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Density estimation for point processes

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  • Ellis, Steven P.

Abstract

A general nonparametric density estimation problem is considered in which the data is generated by a spatial point process. Several practical problems are special cases of it, including those of estimating the common probability density of a sequence of random vectors and estimating the product density of a stationary multivariate point process. Kernel and k-nearest neighbor estimators are defined and in each case the joint asymptotic normality and consistency of the estimates of the density at a given finite number of points is derived.

Suggested Citation

  • Ellis, Steven P., 1991. "Density estimation for point processes," Stochastic Processes and their Applications, Elsevier, vol. 39(2), pages 345-358, December.
    • Handle: RePEc:eee:spapps:v:39:y:1991:i:2:p:345-358
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    Cited by:

    1. Pierre Jacob & Paulo Oliveira, 1999. "Histograms and Associated Point Processes," Statistical Inference for Stochastic Processes, Springer, vol. 2(3), pages 227-251, October.
    2. Dimitrios Tsitsis & George Karavasilis & Alexandros Rigas, 2012. "Measuring the association of stationary point processes using spectral analysis techniques," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(1), pages 23-47, March.
    3. Florens, Danielle & Pham, Huyên, 1999. "Large deviation principle in nonparametric estimation of marked point processes," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 383-388, February.
    4. Helmers, Roelof & Wayan Mangku, I. & Zitikis, Ricardas, 2003. "Consistent estimation of the intensity function of a cyclic Poisson process," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 19-39, January.

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