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 journalArticlepeer-review

    15 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 2011

    All Science Journal Classification (ASJC) codes

    • Statistics and Probability
    • Statistics, Probability and Uncertainty

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