Performance analysis of hypothesis testing for sparse pairwise interaction point processes

The sufficient statistic for performing the likelihood ratio test for pairwise interaction point processes is well-known; however, the evaluation of its performance is a very difficult problem. It is shown that the distribution of the sufficient statistic can be approximated by the distribution of a Poisson-driven shot-noise random variable, which can be readily computed.

[1]  Noel A Cressie,et al.  Inference for spatial processes using subsampling : A simulation study , 1997 .

[2]  Robert Haining,et al.  Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95 , 1993 .

[3]  John A. Gubner,et al.  Computation of Shot-Noise Probability Distributions and Densities , 1996, SIAM J. Sci. Comput..

[4]  R. Saunders,et al.  Poisson limits for a clustering model of strauss , 1977, Journal of Applied Probability.

[5]  Adrian Baddeley,et al.  Stochastic approximation of the MLE for a spatial point pattern , 1989 .

[6]  J. A. Gubner,et al.  Poisson limits and nonparametric estimation for pairwise interaction point processes , 2000, Journal of Applied Probability.

[7]  Donald L. Snyder,et al.  Random Point Processes in Time and Space , 1991 .

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

[9]  P. Diggle,et al.  A nonparametric estimator for pairwise-interaction point processes , 1987 .

[10]  Y. Ogata,et al.  Estimation of interaction potentials of spatial point patterns through the maximum likelihood procedure , 1981 .

[11]  Y. Ogata,et al.  Likelihood Analysis of Spatial Point Patterns , 1984 .

[12]  B. Ripley.  Statistical inference for spatial processes , 1990 .

[14]  C. Geyer,et al.  Simulation Procedures and Likelihood Inference for Spatial Point Processes , 1994 .

[15]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .