Bootstrap Confidence Regions for the Intensity of a Poisson Point Process
作者:
Ann Cowling,
Peter Hall,
MichaelJ. Phillips,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1996)
卷期:
Volume 91,
issue 436
页码: 1516-1524
ISSN:0162-1459
年代: 1996
DOI:10.1080/01621459.1996.10476719
出版商: Taylor & Francis Group
关键词: Confidence band;Inhomogeneous Poisson process;Intensity function;Kernel estimation
数据来源: Taylor
摘要:
Bootstrap methods are developed for constructing confidence regions for the intensity function of a nonstationary Poisson process. Several different resampling algorithms are suggested, ranging from resampling a Poisson process with intensity equal to that estimated nonparametrically from the data to resampling the data points themselves in the same manner that the bootstrap is used in problems involving independent and identically distributed observations. For each different bootstrap method, various percentile-tways of constructing confidence bands are described. The effectiveness of these different approaches is demonstrated both theoretically and numerically, for real and simulated data. Issues such as bias correction are addressed.
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