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Nonparametric Estimation of the Density Function of the Distribution of the Noise in CHARN Models

Author

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  • Joseph Ngatchou-Wandji

    (EHESP French School of Public Health, 35043 Rennes, France
    Institut Élie Cartan de Lorraine, University of Lorraine, 54052 Vandoeuvre-Lès-Nancy, France)

  • Marwa Ltaifa

    (Institut Élie Cartan de Lorraine, University of Lorraine, 54052 Vandoeuvre-Lès-Nancy, France)

  • Didier Alain Njamen Njomen

    (Department of Mathematics and Computer Science, Faculty of Science, University of Maroua, Maroua P.O. Box 814, Cameroon)

  • Jia Shen

    (Department of Statistics, Fudan University, Shanghai 200433, China)

Abstract

This work is concerned with multivariate conditional heteroscedastic autoregressive nonlinear (CHARN) models with an unknown conditional mean function, conditional variance matrix function and density function of the distribution of noise. We study the kernel estimator of the latter function when the former are either parametric or nonparametric. The consistency, bias and asymptotic normality of the estimator are investigated. Confidence bound curves are given. A simulation experiment is performed to evaluate the performance of the results.

Suggested Citation

  • Joseph Ngatchou-Wandji & Marwa Ltaifa & Didier Alain Njamen Njomen & Jia Shen, 2022. "Nonparametric Estimation of the Density Function of the Distribution of the Noise in CHARN Models," Mathematics, MDPI, vol. 10(4), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:624-:d:752022
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