Abstract
For a class of locally stationary processes introduced by Dahlhaus, we derive the LAN theorem under non-Gaussianity and apply the results to asymptotically optimal estimation and testing problems. For a class F of statistics which includes important statistics, we derive the asymptotic distributions of statistics in F under contiguous alternatives of unknown parameter. Because the asymptotics depend on the non-Gaussianity of the process, we discuss the non-Gaussian robustness. An interesting feature of effect of non-Gaussianity is elucidated in terms of LAN. Furthermore, the LAN theorem is applied to adaptive estimation when the innovation density is unknown.
| Original language | English |
|---|---|
| Pages (from-to) | 640-688 |
| Number of pages | 49 |
| Journal | Journal of Statistical Planning and Inference |
| Volume | 136 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2006 Mar 1 |
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Keywords
- Adaptive estimation
- Asymptotically efficient estimator
- Local asymptotic normality
- Locally stationary process
- Non-Gaussian robustness
- Optimal test
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability
Cite this
LAN theorem for non-Gaussian locally stationary processes and its applications. / Hirukawa, Junichi; Taniguchi, Masanobu.
In: Journal of Statistical Planning and Inference, Vol. 136, No. 3, 01.03.2006, p. 640-688.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - LAN theorem for non-Gaussian locally stationary processes and its applications
AU - Hirukawa, Junichi
AU - Taniguchi, Masanobu
PY - 2006/3/1
Y1 - 2006/3/1
N2 - For a class of locally stationary processes introduced by Dahlhaus, we derive the LAN theorem under non-Gaussianity and apply the results to asymptotically optimal estimation and testing problems. For a class F of statistics which includes important statistics, we derive the asymptotic distributions of statistics in F under contiguous alternatives of unknown parameter. Because the asymptotics depend on the non-Gaussianity of the process, we discuss the non-Gaussian robustness. An interesting feature of effect of non-Gaussianity is elucidated in terms of LAN. Furthermore, the LAN theorem is applied to adaptive estimation when the innovation density is unknown.
AB - For a class of locally stationary processes introduced by Dahlhaus, we derive the LAN theorem under non-Gaussianity and apply the results to asymptotically optimal estimation and testing problems. For a class F of statistics which includes important statistics, we derive the asymptotic distributions of statistics in F under contiguous alternatives of unknown parameter. Because the asymptotics depend on the non-Gaussianity of the process, we discuss the non-Gaussian robustness. An interesting feature of effect of non-Gaussianity is elucidated in terms of LAN. Furthermore, the LAN theorem is applied to adaptive estimation when the innovation density is unknown.
KW - Adaptive estimation
KW - Asymptotically efficient estimator
KW - Local asymptotic normality
KW - Locally stationary process
KW - Non-Gaussian robustness
KW - Optimal test
UR - http://www.scopus.com/inward/record.url?scp=28044449583&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=28044449583&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2004.08.017
DO - 10.1016/j.jspi.2004.08.017
M3 - Article
VL - 136
SP - 640
EP - 688
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
SN - 0378-3758
IS - 3
ER -