论文信息 - Short distances, flat triangles and Poisson limits

Short distances, flat triangles and Poisson limits

Motivated by problems in the analysis of spatial data, we prove some general Poisson limit theorems for the U -statistics of Hoeffding (1948). The theorems are applied to tests of clustering or collinearities in plane data; nearest neighbour distances are also considered.

[1] B. M. Brown,et al. Martingale convergence to infinitely divisible laws with finite variances , 1971 .

[2] B. Silverman,et al. Limit theorems for dissociated random variables , 1976, Advances in Applied Probability.

[3] Bernard W. Silverman,et al. RATES OF POISSON CONVERGENCE FOR U-STATISTICS , 1979 .

[4] O. Kallenberg. Characterization and convergence of random measures and point processes , 1973 .

[5] B. Ripley. Modelling Spatial Patterns , 1977 .

[6] W. Hoeffding. A Class of Statistics with Asymptotically Normal Distribution , 1948 .

[7] Timothy C. Brown,et al. A Martingale Approach to the Poisson Convergence of Simple Point Processes , 1978 .

[8] Brian D. Ripley,et al. Quick tests for spatial interaction , 1978 .

[9] N. Kaplan. Two Applications of a Poisson Approximation for Dependent Events , 1977 .

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