Resistant estimates for high dimensional and functional data based on random projections

We herein propose a new robust estimation method based on random projections that is adaptive and, automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted contamination models, the procedure is robust and attains full efficiency. We tested the method using both simulated and real data.Comment: 24 pages, 6 figure

Mass accretion rates of clusters of galaxies: CIRS and HeCS

We use a new spherical accretion recipe tested on N-body simulations to measure the observed mass accretion rate (MAR) of 129 clusters in the Cluster Infall Regions in the Sloan Digital Sky Survey (CIRS) and in the Hectospec Cluster Survey (HeCS). The observed clusters cover the redshift range of $0.01<z<0.30$ and the mass range of $\sim 10^{14}-10^{15} {h^{-1}~\rm{M_\odot}}$. Based on three-dimensional mass profiles of simulated clusters reaching beyond the virial radius, our recipe returns MARs that agree with MARs based on merger trees. We adopt this recipe to estimate the MAR of real clusters based on measurements of the mass profile out to $\sim 3R_{200}$. We use the caustic method to measure the mass profiles to these large radii. We demonstrate the validity of our estimates by applying the same approach to a set of mock redshift surveys of a sample of 2000 simulated clusters with a median mass of $M_{200}= 10^{14} {h^{-1}~\rm{M_{\odot}}}$ as well as a sample of 50 simulated clusters with a median mass of $M_{200}= 10^{15} {h^{-1}~\rm{M_{\odot}}}$: the median MARs based on the caustic mass profiles of the simulated clusters are unbiased and agree within $19\%$ with the median MARs based on the real mass profile of the clusters. The MAR of the CIRS and HeCS clusters increases with the mass and the redshift of the accreting cluster, which is in excellent agreement with the growth of clusters in the $\Lambda$CDM model.Comment: 25 pages, 19 figures, 7 table

Resistant estimates for high dimensional and functional data based on random projections

We herein propose a new robust estimation method based on random projections that is adaptive and automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted contamination models, the procedure is robust and attains full efficiency. We tested the method using both simulated and real data.Fil: Fraiman, Jacob Ricardo. Universidad de San Andrés; Argentina. Universidad de la República; Uruguay. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Svarc, Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; Argentin

Mass estimation in the outer regions of galaxy clusters

We present a technique for estimating the mass in the outskirts of galaxy clusters where the usual assumption of dynamical equilibrium is not valid. The method assumes that clusters form through hierarchical clustering and requires only galaxy redshifts and positions on the sky. We apply the method to dissipationless cosmological N-body simulations where galaxies form and evolve according to semi-analytic modelling. The method recovers the actual cluster mass profile within a factor of two to several megaparsecs from the cluster centre. This error originates from projection effects, sparse sampling, and contamination by foreground and background galaxies. In the absence of velocity biases, this method can provide an estimate of the mass-to-light ratio on scales ~1-10 Mpc/h where this quantity is still poorly known.Comment: 14 pages, 7 figures, MN LaTeX style, MNRAS, in pres

Spatial Sign Correlation

A new robust correlation estimator based on the spatial sign covariance matrix (SSCM) is proposed. We derive its asymptotic distribution and influence function at elliptical distributions. Finite sample and robustness properties are studied and compared to other robust correlation estimators by means of numerical simulations.Comment: 20 pages, 7 figures, 2 table

Quasiconvex Programming

We define quasiconvex programming, a form of generalized linear programming in which one seeks the point minimizing the pointwise maximum of a collection of quasiconvex functions. We survey algorithms for solving quasiconvex programs either numerically or via generalizations of the dual simplex method from linear programming, and describe varied applications of this geometric optimization technique in meshing, scientific computation, information visualization, automated algorithm analysis, and robust statistics.Comment: 33 pages, 14 figure