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Nonparametric estimation in [alpha]-series processes

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  • Aydogdu, Halil
  • Kara, Mahmut

Abstract

A counting process with the interoccurrence times X1,X2,... is an [alpha]-series process if there exists a real number [alpha] such that (k[alpha]Xk)k=1,2,... forms a renewal process. The nonparametric inference problem in an [alpha]-series process is taken into consideration. The Mann test is applied for trend analysis and a graphical technique is presented in order to test whether the data come from an [alpha]-series process. Some nonparametric estimators for three important parameters of the [alpha]-series process are obtained by using a linear regression method. The consistency and asymptotic normality properties are investigated. The performances of the estimators are evaluated by a simulation study. Some suggestions on the choice of the estimators are made based on the theoretical and simulation results. Further, the method is illustrated through a real-life example.

Suggested Citation

  • Aydogdu, Halil & Kara, Mahmut, 2012. "Nonparametric estimation in [alpha]-series processes," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 190-201, January.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:1:p:190-201
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    References listed on IDEAS

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    1. Lam Yeh & So Kuen Chan, 1998. "Statistical inference for geometric processes with lognormal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 27(1), pages 99-112, March.
    2. Chan, Jennifer S. K. & Lam, Yeh & Leung, Doris Y. P., 2004. "Statistical inference for geometric processes with gamma distributions," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 565-581, October.
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    Cited by:

    1. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).

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