Related papers: A comparison of estimators for the two-point corre…
We show how to increase the accuracy of estimates of the two-point correlation function without sacrificing efficiency. We quantify the error of the pair-counts and of the Landy-Szalay estimator by comparing them with exact reference…
Measuring the two-point correlation function of the galaxies in the Universe gives access to the underlying dark matter distribution, which is related to cosmological parameters and to the physics of the primordial Universe. The estimation…
Second-order measures, such as the two-point correlation function, are geometrical quantities describing the clustering properties of a point distribution. In this article well-known estimators for the correlation integral are reviewed and…
We define a Maximum Likelihood (ML for short) estimator for the correlation function, {\xi}, that uses the same pair counting observables (D, R, DD, DR, RR) as the standard Landy and Szalay (1993, LS for short) estimator. The ML estimator…
The two-point correlation function (2PCF) is a cornerstone of precision cosmology, yet its estimation from imaging surveys is vulnerable to contamination and incompleteness arising from imperfect target selection and pipeline-level…
All estimators of the two-point correlation function are based on a random catalogue, a set of points with no intrinsic clustering following the selection function of a survey. High-accuracy estimates require the use of large random…
The two-point correlation function of the galaxy distribution is a key cosmological observable that allows us to constrain the dynamical and geometrical state of our Universe. To measure the correlation function we need to know both the…
A class of improved estimators is proposed for N-point correlation functions of galaxy clustering, and for discrete spatial random processes in general. In the limit of weak clustering, the variance of the unbiased estimator converges to…
The two-point correlation function (2pcf) is the key statistic in structure formation; it measures the clustering of galaxies or other density field tracers. Estimators of the 2pcf, including the standard Landy-Szalay (LS) estimator,…
A finite-support constraint on the parameter space is used to derive a lower bound on the error of an estimator of the correlation coefficient in the bivariate exponential distribution. The bound is then exploited to examine optimality of…
We developed a modification to the calculation of the two-point correlation function commonly used in the analysis of large scale structure in cosmology. An estimator of the two-point correlation function is constructed by contrasting the…
We present a systematic comparison of some usual estimators of the 2--point correlation function, some of them currently used in Cosmology, others extensively employed in the field of the statistical analysis of point processes. At small…
I present a new improved estimator for the correlation function of 2D nonlinear sigma models. Numerical tests for the 2D XY model and the 2D O(3)-invariant vector model were performed. For small physical volume, i.e. a lattice size small…
The 2-point spatial correlation function (CF), $\xi(s)$, has been used to study the clustering of the galaxies in the preliminary version of the HIPASS Bright Galaxy Catalogue (HIPASS BGC), which includes the 1,000 HI brightest galaxies in…
The angular two-point correlation function is calculated for the first 300 square degrees of the FIRST radio survey. Results for various subsamples are also obtained. Double-lobed sources are shown to have a higher clustering amplitude than…
Two-point correlation functions (2PCF) are widely used to characterize how points cluster in space. In this work, we study the problem of measuring the 2PCF over a large set of points, restricted to a subset satisfying a property of…
We are presenting in this paper a detailed account of the methods used to compute the three-dimensional two-point galaxy correlation function in the VIMOS-VLT deep survey (VVDS). We investigate how instrumental selection effects and…
We present the three-dimensional power spectrum of galaxy clustering using measurements of the angular correlation function from the second incremental release of the Two-Micron All Sky Survey (2MASS). The angular positions of galaxies out…
The exchange or geometric cluster algorithm allows us to define a variance reduced estimator of the connected two-point function in the presence of a broken Z_2-symmetry. We present first numerical tests for the improved Blume-Capel model…
We develop estimators of agreement and disagreement between correlated cosmological data sets. These account for data correlations when computing the significance of both tensions and excess confirmation while remaining statistically…