A least-squares cross-validation bandwidth selection approach in pair correlation function estimations

The pair correlation function is a useful tool to analyze spatial point patterns. It is often estimated nonparametrically by a procedure such as kernel smoothing. This article develops a data-driven method for the selection of the bandwidth involved in the estimation. The proposed method uses the idea of least-squares cross-validation which has been often applied for bandwidth selection in density estimation and many other nonparametric estimations. The asymptotic property of the proposed approach will be investigated under an increasing-domain setting in this paper.