• Bernoulli
  • Volume 6, Number 5 (2000), 783-808.

Time-invariance estimating equations

A.J. Baddeley

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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 θ̂ 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 θ. 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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Bernoulli, Volume 6, Number 5 (2000), 783-808.

First available in Project Euclid: 6 April 2004

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censored data conditional intensity dead leaves model diffusions generator Gibbs point processes Gibbs random fields Gibbs sampler Godambe optimality highly structured stochastic systems infinitesimal generator Markov random fields maximum likelihood maximum pseudolikelihood method of moments Nguyen-Zessin formula pseudo-likelihood reduced sample estimator spatial birth-and-death processes Stein-Chen method Takacs-Fiksel method unbiased estimating equations variational estimators


Baddeley, A.J. Time-invariance estimating equations. Bernoulli 6 (2000), no. 5, 783--808.

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