Notes on estimating inverse-Gaussian and gamma subordinators under high-frequency sampling

Hiroki Masuda

doi:10.1007/s10463-007-0131-7

Notes on estimating inverse-Gaussian and gamma subordinators under high-frequency sampling

Hiroki Masuda

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We study joint efficient estimation of two parameters dominating either the inverse-Gaussian or gamma subordinator, based on discrete observations sampled at (t_iⁿ)t_i=nⁿ satisfying h _n : max _i≤n(t_iⁿ) - t _i-nⁿ) → 0 as n → ∞. Under the condition that T_n:=t_nⁿ → ∞ as n → ∞ we have two kinds of optimal rates, √n and √T_n . Moreover, as in estimation of diffusion coefficient of a Wiener process the √n -consistent component of the estimator is effectively workable even when T_n does not tend to infinity. Simulation experiments are given under several h _n's behaviors.

Original language	English
Pages (from-to)	181-195
Number of pages	15
Journal	Annals of the Institute of Statistical Mathematics
Volume	61
Issue number	1
DOIs	https://doi.org/10.1007/s10463-007-0131-7
Publication status	Published - Mar 2009

All Science Journal Classification (ASJC) codes

Statistics and Probability

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abstract = "We study joint efficient estimation of two parameters dominating either the inverse-Gaussian or gamma subordinator, based on discrete observations sampled at (tin)ti=nn satisfying h n : max i≤n(tin) - t i-nn) → 0 as n → ∞. Under the condition that Tn:=tnn → ∞ as n → ∞ we have two kinds of optimal rates, √n and √Tn . Moreover, as in estimation of diffusion coefficient of a Wiener process the √n -consistent component of the estimator is effectively workable even when Tn does not tend to infinity. Simulation experiments are given under several h n's behaviors.",

author = "Hiroki Masuda",

note = "Funding Information: Acknowledgments The author is grateful to the two anonymous referees for their valuable comments, which improved the presentation of the first version. This work was partly supported by Grant-in-Aid for Scientific Research from the Ministry of Education, Japan, and by the twenty-first century COE Program “Development of Dynamic Mathematics with High Functionality” at Kyushu University.",

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N1 - Funding Information: Acknowledgments The author is grateful to the two anonymous referees for their valuable comments, which improved the presentation of the first version. This work was partly supported by Grant-in-Aid for Scientific Research from the Ministry of Education, Japan, and by the twenty-first century COE Program “Development of Dynamic Mathematics with High Functionality” at Kyushu University.

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