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

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  • Guan, Yongtao

Abstract

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.

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  • Guan, Yongtao, 2007. "A least-squares cross-validation bandwidth selection approach in pair correlation function estimations," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1722-1729, December.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:18:p:1722-1729
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    References listed on IDEAS

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    1. Yongtao Guan & Michael Sherman & James A. Calvin, 2006. "Assessing Isotropy for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 62(1), pages 119-125, March.
    2. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    3. D. Stoyan & U. Bertram & H. Wendrock, 1993. "Estimation variances for estimators of product densities and pair correlation functions of planar point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 211-221, June.
    4. Dietrich Stoyan & Helga Stoyan, 2000. "Improving Ratio Estimators of Second Order Point Process Characteristics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 641-656, December.
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    Cited by:

    1. Ji Meng Loh & Woncheol Jang, 2010. "Estimating a cosmological mass bias parameter with bootstrap bandwidth selection," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(5), pages 761-779, November.
    2. Ka Yiu Wong & Dietrich Stoyan, 2021. "Poles of pair correlation functions: When they are real?," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 425-440, April.
    3. Tilman M. Davies & Martin L. Hazelton, 2013. "Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 355-389, November.

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