and Jones’ bandwidth selector for difficult densities in kernel density estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(1), pages 105-114.
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