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 \(\mathbb {R}^{d}\) 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.

中文翻译：

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空间强度函数的核估计的填充渐近性和带宽选择

我们调查空间点过程的强度函数的核估计量的渐近均方误差。在\（\ mathbb {R} ^ {d} \）中的点过程的n个独立副本被叠加的情况下，我们导出了偏差和方差的展开。当在所有d维上使用相同的带宽时，我们表明在适当的平滑度条件下，在真实强度函数上，存在一个最佳带宽，其大小为n ^{− 1 /（d + 4）}。