Time-invariance estimating equations

Adrian Baddeley

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    We describe a general method for deriving estimators of the parameter of a statistical model, with particular relevance to highly structured stochastic systems such as spatial random processes and 'graphical' conditional independence models. The method is based on representing the stochastic model X as the equilibrium distribution of an auxiliary Markov process Y = (Y-t, t > 0) where the discrete or continuous 'time' index t is to be understood as a fictional extra dimension added to the original setting. The parameter estimate is obtained by equating to zero the generator of Y applied to a suitable statistic and evaluated at the data x. This produces an unbiased estimating equation for theta. Natural special cases include maximum likelihood the method of moments, the reduced sample estimator in survival analysis, the maximum pseudolikelihood estimator for random fields and for point processes, the Takacs-Fiksel method for point processes, 'variational' estimators for random fields and multivariate distributions, and many standard estimators in stochastic geometry. The approach has some affinity with the Stein-Chen method for distributional approximation.
    Original languageEnglish
    Pages (from-to)783-808
    JournalBernoulli
    Volume6
    Issue number5
    DOIs
    Publication statusPublished - 2000

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    Estimating Equation
    Invariance
    Estimator
    Point Process
    Random Field
    Stein-Chen Method
    Stochastic Geometry
    Pseudo-likelihood
    Spatial Process
    Conditional Independence
    Equilibrium Distribution
    Extra Dimensions
    Survival Analysis
    Method of Moments
    Multivariate Distribution
    Random process
    Stochastic Systems
    Markov Process
    Statistical Model
    Affine transformation

    Cite this

    Baddeley, Adrian. / Time-invariance estimating equations. In: Bernoulli. 2000 ; Vol. 6, No. 5. pp. 783-808.
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    year = "2000",
    doi = "10.2307/3318756",
    language = "English",
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    Baddeley, A 2000, 'Time-invariance estimating equations' Bernoulli, vol. 6, no. 5, pp. 783-808. https://doi.org/10.2307/3318756

    Time-invariance estimating equations. / Baddeley, Adrian.

    In: Bernoulli, Vol. 6, No. 5, 2000, p. 783-808.

    Research output: Contribution to journalArticle

    TY - JOUR

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    AB - We describe a general method for deriving estimators of the parameter of a statistical model, with particular relevance to highly structured stochastic systems such as spatial random processes and 'graphical' conditional independence models. The method is based on representing the stochastic model X as the equilibrium distribution of an auxiliary Markov process Y = (Y-t, t > 0) where the discrete or continuous 'time' index t is to be understood as a fictional extra dimension added to the original setting. The parameter estimate is obtained by equating to zero the generator of Y applied to a suitable statistic and evaluated at the data x. This produces an unbiased estimating equation for theta. Natural special cases include maximum likelihood the method of moments, the reduced sample estimator in survival analysis, the maximum pseudolikelihood estimator for random fields and for point processes, the Takacs-Fiksel method for point processes, 'variational' estimators for random fields and multivariate distributions, and many standard estimators in stochastic geometry. The approach has some affinity with the Stein-Chen method for distributional approximation.

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