TY - JOUR

T1 - Notes on estimating inverse-Gaussian and gamma subordinators under high-frequency sampling

AU - Masuda, Hiroki

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.

PY - 2009/3

Y1 - 2009/3

N2 - 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.

AB - 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.

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U2 - 10.1007/s10463-007-0131-7

DO - 10.1007/s10463-007-0131-7

M3 - Article

AN - SCOPUS:59849102710

VL - 61

SP - 181

EP - 195

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 1

ER -