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Exact Confidence Intervals of the Extended Orey Index for Gaussian Processes

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  • Kęstutis Kubilius

    (Vilnius University)

  • Dmitrij Melichov

    (Vilnius Gediminas Technical University)

Abstract

In this paper exact confidence intervals for the Orey index of Gaussian processes are obtained using concentration inequalities for Gaussian quadratic forms and discrete observations of the underlying process. The obtained result is applied to Gaussian processes with the Orey index which not necessarily have stationary increments.

Suggested Citation

  • Kęstutis Kubilius & Dmitrij Melichov, 2016. "Exact Confidence Intervals of the Extended Orey Index for Gaussian Processes," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 785-804, September.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:3:d:10.1007_s11009-015-9460-9
    DOI: 10.1007/s11009-015-9460-9
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    References listed on IDEAS

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    1. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2004. "Sub-fractional Brownian motion and its relation to occupation times," RePAd Working Paper Series lrsp-TRS376, Département des sciences administratives, UQO.
    2. Jean-Christophe Breton & Jean-François Coeurjolly, 2012. "Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 1-26, April.
    3. Jean-François Coeurjolly, 2001. "Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 199-227, May.
    4. Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
    5. Junfeng Liu & Litan Yan & Zhihang Peng & Deqing Wang, 2012. "Remarks on Confidence Intervals for Self-Similarity Parameter of a Subfractional Brownian Motion," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, January.
    6. Benassi, Albert & Cohen, Serge & Istas, Jacques & Jaffard, Stéphane, 1998. "Identification of filtered white noises," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 31-49, June.
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    Cited by:

    1. Kubilius, K., 2020. "CLT for quadratic variation of Gaussian processes and its application to the estimation of the Orey index," Statistics & Probability Letters, Elsevier, vol. 165(C).

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