Non-regular estimation theory for piecewise continuous spectral densities

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    For a class of Gaussian stationary processes, the spectral density fθ (λ), θ = (τ, η), is assumed to be a piecewise continuous function, where τ describes the discontinuity points, and the piecewise spectral forms are smoothly parameterized by η. Although estimating the parameter θ is a very fundamental problem, there has been no systematic asymptotic estimation theory for this problem. This paper develops the systematic asymptotic estimation theory for piecewise continuous spectra based on the likelihood ratio for contiguous parameters. It is shown that the log-likelihood ratio is not locally asymptotic normal (LAN). Two estimators for θ, i.e., the maximum likelihood estimator over(θ, ̂)ML and the Bayes estimator over(θ, ̂)B, are introduced. Then the asymptotic distributions of over(θ, ̂)ML and over(θ, ̂)B are derived and shown to be non-normal. Furthermore we observe that over(θ, ̂)B is asymptotically efficient, but over(θ, ̂)ML is not so. Also various versions of step spectra are considered.

    Original languageEnglish
    Pages (from-to)153-170
    Number of pages18
    JournalStochastic Processes and their Applications
    Volume118
    Issue number2
    DOIs
    Publication statusPublished - 2008 Feb

    Fingerprint

    Estimation Theory
    Piecewise continuous
    Spectral density
    Spectral Density
    Asymptotic Theory
    Stationary Gaussian Process
    Log-likelihood Ratio
    Bayes Estimator
    Continuous Spectrum
    Likelihood Ratio
    Maximum Likelihood Estimator
    Maximum likelihood
    Asymptotic distribution
    Discontinuity
    Continuous Function
    Estimator
    Likelihood ratio
    Class
    Form

    Keywords

    • Asymptotic efficiency
    • Bayes estimator
    • Likelihood ratio
    • Maximum likelihood estimator
    • Non-regular estimation
    • Piecewise continuous spectra

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Mathematics(all)
    • Statistics and Probability
    • Modelling and Simulation

    Cite this

    Non-regular estimation theory for piecewise continuous spectral densities. / Taniguchi, Masanobu.

    In: Stochastic Processes and their Applications, Vol. 118, No. 2, 02.2008, p. 153-170.

    Research output: Contribution to journalArticle

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