A Kernel Method for Smoothing Point Process Data

@article{Diggle1985AKM,
  title={A Kernel Method for Smoothing Point Process Data},
  author={Peter John Diggle},
  journal={Journal of The Royal Statistical Society Series C-applied Statistics},
  year={1985},
  volume={34},
  pages={138-147}
}
  • P. Diggle
  • Published 1 June 1985
  • Mathematics
  • Journal of The Royal Statistical Society Series C-applied Statistics
A method for estimating the local intensity of a one‐dimensional point process is described. The estimator uses an adaptation of Rosenblatt's kernel method of non‐parametric probability density estimation, with a correction for end‐effects. An expression for the mean squared error is derived on the assumption that the underlying process is a stationary Cox process, and this result is used to suggest a practical method for choosing the value of the smoothing constant. The performance of the… Expand
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Two approaches are described to the analysis of spatial patterns consisting of several types of points. The first approach uses a method of asymptotically unbiased estimation of the second momentExpand
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1. BASIC FORMULAE In a previous paper (Bartlett, 1963 b) I have developed in some detail statistical techniques for estimating and analysing the spectrum of a stationary point stochastic process inExpand
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