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On central and non-central limit theorems in density estimation for sequences of long-range dependence

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  • Hwai-Chung, Ho

Abstract

This paper studies the asymptotic properties of the kernel probability density estimate of stationary sequences which are observed through some non-linear instantaneous filter applied to long-range dependent Gaussian sequences. It is shown that the limiting distribution of the kernel estimator can be, in quite contrast to the case of short-range dependence, Gaussian or non-Gaussian depending on the choice of the bandwidth sequences. In particular, if the bandwidth h(N) for sample of size N is selected to converge to zero fast enough, the usual [radical sign]Nh(N) rate asymptotic normality still holds.

Suggested Citation

  • Hwai-Chung, Ho, 1996. "On central and non-central limit theorems in density estimation for sequences of long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 153-174, November.
    • Handle: RePEc:eee:spapps:v:63:y:1996:i:2:p:153-174
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    References listed on IDEAS

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    1. George Roussas, 1969. "Nonparametric estimation in Markov processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 73-87, December.
    2. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    3. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318.
    4. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905.
    5. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
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    Cited by:

    1. Toshio Honda, 2009. "Nonparametric density estimation for linear processes with infinite variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 413-439, June.

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