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

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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 (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.

Original languageEnglish
Pages (from-to)181-195
Number of pages15
JournalAnnals of the Institute of Statistical Mathematics
Volume61
Issue number1
DOIs
Publication statusPublished - Mar 1 2009

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Discrete Observations
Subordinator
Inverse Gaussian
Optimal Rates
Efficient Estimation
Wiener Process
Diffusion Coefficient
Simulation Experiment
Two Parameters
Infinity
Tend
Estimator

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

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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.

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