Bandwidth selection for estimating the two-point correlation function of a spatial point pattern using AMSE

Woncheol Jang; Ji Meng Loh

doi:10.5705/ss.202015.0426

Bandwidth selection for estimating the two-point correlation function of a spatial point pattern using AMSE

Woncheol Jang, Ji Meng Loh

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1401-1418
Number of pages	18
Journal	Statistica Sinica
Volume	27
Issue number	3
DOIs	https://doi.org/10.5705/ss.202015.0426
State	Published - Jul 2017

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Bandwidth selection
Second-order properties
Spatial point patterns
Two-point correlation function

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10.5705/ss.202015.0426

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title = "Bandwidth selection for estimating the two-point correlation function of a spatial point pattern using AMSE",

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.",

keywords = "Bandwidth selection, Second-order properties, Spatial point patterns, Two-point correlation function",

author = "Woncheol Jang and Loh, {Ji Meng}",

note = "Funding Information: We are grateful to the referees for their ideas and suggestions toward improving this work. Woncheol Jang's work was supported by the Basic Science Research Program through the National Research Foundation (NRF) of Korea grant by the Ministry of Education (No. 2013R1A1A2010065) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A4A1007895).",

year = "2017",

month = jul,

doi = "10.5705/ss.202015.0426",

language = "English (US)",

volume = "27",

pages = "1401--1418",

journal = "Statistica Sinica",

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T1 - Bandwidth selection for estimating the two-point correlation function of a spatial point pattern using AMSE

AU - Jang, Woncheol

AU - Loh, Ji Meng

N1 - Funding Information: We are grateful to the referees for their ideas and suggestions toward improving this work. Woncheol Jang's work was supported by the Basic Science Research Program through the National Research Foundation (NRF) of Korea grant by the Ministry of Education (No. 2013R1A1A2010065) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A4A1007895).

PY - 2017/7

Y1 - 2017/7

N2 - 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.

AB - 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.

KW - Bandwidth selection

KW - Second-order properties

KW - Spatial point patterns

KW - Two-point correlation function

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DO - 10.5705/ss.202015.0426

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JO - Statistica Sinica

JF - Statistica Sinica

IS - 3

ER -

Bandwidth selection for estimating the two-point correlation function of a spatial point pattern using AMSE

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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