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Asymptotic Normality of Binned Kernel Density Estimators for Non-stationary Dependent Random Variables

In: Mathematical Statistics and Limit Theorems

Author

Listed:
  • Michel Harel

    (ÉSPÉ de Limoges
    Université Paul Sabatier)

  • Jean-François Lenain

    (Faculté des Sciences et Techniques)

  • Joseph Ngatchou-Wandji

    (Université de Lorraine, EHESP de Rennes, Institut Élie Cartan de Lorraine)

Abstract

We establish the asymptotic normality of binned kernel density estimators for a sequence of dependent and nonstationary random variables converging to a sequence of stationary random variables. We compute the asymptotic variance of a suitably normalized binned kernel density estimator and study its absolute third-order moment. Then, we show that its characteristic function tends to that of a zero-mean Gaussian random variable (rv). We illustrate our results with a simulation experiment.

Suggested Citation

  • Michel Harel & Jean-François Lenain & Joseph Ngatchou-Wandji, 2015. "Asymptotic Normality of Binned Kernel Density Estimators for Non-stationary Dependent Random Variables," Springer Books, in: Marc Hallin & David M. Mason & Dietmar Pfeifer & Josef G. Steinebach (ed.), Mathematical Statistics and Limit Theorems, edition 127, pages 167-187, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-12442-1_10
    DOI: 10.1007/978-3-319-12442-1_10
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