Selecting the number of principal components: estimation of the true rank of a noisy matrix

Principal component analysis (PCA) is a well-known tool in multivariate statistics. One significant challenge in using PCA is the choice of the number of components. In order to address this challenge, we propose an exact distribution-based method for hypothesis testing and construction of confidence intervals for signals in a noisy matrix. Assuming Gaussian noise, we use the conditional distribution of the singular values of a Wishart matrix and derive exact hypothesis tests and confidence intervals for the true signals. Our paper is based on the approach of Taylor, Loftus and Tibshirani (2013) for testing the global null: we generalize it to test for any number of principal components, and derive an integrated version with greater power. In simulation studies we find that our proposed methods compare well to existing approaches.Comment: 29 pages, 9 figures, 4 table

Where are compact groups in the local Universe?

The purpose of this work is to perform a statistical analysis of the location of compact groups in the Universe from observational and semi-analytical points of view. We used the velocity-filtered compact group sample extracted from the Two Micron All Sky Survey for our analysis. We also used a new sample of galaxy groups identified in the 2M++ galaxy redshift catalogue as tracers of the large-scale structure. We defined a procedure to search in redshift space for compact groups that can be considered embedded in other overdense systems and applied this criterion to several possible combinations of different compact and galaxy group subsamples. We also performed similar analyses for simulated compact and galaxy groups identified in a 2M++ mock galaxy catalogue constructed from the Millennium Run Simulation I plus a semi-analytical model of galaxy formation. We observed that only $\sim27\%$ of the compact groups can be considered to be embedded in larger overdense systems, that is, most of the compact groups are more likely to be isolated systems. The embedded compact groups show statistically smaller sizes and brighter surface brightnesses than non-embedded systems. No evidence was found that embedded compact groups are more likely to inhabit galaxy groups with a given virial mass or with a particular dynamical state. We found very similar results when the analysis was performed using mock compact and galaxy groups. Based on the semi-analytical studies, we predict that $70\%$ of the embedded compact groups probably are 3D physically dense systems. Finally, real space information allowed us to reveal the bimodal behaviour of the distribution of 3D minimum distances between compact and galaxy groups. The location of compact groups should be carefully taken into account when comparing properties of galaxies in environments that are a priori different.Comment: 14 pages, 5 figures, 8 tables. Accepted for publication in Astronomy & Astrophysics. Tables B1 and B2 will only be available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A

Evaluation of cosmic ray rejection algorithms on single-shot exposures

To maximise data output from single-shot astronomical images, the rejection of cosmic rays is important. We present the results of a benchmark trial comparing various cosmic ray rejection algorithms. The procedures assess relative performances and characteristics of the processes in cosmic ray detection, rates of false detections of true objects and the quality of image cleaning and reconstruction. The cosmic ray rejection algorithms developed by Rhoads (2000), van Dokkum (2001), Pych (2004) and the IRAF task xzap by Dickinson are tested using both simulated and real data. It is found that detection efficiency is independent of the density of cosmic rays in an image, being more strongly affected by the density of real objects in the field. As expected, spurious detections and alterations to real data in the cleaning process are also significantly increased by high object densities. We find the Rhoads' linear filtering method to produce the best performance in detection of cosmic ray events, however, the popular van Dokkum algorithm exhibits the highest overall performance in terms of detection and cleaning.Comment: 12 pages, 4 figures, accepted for publication in PAS

Selecting Comparables for the Valuation of European Firms

This paper investigates which comparables selection method generates the most precise forecasts when valuing European companies with the enterprise value to EBIT multiple. We also consider the USA as a reference point. It turns out that selecting comparable companies with similar return on assets clearly outperforms selections according to industry membership or total assets. Moreover, we investigate whether comparables should be selected from the same country, from the same region, or from all OECD members. For most European countries, choosing comparables from the 15 European Union member states yields the best forecasts. In contrast, for the UK and the US, comparables should be chosen from the same country only.comparables, selection method, valuing companies, forecasts, EBIT, industry membership, ROA