Statistica Sinica 27 (2017), 1401-1418
Abstract: The two-point correlation function (2PCF) is a measure of the second- order properties of a spatial point pattern and is commonly used in astronomy. We introduce an asymptotic mean squared error (AMSE) approach to obtain closed- form expressions of adaptive optimal bandwidths for estimating the two-point correlation function of a homogeneous spatial point pattern. This approach provides a simple, quick method for optimal bandwidth selection for 2PCF estimation. Using optimal bandwidths allows more information to be extracted from the data. Numerical studies suggest that the mean squared error of estimates obtained using AMSE optimal bandwidths are close to those obtained with the empirical optimal bandwidths. We illustrate this with an application to a galaxy cluster catalog from the Sloan Digital Sky Survey.
Key words and phrases: Bandwidth selection, second-order properties, spatial point patterns, two-point correlation function.