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

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6 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 languageEnglish
Pages (from-to)193-211
Number of pages19
JournalAnnals of the Institute of Statistical Mathematics
Volume64
Issue number1
DOIs
Publication statusPublished - 2012 Feb
Externally publishedYes

Fingerprint

Ornstein-Uhlenbeck Process
Normality
Discrete Observations
Likelihood Ratio
Asymptotically Optimal
Estimator
Unknown
Estimate

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability

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.",
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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.

KW - Asymptotic optimality

KW - Discrete observations

KW - Joint estimation

KW - Non-recurrency

KW - Ornstein-Uhlenbeck processes

KW - ULAMN property

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JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

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