论文信息 - On asymptotic normality of pseudo likelihood estimates for pairwise interaction processes

On asymptotic normality of pseudo likelihood estimates for pairwise interaction processes

We consider point processes defined through a pairwise interaction potential and admitting a two-dimensional sufficient statistic. It is shown that the pseudo maximum likelihood estimate can be stochastically normed so that the limiting distribution is a standard normal distribution. This result is true irrespectively of the possible existence of phase transitions. The work here is an extension of the work Guyon and Künsch (1992,Lecture Notes in Statist.,74, Springer, New York) and is based on viewing a point process interchangeably as a lattice field.

H. Künsch | J. L. Jensen

[1] T. Sweeting. Uniform Asymptotic Normality of the Maximum Likelihood Estimator , 1980 .

[2] Erwin Bolthausen,et al. On the Central Limit Theorem for Stationary Mixing Random Fields , 1982 .

[3] ON THE CENTRAL LIMIT THEOREM FOR WEAKLY DEPENDENT RANDOM FIELDS , 1983 .

[4] Hans-Otto Georgii,et al. Gibbs Measures and Phase Transitions , 1988 .

[5] Jesper Møller. On the rate of convergence of spatial birth-and-death processes , 1989 .

[6] P. Green. Discussion of 'Bayesian image restoration with two applications in spatial statistics' by J Besag, J C York & A Mollie , 1991 .

[7] J. L. Jensen,et al. Pseudolikelihood for Exponential Family Models of Spatial Point Processes , 1991 .

[8] J. Besag,et al. Bayesian image restoration, with two applications in spatial statistics , 1991 .

[9] H. Künsch,et al. Asymptotic Comparison of Estimators in the Ising Model , 1992 .

[10] Jens Ledet Jensen,et al. Asymptotic Normality of Estimates in Spatial Point Processes , 1993 .

[11] P. Diggle,et al. On parameter estimation for pairwise interaction point processes , 1994 .