### Abstract

We study joint efficient estimation of two parameters dominating either the inverse-Gaussian or gamma subordinator, based on discrete observations sampled at (t_{i}
^{n})t_{i=n}
^{n} satisfying h _{n} : max _{i≤n}(t_{i}
^{n}) - t _{i-n}
^{n}) → 0 as n → ∞. Under the condition that T_{n}:=t_{n}
^{n} → ∞ 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 | |

Publication status | Published - Mar 1 2009 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability

### Cite this

**Notes on estimating inverse-Gaussian and gamma subordinators under high-frequency sampling.** / Masuda, Hiroki.

Research output: Contribution to journal › Article

}

TY - JOUR

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

AU - Masuda, Hiroki

PY - 2009/3/1

Y1 - 2009/3/1

N2 - We study joint efficient estimation of two parameters dominating either the inverse-Gaussian or gamma subordinator, based on discrete observations sampled at (ti n)ti=n n satisfying h n : max i≤n(ti n) - t i-n n) → 0 as n → ∞. Under the condition that Tn:=tn n → ∞ 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 (ti n)ti=n n satisfying h n : max i≤n(ti n) - t i-n n) → 0 as n → ∞. Under the condition that Tn:=tn n → ∞ 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.

UR - http://www.scopus.com/inward/record.url?scp=59849102710&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=59849102710&partnerID=8YFLogxK

U2 - 10.1007/s10463-007-0131-7

DO - 10.1007/s10463-007-0131-7

M3 - Article

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 -