Huberian approach for reduced order ARMA modeling of neurodegenerative disorder signal

The purpose of this paper is to address the question of the existence of auto regressive moving average (ARMA) models with reduced order for neurodegenerative disorder signals by using Huberian approach. Since gait rhythm dynamics between Parkinson's disease (PD) or Huntington's disease (HD) and healthy control (CO) differ, and since the stride interval presents great variability, we propose a different ARMA modeling approach based on a Huberian function to assess parameters. Huberian function as a mixture of L2 and L1 norms, tuned with a threshold γ from a new curve, is chosen to deal with stride signal disorders. The choice of γ is crucial to ensure a good treatment of NO and allows to reduce the model order. The disorders induce disturbances in the classical estimation methods and increase of the number of parameters of the ARMA model. Here, the use of the Huberian function reduces the number of parameters of the estimated models leading to a disease transfer function with low order for PD and HD. Mathematical approach is discussed and experimental results based on a database containing 16 CO, 15 PD, and 19 HD are presented. Author-HighlightsReduced order ARMA Modeling.New curve to deal with Natural Outliers in the estimated residuals involving reduced order.Proof of the asymptotic convergence in law of the robust estimator including stochastic differentiability and m-dependence approaches.Application to the ARMA modeling of neurodegenerative disorder signals such that Parkinson and Huntington.