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 |
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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 |
Keywords
- Adaptive estimation
- Asymptotically efficient estimator
- Local asymptotic normality
- Locally stationary process
- Non-Gaussian robustness
- Optimal test
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics