Abstract of Bootstrap confidence regions for the intensity of a Poisson point process

Research Report SRR95-001

Bootstrap confidence regions for the intensity of a Poisson point process

Ann Cowling, Peter Hall, Michael J. Phillips

Abstract: We develop bootstrap methods for constructing confidence regions, including intervals and simultaneous bands, in the context of estimating the intensity function of a non-stationary 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 much the same way one would use the bootstrap in problems involving independent and identically distributed observations. For each different bootstrap method a variety of percentile-t ways of constructing confidence bands is described, producing bands whose width varies in proportion to standard deviation, or is approximately constant, depending on the application. 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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