My work on covariance estimation has not too long ago been revealed as an Superior Evaluation in WIREs Computational Statistics, a extremely regarded, peer-reviewed journal within the discipline. It feels remarkably rewarding to see a decade of my curiosity lastly sure collectively in a single place.
The writing course of began about 4.5 years in the past on evenings, weekends, and holidays as a side-project. However I really wrote my first publish about multivariate volatility forecasting nicely over a decade in the past, which turned out to be the primary of a collection of (at the moment..) 11 posts on this subject. A decade of studying, coding, tinkering, and revisiting the issue from completely different angles. This jogs my memory of the quote (generally attributed to Albert Einstein):
It’s not that I’m so sensible, it’s simply that I stick with issues longer.
Progress doesn’t should be loud, and it doesn’t should be quick. Even few hours right here and there on weekends and holidays compound properly over time. Crossing the end line is totally gratifying, however the climb is the place the precise worth is. Stick with the issue, and don’t let go of your back-burner concepts.
A fast phrase on what’s contained in the paper (eject right here if covariance estimation will not be related for you). When the variety of variables exceeds the variety of observations (), estimating covariance matrices turns into particularly difficult. The publication brings collectively completely different approaches often siloed throughout statistics, econometrics, and machine studying: issue fashions, linear & nonlinear shrinkage, thresholding estimation, block averaging, graphical fashions, random matrix idea, in addition to a devoted part on guaranteeing a legitimate (e.g. invertible) covariance matrix estimate in real-world functions. After strolling the reader by means of these numerous methodologies, I positioned all of them below a single umbrella – a unified view can assist pinpoint express assumptions behind every of the numerous modelling decisions we face.
For those who’re working in high-dimensional dependence estimation, I hope this pleasant paper (in as a lot as as high-dimensional statistics permits), its in depth assortment of strategies, clear taxonomy, unified notation and framework, can function a helpful reference for real-world functions. Blissful to debate with anybody .
