2024-03-29T07:54:10Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/1540262023-03-09T11:27:45Zcom_10234_43662com_10234_9col_10234_43643
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Rodríguez-Cortés, Francisco Javier
author
Mateu, Jorge
author
2015-01
We consider kernel-based non-parametric estimation of second-order product densities of spatial point patterns. We present a new family of optimal and positive kernels that shows less variance and more flexibility than optimal kernels. This family generalises most of the classical and widely used kernel functions, such as Box or Epanechnikov kernels. We propose an alternative asymptotically unbiased estimator for the second-order product density function, and compare the performance of the estimator for several members of the family of optimal and positive kernels through MISE and relative efficiency. We present a simulation study to analyse the behaviour of such kernel functions, for three different spatial structures, for which we know the exact analytical form of the product density, and under small sample sizes. Some known datasets are revisited, and we also analyse the IMD dataset in the Rhineland Regional Council in Germany.
RODRÍGUEZ-CORTÉS, F. J.; MATEU, J. Second-order smoothing of spatial point patterns with small sample sizes: a family of kernels. Stochastic environmental research and risk assessment, 2015, vol. 29, no 1, p. 295-308.
http://hdl.handle.net/10234/154026
http://dx.doi.org/10.1007/s00477-014-0944-x
Kernel smoothing
Mean integrated square error
Non-parametric estimation
Relative efficiency
Second-order product density function
Second-order smoothing of spatial point patterns with small sample sizes: a family of kernels