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

@article{Loh2018BandwidthSF,
  title={Bandwidth selection for estimating the two-point correlation function of a spatial point pattern using AMSE},
  author={Ji Meng Loh and Woncheol Jang},
  journal={Statistica Sinica},
  year={2018}
}
The two-point correlation function (2PCF) is a measure of the secondorder properties of a spatial point pattern and is commonly used in astronomy. We introduce an asymptotic mean squared error (AMSE) approach to obtain closedform 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… 
1 Citations

Figures and Tables from this paper

Quantitative Comparison of Two-point Correlation Functions from Real and Mock SDSS Galaxy Catalogs

We present a simple closed-form bandwidth selection method to obtain the optimal bin size for estimating the two-point correlation function (2PCF). To demonstrate its effectiveness, we apply this

References

SHOWING 1-10 OF 24 REFERENCES

A Comparison of Estimators for the Two-Point Correlation Function

Nine of the most important estimators known for the two-point correlation function are compared using a predetermined, rigorous criterion and a clear recommendation has emerged: the Landy & Szalay estimator is preferred in comparison with the other indicators examined, with a performance almost indistinguishable from the Hamilton estimator.

Estimating a cosmological mass bias parameter with bootstrap bandwidth selection

Summary.  We focus on selecting optimal bandwidths for non‐parametric estimation of the two‐point correlation function of a point pattern. We obtain these optimal bandwidths by using a bootstrap

Bias and variance of angular correlation functions

We present a general method for calculating the bias and variance of estimators for w(θ) based on galaxy-galaxy (DD), random-random (RR), and galaxy-random (DR) pair counts and describe a procedure

Comparing Estimators of the Galaxy Correlation Function

We present a systematic comparison of some of the usual estimators of the two-point correlation function, some of them currently used in cosmology, others extensively employed in the field of the

Asymptotically optimal estimation for the reduced second moment measure of point processes

SUMMARY A modification of the rigid motion correction estimator for the reduced second moment measure of a stationary, isotropic point process is shown to possess an asymptotic optimality property as

The Cut-and-Enhance Method: Selecting Clusters of Galaxies from the Sloan Digital Sky Survey Commissioning Data

We describe an automated method, the cut-and-enhance (CE) method, for detecting clusters of galaxies in multicolor optical imaging surveys. This method uses simple color cuts, combined with a density

Modelling the two-point correlation function of galaxy clusters in the Sloan Digital Sky Survey

ABSTRACT We study the clustering properties of the recently compiled SDSS cluster cat-alog using the two point correlation function in redshift space. We divide thetotal SDSS sample into two richness

Observational Constraints on Higher Order Clustering up to z ≃ 1

We present constraints on the validity of the hierarchical gravitational instability theory and the evolution of biasing based on measurements of higher order clustering statistics in the Deeprange