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Asymptotic optimality of the least-squares cross-validation bandwidth for kernel estimates of intensity functions

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  • Brooks, Maria Mori
  • Marron, J. Stephen

Abstract

In this paper, kernel function methods are considered for estimating the intensity function of a non-homogeneous Poisson process. A least-squares cross-validation bandwidth for the kernel intensity estimator is introduced, and it is proven that this bandwidth is asymptotically optimal for kernel intensity estimation.

Suggested Citation

  • Brooks, Maria Mori & Marron, J. Stephen, 1991. "Asymptotic optimality of the least-squares cross-validation bandwidth for kernel estimates of intensity functions," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 157-165, June.
    • Handle: RePEc:eee:spapps:v:38:y:1991:i:1:p:157-165
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    Cited by:

    1. M. N. M. Lieshout, 2020. "Infill Asymptotics and Bandwidth Selection for Kernel Estimators of Spatial Intensity Functions," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 995-1008, September.
    2. Isabel Fuentes-Santos & Wenceslao González-Manteiga & Jorge Mateu, 2016. "Consistent Smooth Bootstrap Kernel Intensity Estimation for Inhomogeneous Spatial Poisson Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 416-435, June.
    3. Borrajo, M.I. & González-Manteiga, W. & Martínez-Miranda, M.D., 2020. "Bootstrapping kernel intensity estimation for inhomogeneous point processes with spatial covariates," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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