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A Kernel Method for Smoothing Point Process Data

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 estimator is illustrated using simulated data. An application to data on the locations of joints along a coal seam is described. The extension to two‐dimensional point processes is noted.