A good approximation of the Gaussian likelihood of simultaneous autoregressive model which yields us an asymptotically efficient estimate of parameters

Yuki Rikimaru, Ritei Shibata

    Research output: Contribution to journalArticle

    Abstract

    A good approximation of the Gaussian likelihood of simultaneous autoregressive (SAR) model is proposed. The approximation yields us an asymptotically efficient estimate of the parameters. No integration of the spectral density nor any other expensive calculation is necessary, so that our estimation procedure is applicable for any SAR model without restriction. Numerical experiments show that our estimate has less bias and variance than the other estimate, although our comparison is limited to the case where random number generation and the calculation of the other estimate are both feasible.

    Original languageEnglish
    Pages (from-to)31-46
    Number of pages16
    JournalJournal of Statistical Planning and Inference
    Volume173
    DOIs
    Publication statusPublished - 2016 Jun 1

    Fingerprint

    Autoregressive Model
    Likelihood
    Random number generation
    Spectral density
    Approximation
    Estimate
    Random number Generation
    Spectral Density
    Experiments
    Numerical Experiment
    Restriction
    Necessary
    Autoregressive model

    Keywords

    • Circulant matrix
    • Maximum likelihood
    • Simultaneous autoregressive model
    • Spatial process
    • Whittle approximation

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Applied Mathematics
    • Statistics and Probability

    Cite this

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    abstract = "A good approximation of the Gaussian likelihood of simultaneous autoregressive (SAR) model is proposed. The approximation yields us an asymptotically efficient estimate of the parameters. No integration of the spectral density nor any other expensive calculation is necessary, so that our estimation procedure is applicable for any SAR model without restriction. Numerical experiments show that our estimate has less bias and variance than the other estimate, although our comparison is limited to the case where random number generation and the calculation of the other estimate are both feasible.",
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    author = "Yuki Rikimaru and Ritei Shibata",
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    AB - A good approximation of the Gaussian likelihood of simultaneous autoregressive (SAR) model is proposed. The approximation yields us an asymptotically efficient estimate of the parameters. No integration of the spectral density nor any other expensive calculation is necessary, so that our estimation procedure is applicable for any SAR model without restriction. Numerical experiments show that our estimate has less bias and variance than the other estimate, although our comparison is limited to the case where random number generation and the calculation of the other estimate are both feasible.

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    KW - Spatial process

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