Maximum likelihood estimation for linear Gaussian covariance models

P. Zwiernik, C. Uhler, D. Richards, Journal of the Royal Statistical Society. Series B: Statistical Methodology 79 (2017) 1269–1292.


Journal Article | Published | English
Author
; ;
Department
Abstract
We study parameter estimation in linear Gaussian covariance models, which are p-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex optimization problem which typically has many local maxima. Using recent results on the asymptotic distribution of extreme eigenvalues of the Wishart distribution, we provide sufficient conditions for any hill climbing method to converge to the global maximum. Although we are primarily interested in the case in which n≫p, the proofs of our results utilize large sample asymptotic theory under the scheme n/p→γ>1. Remarkably, our numerical simulations indicate that our results remain valid for p as small as 2. An important consequence of this analysis is that, for sample sizes n≃14p, maximum likelihood estimation for linear Gaussian covariance models behaves as if it were a convex optimization problem. © 2016 The Royal Statistical Society and Blackwell Publishing Ltd.
Publishing Year
Date Published
2017-09-01
Journal Title
Journal of the Royal Statistical Society. Series B: Statistical Methodology
Volume
79
Issue
4
Page
1269 - 1292
ISSN
IST-REx-ID

Cite this

Zwiernik P, Uhler C, Richards D. Maximum likelihood estimation for linear Gaussian covariance models. Journal of the Royal Statistical Society Series B: Statistical Methodology. 2017;79(4):1269-1292. doi:10.1111/rssb.12217
Zwiernik, P., Uhler, C., & Richards, D. (2017). Maximum likelihood estimation for linear Gaussian covariance models. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 79(4), 1269–1292. https://doi.org/10.1111/rssb.12217
Zwiernik, Piotr, Caroline Uhler, and Donald Richards. “Maximum Likelihood Estimation for Linear Gaussian Covariance Models.” Journal of the Royal Statistical Society. Series B: Statistical Methodology 79, no. 4 (2017): 1269–92. https://doi.org/10.1111/rssb.12217.
P. Zwiernik, C. Uhler, and D. Richards, “Maximum likelihood estimation for linear Gaussian covariance models,” Journal of the Royal Statistical Society. Series B: Statistical Methodology, vol. 79, no. 4, pp. 1269–1292, 2017.
Zwiernik P, Uhler C, Richards D. 2017. Maximum likelihood estimation for linear Gaussian covariance models. Journal of the Royal Statistical Society. Series B: Statistical Methodology. 79(4), 1269–1292.
Zwiernik, Piotr, et al. “Maximum Likelihood Estimation for Linear Gaussian Covariance Models.” Journal of the Royal Statistical Society. Series B: Statistical Methodology, vol. 79, no. 4, Wiley-Blackwell, 2017, pp. 1269–92, doi:10.1111/rssb.12217.

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar