Infill Asymptotics and Bandwidth Selection for Kernel Estimators of Spatial Intensity Functions

M. N. M. Lieshout ()
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M. N. M. Lieshout: CWI

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 3, 995-1008

Abstract: Abstract We investigate the asymptotic mean squared error of kernel estimators of the intensity function of a spatial point process. We derive expansions for the bias and variance in the scenario that n independent copies of a point process in ℝ d $\mathbb {R}^{d}$ are superposed. When the same bandwidth is used in all d dimensions, we show that an optimal bandwidth exists and is of the order n− 1/(d+ 4) under appropriate smoothness conditions on the true intensity function.

Keywords: Bandwidth; Infill asymptotics; Intensity function; Kernel estimator; Mean squared error; Point process; 60G55; 62G07; 60D05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-019-09749-x

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