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 journal › Article

    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

    A good approximation of the Gaussian likelihood of simultaneous autoregressive model which yields us an asymptotically efficient estimate of parameters. / Rikimaru, Yuki; Shibata, Ritei.

    In: Journal of Statistical Planning and Inference, Vol. 173, 01.06.2016, p. 31-46.

    Research output: Contribution to journal › Article

    Rikimaru, Y & Shibata, R 2016, 'A good approximation of the Gaussian likelihood of simultaneous autoregressive model which yields us an asymptotically efficient estimate of parameters', Journal of Statistical Planning and Inference, vol. 173, pp. 31-46. https://doi.org/10.1016/j.jspi.2016.01.003
    Rikimaru Y, Shibata R. A good approximation of the Gaussian likelihood of simultaneous autoregressive model which yields us an asymptotically efficient estimate of parameters. Journal of Statistical Planning and Inference. 2016 Jun 1;173:31-46. https://doi.org/10.1016/j.jspi.2016.01.003
    Rikimaru, Yuki ; Shibata, Ritei. / A good approximation of the Gaussian likelihood of simultaneous autoregressive model which yields us an asymptotically efficient estimate of parameters. In: Journal of Statistical Planning and Inference. 2016 ; Vol. 173. pp. 31-46.
    @article{4f31e38887be45f883d1f3a62717b2ca,
    title = "A good approximation of the Gaussian likelihood of simultaneous autoregressive model which yields us an asymptotically efficient estimate of parameters",
    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.",
    keywords = "Circulant matrix, Maximum likelihood, Simultaneous autoregressive model, Spatial process, Whittle approximation",
    author = "Yuki Rikimaru and Ritei Shibata",
    year = "2016",
    month = "6",
    day = "1",
    doi = "10.1016/j.jspi.2016.01.003",
    language = "English",
    volume = "173",
    pages = "31--46",
    journal = "Journal of Statistical Planning and Inference",
    issn = "0378-3758",
    publisher = "Elsevier",

    }

    TY - JOUR

    T1 - A good approximation of the Gaussian likelihood of simultaneous autoregressive model which yields us an asymptotically efficient estimate of parameters

    AU - Rikimaru, Yuki

    AU - Shibata, Ritei

    PY - 2016/6/1

    Y1 - 2016/6/1

    N2 - 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.

    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.

    KW - Circulant matrix

    KW - Maximum likelihood

    KW - Simultaneous autoregressive model

    KW - Spatial process

    KW - Whittle approximation

    UR - http://www.scopus.com/inward/record.url?scp=84959099802&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84959099802&partnerID=8YFLogxK

    U2 - 10.1016/j.jspi.2016.01.003

    DO - 10.1016/j.jspi.2016.01.003

    M3 - Article

    VL - 173

    SP - 31

    EP - 46

    JO - Journal of Statistical Planning and Inference

    JF - Journal of Statistical Planning and Inference

    SN - 0378-3758

    ER -

    Access to Document