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 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.
In: Annals of the Institute of Statistical Mathematics, Vol. 61, No. 1, 01.03.2009, p. 181-195.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 -