TY - JOUR
T1 - LAN theorem for non-Gaussian locally stationary processes and its applications
AU - Hirukawa, Junichi
AU - Taniguchi, Masanobu
N1 - Copyright:
Copyright 2005 Elsevier B.V., All rights reserved.
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
AN - SCOPUS:28044449583
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 -