On the local asymptotic behavior of the likelihood function for Meixner Lévy processes under high-frequency sampling

Reiichiro Kawai, Hiroki Masuda

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We discuss the local asymptotic behavior of the likelihood function associated with all the four characterizing parameters (α, β, δ, μ) of the Meixner Lévy process under high-frequency sampling scheme. We derive the optimal rate of convergence for each parameter and the Fisher information matrix in a closed form. The skewness parameter β exhibits a slower rate alone, relative to the other three parameters free of sampling rate. An unusual aspect is that the Fisher information matrix is constantly singular for full joint estimation of the four parameters. This is a particular phenomenon in the regular high-frequency sampling setting and is of essentially different nature from low-frequency sampling. As soon as either α or δ is fixed, the Fisher information matrix becomes diagonal, implying that the corresponding maximum likelihood estimators are asymptotically orthogonal.

Original languageEnglish
Pages (from-to)460-469
Number of pages10
JournalStatistics and Probability Letters
Volume81
Issue number4
DOIs
Publication statusPublished - Apr 1 2011

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Likelihood Function
Asymptotic Behavior
Fisher Information Matrix
Optimal Rate of Convergence
Skewness
Maximum Likelihood Estimator
Low Frequency
Closed-form
Asymptotic behavior
Sampling
Fisher information

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

On the local asymptotic behavior of the likelihood function for Meixner Lévy processes under high-frequency sampling. / Kawai, Reiichiro; Masuda, Hiroki.

In: Statistics and Probability Letters, Vol. 81, No. 4, 01.04.2011, p. 460-469.

Research output: Contribution to journalArticle

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