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.
|Original language||English (US)|
|Number of pages||10|
|Journal||Journal of the Royal Statistical Society. Series C: Applied Statistics|
|State||Published - 1985|
ASJC Scopus subject areas
- Statistics and Probability