This paper provides a comprehensive estimation framework for large covariancematrices via a log-det heuristics augmented by a nuclear norm plus$\ell_{1}$-norm penalty. We develop the model framework, which includeshigh-dimensional approximate factor models with a sparse residual covariance.We prove that the aforementioned log-det heuristics is locally convex with aLipschitz-continuous gradient, so that a proximal gradient algorithm may bestated to numerically solve the problem while controlling the thresholdparameters. The proposed optimization strategy recovers in a single step boththe covariance matrix components and the latent rank and the residual sparsitypattern with high probability, and performs systematically not worse than thecorresponding estimators employing Frobenius loss in place of the log-detheuristics. The error bounds for the ensuing low rank and sparse covariancematrix estimators are established, and the identifiability conditions for thelatent geometric manifolds are provided, improving existing literature. Thevalidity of outlined results is highlighted by an exhaustive simulation studyand a financial data example involving Euro Area banks.
We develop a variational Bayes approach for dynamic variable selection inhigh-dimensional regression models with time-varying parameters and predictorsthat exhibit a predefined group structure. Through comprehensive simulationstudies, we demonstrate that our method yields more accurate parameterestimates than existing Bayesian static and dynamic variable selectionapproaches while maintaining computational efficiency. We illustrate theperformance of our approach within the context of a popular problem ineconomics: forecasting inflation based on a large set of macroeconomicpredictors. Our approach demonstrates significant improvements in out-of-samplepoint and density forecasting accuracy. A retrospective analysis of thetime-varying parameter estimates reveals economically interpretable patterns ininflation dynamics.
Detection of the faint 21 cm line emission from the Cosmic Dawn and Epoch ofReionisation will require not only exquisite control over instrumentalcalibration and systematics to achieve the necessary dynamic range ofobservations but also validation of analysis techniques to demonstrate theirstatistical properties and signal loss characteristics. A key ingredient inachieving this is the ability to perform high-fidelity simulations of the kindsof data that are produced by the large, many-element, radio interferometricarrays that have been purpose-built for these studies. The large scale of thesearrays presents a computational challenge, as one must simulate a detailed skyand instrumental model across many hundreds of frequency channels, thousands oftime samples, and tens of thousands of baselines for arrays with hundreds ofantennas. In this paper, we present a fast matrix-based method for simulatingradio interferometric measurements (visibilities) at the necessary scale. Weachieve this through judicious use of primary beam interpolation, fastapproximations for coordinate transforms, and a vectorised outer product toexpand per-antenna quantities to per-baseline visibilities, coupled withstandard parallelisation techniques. We validate the results of this method,implemented in the publicly-available matvis code, against a high-precisionreference simulator, and explore its computational scaling on a variety ofproblems.