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On the conditional density estimation for continuous time processes with values in functional spaces

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  • Maillot, Bertrand
  • Chesneau, Christophe

Abstract

This paper is devoted to the conditional density estimation for continuous time processes with values in functional spaces. Under standard assumptions, we prove the uniform convergence of the conditional density estimator, from which we deduce the almost sure convergence of the conditional mode estimator. Then, the convergence of the conditional distribution function and the regression function estimators are established.

Suggested Citation

  • Maillot, Bertrand & Chesneau, Christophe, 2021. "On the conditional density estimation for continuous time processes with values in functional spaces," Statistics & Probability Letters, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:stapro:v:178:y:2021:i:c:s0167715221001413
    DOI: 10.1016/j.spl.2021.109179
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    References listed on IDEAS

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    1. Frédéric Ferraty & Ali Laksaci & Philippe Vieu, 2006. "Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models," Statistical Inference for Stochastic Processes, Springer, vol. 9(1), pages 47-76, May.
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    Cited by:

    1. Ibrahim M. Almanjahie & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Estimating the Conditional Density in Scalar-On-Function Regression Structure: k -N-N Local Linear Approach," Mathematics, MDPI, vol. 10(6), pages 1-16, March.
    2. Bouabsa Wahiba, 2023. "The Estimating of the Conditional Density with Application to the Mode Function in Scalar-On-Function Regression Structure: Local Linear Approach with Missing at Random," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 27(1), pages 17-32, March.

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