A criterion for the number of factors

This note proposes a new criterion for the determination of the number of factors in an approximate static factor model. The criterion is strongly associated with the scree test and compares the differences between consecutive eigenvalues to a threshold. The size of the threshold is derived from a hyperbola and depends only on the sample size and the number of factors k. Monte Carlo simulations compare its properties with well-established estimators from the literature. Our criterion shows similar results as the standard implementations of these estimators, but is not prone to a lack of robustness against a too large a priori determined maximum number of factors kmax

A criterion for the number of factors in a data-rich environment

This paper derives a new criterion for the determination of the number of factors in static approximate factor models, that is strongly associated with the scree test. Our criterion looks for the number of eigenvalues for which the difference between adjacent eigenvalue-component number blocks is maximized. Monte Carlo experiments compare the properties of our criterion to the Edge Distribution (ED) estimator of Onatski (2010) and the two eigenvalue ratio estimators of Ahn and Horenstein (2013). Our criterion outperforms the latter two for all sample sizes and the ED estimator of Onatski (2010) for samples up to 300 variables/observation

Reproduction package for the paper "The Apertif Radio Transient System (ARTS): Design, Commissioning, Data Release, and Detection of the first 5 Fast Radio Bursts"

This is a basic reproduction package for the paper "The Apertif Radio Transient System (ARTS): Design, Commissioning, Data Release, and Detection of the first 5 Fast Radio Bursts" by van Leeuwen et al. (2023). * arXiv:arXiv:2205.12362 * DOI: 10.1051/0004-6361/20224410

The Apertif Radio Transient System (ARTS): Design, commissioning, data release, and detection of the first five fast radio bursts

Fast radio bursts (FRBs) must be powered by uniquely energetic emission mechanisms. This requirement has eliminated a number of possible source types, but several remain. Identifying the physical nature of FRB emitters arguably requires good localisation of more detections, as well as broad-band studies enabled by real-time alerting. In this paper, we present the Apertif Radio Transient System (ARTS), a supercomputing radio-telescope instrument that performs real-time FRB detection and localisation on the Westerbork Synthesis Radio Telescope (WSRT) interferometer. It reaches coherent-addition sensitivity over the entire field of the view of the primary-dish beam. After commissioning results verified that the system performed as planned, we initiated the Apertif FRB survey (ALERT). Over the first 5 weeks we observed at design sensitivity in 2019, we detected five new FRBs, and interferometrically localised each of them to 0.4–10 sq. arcmin. All detections are broad band, very narrow, of the order of 1 ms in duration, and unscattered. Dispersion measures are generally high. Only through the very high time and frequency resolution of ARTS are these hard-to-find FRBs detected, producing an unbiased view of the intrinsic population properties. Most localisation regions are small enough to rule out the presence of associated persistent radio sources. Three FRBs cut through the halos of M31 and M33. We demonstrate that Apertif can localise one-off FRBs with an accuracy that maps magneto-ionic material along well-defined lines of sight. The rate of one every ~7 days ensures a considerable number of new sources are detected for such a study. The combination of the detection rate and localisation accuracy exemplified by the first five ARTS FRBs thus marks a new phase in which a growing number of bursts can be used to probe our Universe