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On the strong uniform consistency of the mode estimator for censored time series

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Abstract

Let (T n ) n≥1 be a sequence random variables (rv) of interest distributed as T. In censorship models the rv T is subject to random censoring by another rv C. Let θ be the mode of T. In this paper we define a new smooth kernel estimator \({\hat{\theta}_n}\) of θ and establish its almost sure convergence under an α-mixing condition.

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Authors and Affiliations

  1. Univ. Lille Nord de France, 59000, Lille, France

    Salah Khardani, Mohamed Lemdani & Elias Ould Saïd

  2. ULCO, LMPA, 62000, Calais, France

    Salah Khardani & Elias Ould Saïd

  3. Lab. de Biomathématiques, Univ. de Lille 2. Fac. de Pharmacie, 3, rue du Pr. Laguesse, 59006, Lille, France

    Mohamed Lemdani

Authors
  1. Salah Khardani
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  2. Mohamed Lemdani
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  3. Elias Ould Saïd
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Correspondence to Mohamed Lemdani.

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Khardani, S., Lemdani, M. & Ould Saïd, E. On the strong uniform consistency of the mode estimator for censored time series. Metrika 75, 229–241 (2012). https://doi.org/10.1007/s00184-010-0324-6

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  • DOI: https://doi.org/10.1007/s00184-010-0324-6

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