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Nonparametric density estimation for linear processes with infinite variance

Listed author(s):
  • Toshio Honda

    ()

We consider nonparametric estimation of marginal density functions of linear processes by using kernel density estimators. We assume that the innovation processes are i.i.d. and have infinite-variance. We present the asymptotic distributions of the kernel density estimators with the order of bandwidths fixed as h=cn-1/5, where n is the sample size. The asymptotic distributions depend on both the coefficients of linear processes and the tail behavior of the innovations. In some cases, the kernel estimators have the same asymptotic distributions as for i.i.d. observations. In other cases, the normalized kernel density estimators converge in distribution to stable distributions. A simulation study is also carried out to examine small sample properties.

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File URL: http://hdl.handle.net/10.1007/s10463-007-0149-x
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Article provided by Springer & The Institute of Statistical Mathematics in its journal Annals of the Institute of Statistical Mathematics.

Volume (Year): 61 (2009)
Issue (Month): 2 (June)
Pages: 413-439

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Handle: RePEc:spr:aistmt:v:61:y:2009:i:2:p:413-439
DOI: 10.1007/s10463-007-0149-x
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  1. Toshio Honda, 2000. "Nonparametric Density Estimation for a Long-Range Dependent Linear Process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 599-611, December.
  2. Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
  3. Marc Hallin & Lanh Tran, 1996. "Kernel density estimation for linear processes: Asymptotic normality and optimal bandwidth derivation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 429-449, September.
  4. Liang Peng & Qiwei Yao, 2004. "Nonparametric regression under dependent errors with infinite variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 73-86, March.
  5. 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.
  6. Koul, Hira L. & Surgailis, Donatas, 2001. "Asymptotics of empirical processes of long memory moving averages with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 309-336, February.
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