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<p>In this paper, we are interested in the estimation of the parameters of a stationary stochastic process using the minimum Hellinger distance method. The purpose of this paper is to generalize the results concerning the properties of the minimum Hellinger distance estimator using the recursive kernel density estimator of Wolverton and Wagner N’drin and Hili (<CitationRef CitationID="CR20">2022</CitationRef>) to a more general class of recursive kernel density estimators proposed by Hall and Patil. Under the conditions of ergodicity and geometric strong mixing of the stochastic process, we study the asymptotic properties of the estimator (strong pointwise convergence and asymptotic distribution). As in the nonrecursive case using Rosenblatt kernel density, the minimum Hellinger distance estimator obtained with the recursive kernel density estimator of Hall and Patil (MHDHP estimator) is consistent and asymptotically normal. We compare the properties (bias, standard deviation) of this class of estimators to those obtained with the nonrecursive kernel density estimator of Rosenblatt (MHDR estimator) through simulations. Simulation results show that the MHDHP estimator is preferable to the MHDR estimator in terms of standard deviation.</p>

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Parametric Estimation for Stochastic Processes Using the Class of Recursive Kernel Density Estimators of Hall and Patil

  • 期刊论文

  • 发表日期：

    2026年4月6日

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  • Apala Julien N’drin,
  • Kouamé Florent Kouakou,
  • Sylvestre Placide Ekra

摘要

In this paper, we are interested in the estimation of the parameters of a stationary stochastic process using the minimum Hellinger distance method. The purpose of this paper is to generalize the results concerning the properties of the minimum Hellinger distance estimator using the recursive kernel density estimator of Wolverton and Wagner N’drin and Hili (2022) to a more general class of recursive kernel density estimators proposed by Hall and Patil. Under the conditions of ergodicity and geometric strong mixing of the stochastic process, we study the asymptotic properties of the estimator (strong pointwise convergence and asymptotic distribution). As in the nonrecursive case using Rosenblatt kernel density, the minimum Hellinger distance estimator obtained with the recursive kernel density estimator of Hall and Patil (MHDHP estimator) is consistent and asymptotically normal. We compare the properties (bias, standard deviation) of this class of estimators to those obtained with the nonrecursive kernel density estimator of Rosenblatt (MHDR estimator) through simulations. Simulation results show that the MHDHP estimator is preferable to the MHDR estimator in terms of standard deviation.