Local asymptotic mixed normality for discretely observed non-recurrent Ornstein-Uhlenbeck processes

Yasutaka Shimizu

doi:10.1007/s10463-010-0307-4

Local asymptotic mixed normality for discretely observed non-recurrent Ornstein-Uhlenbeck processes

Yasutaka Shimizu^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

Consider non-recurrent Ornstein-Uhlenbeck processes with unknown drift and diffusion parameters. Our purpose is to estimate the parameters jointly from discrete observations with a certain asymptotics. We show that the likelihood ratio of the discrete samples has the uniform LAMN property, and that some kind of approximated MLE is asymptotically optimal in a sense of asymptotic maximum concentration probability. The estimator is also asymptotically efficient in ergodic cases.

Original language	English
Pages (from-to)	193-211
Number of pages	19
Journal	Annals of the Institute of Statistical Mathematics
Volume	64
Issue number	1
DOIs	https://doi.org/10.1007/s10463-010-0307-4
Publication status	Published - 2012 Feb
Externally published	Yes

Keywords

Asymptotic optimality
Discrete observations
Joint estimation
Non-recurrency
Ornstein-Uhlenbeck processes
ULAMN property

ASJC Scopus subject areas

Statistics and Probability

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10.1007/s10463-010-0307-4

Cite this

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abstract = "Consider non-recurrent Ornstein-Uhlenbeck processes with unknown drift and diffusion parameters. Our purpose is to estimate the parameters jointly from discrete observations with a certain asymptotics. We show that the likelihood ratio of the discrete samples has the uniform LAMN property, and that some kind of approximated MLE is asymptotically optimal in a sense of asymptotic maximum concentration probability. The estimator is also asymptotically efficient in ergodic cases.",

keywords = "Asymptotic optimality, Discrete observations, Joint estimation, Non-recurrency, Ornstein-Uhlenbeck processes, ULAMN property",

author = "Yasutaka Shimizu",

note = "Funding Information: Acknowledgments The author expresses many thanks to anonymous referees for accurate comments and instructions, which improve the paper so much. The author is also grateful to Dr. Hiroki Masuda for his helpful comments. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B), 2009, no. 21740073; Japan Science and Technology Agency, CREST; Cooperative Research Meetings, the Institute of Statistical Mathematics: no. 21-2053–21-2055.",

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AU - Shimizu, Yasutaka

N1 - Funding Information: Acknowledgments The author expresses many thanks to anonymous referees for accurate comments and instructions, which improve the paper so much. The author is also grateful to Dr. Hiroki Masuda for his helpful comments. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B), 2009, no. 21740073; Japan Science and Technology Agency, CREST; Cooperative Research Meetings, the Institute of Statistical Mathematics: no. 21-2053–21-2055.

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AB - Consider non-recurrent Ornstein-Uhlenbeck processes with unknown drift and diffusion parameters. Our purpose is to estimate the parameters jointly from discrete observations with a certain asymptotics. We show that the likelihood ratio of the discrete samples has the uniform LAMN property, and that some kind of approximated MLE is asymptotically optimal in a sense of asymptotic maximum concentration probability. The estimator is also asymptotically efficient in ergodic cases.

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KW - Discrete observations

KW - Joint estimation

KW - Non-recurrency

KW - Ornstein-Uhlenbeck processes

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Local asymptotic mixed normality for discretely observed non-recurrent Ornstein-Uhlenbeck processes

Abstract

Keywords

ASJC Scopus subject areas

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