On Rescaled Poisson Processes and the Brownian Bridge

被引：0
作者：
Frederic Paik Schoenberg
机构：
[1] University of California,Department of Statistics
[2] Los Angeles,undefined
来源：
Annals of the Institute of Statistical Mathematics | 2002年 / 54卷
关键词：
Brownian bridge; Poisson bridge; intensity; point process; Poisson process; residual analysis;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The process obtained by rescaling a homogeneous Poisson process by the maximum likelihood estimate of its intensity is shown to have surprisingly strong self-correcting behavior. Formulas for the conditional intensity and moments of the rescaled Poisson process are derived, and its behavior is demonstrated using simulations. Relationships to the Brownian bridge are explored, and implications for point process residual analysis are discussed.
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页码：445 / 457
页数：12
相关论文
共 34 条
[1]  
Aalen O.(1978)Random time changes for multivariate counting processes Scand. Actuar. J. 17 81-101
[2]  
Hoem J.(1987)A modified one-sided K-S confidence region narrower in one tail Comm. Statist. Theory Methods 16 17-28
[3]  
Arsham H.(1989)Hungarian constructions from the nonasymptotic viewpoint Ann. Probab. 17 239-256
[4]  
Bretagnolle J.(1988)Poisson approximations for time-changed point processes Stoch. Process. Appl. 29 247-256
[5]  
Massart P.(1992)Rényi-type empirical processes J. Multivariate Anal. 41 338-358
[6]  
Brown T.(1977)Testing the hypothesis that a point process is Poisson Adv. in Appl. Probab. 9 724-746
[7]  
Nair M.(1971)Spectra of some self-exciting and mutually exciting point processes Biometrika 58 83-90
[8]  
Csörgő M.(1991)Goodness-of-fit tests for the second moment function of a stationary multidimensional Poisson process Statistics 22 245-278
[9]  
Horváth L.(1979)A self-correcting point process Stochastic Process. Appl. 8 335-347
[10]  
Davies R.(1949)On deviations between theoretical and empirical distributions Proc. Nat. Acad. Sci. U.S.A. 35 252-257
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