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Uniform strong consistency of kernel density estimators under dependence

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  • Kim, Tae Yoon
  • Cox, Dennis D.

Abstract

In this note it is shown that the kernel density estimators converge a.s. uniformly on compact subsets of the variable under [alpha]-mixing. In particular, the rates of convergence for the estimators will be investigated to analyze dependency effects.

Suggested Citation

  • Kim, Tae Yoon & Cox, Dennis D., 1996. "Uniform strong consistency of kernel density estimators under dependence," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 179-185, February.
    • Handle: RePEc:eee:stapro:v:26:y:1996:i:2:p:179-185
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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. Cox, Dennis D. & Kim, Tae Yoon, 1995. "Moment bounds for mixing random variables useful in nonparametric function estimation," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 151-158, March.
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    Cited by:

    1. Lin, Lu & Li, Feng & Zhu, Lixing & Härdle, Wolfgang Karl, 2010. "Mean volatility regressions," SFB 649 Discussion Papers 2011-003, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. Hwang, Eunju & Shin, Dong Wan, 2012. "Stationary bootstrap for kernel density estimators under ψ-weak dependence," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1581-1593.

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