Cholesky-based multivariate Gaussian regression

Thomas Muschinski, Georg J. Mayr, Thorsten Simon, Nikolaus Umlauf and Achim Zeileis

Econometrics and Statistics, 2024, vol. 29, issue C, 261-281

Abstract: Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix Σ of the response distribution using the entries of its Cholesky decomposition. The more common variance-correlation parameterization limits such regressions to bivariate responses because higher dimensions require complicated constraints among the correlations to ensure positive definite Σ and a well-defined probability density function. In contrast, Cholesky-based parameterizations ensure positive definiteness for all distributional dimensions regardless of the values the parameters take, enabling estimation and regularization as for other distributional regression models. In cases where components of the response vector are assumed to be conditionally independent beyond a certain lag, model complexity can be further reduced by setting the corresponding Cholesky parameters to zero a priori. Cholesky-based multivariate Gaussian regression is first illustrated and assessed on artificial data and subsequently applied to a real-world 10-dimensional weather forecasting problem. There the regression is used to obtain reliable joint probabilities of temperature across ten future time points, leveraging temporal correlations over the prediction period to obtain more precise and meteorologically consistent probabilistic forecasts.

Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S2452306222000168
Full text for ScienceDirect subscribers only. Contains open access articles

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ecosta:v:29:y:2024:i:c:p:261-281

DOI: 10.1016/j.ecosta.2022.03.001

Access Statistics for this article

Econometrics and Statistics is currently edited by E.J. Kontoghiorghes, H. Van Dijk and A.M. Colubi

More articles in Econometrics and Statistics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().