---
_id: '1208'
abstract:
- lang: eng
  text: 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.
article_processing_charge: No
author:
- first_name: Piotr
  full_name: Zwiernik, Piotr
  last_name: Zwiernik
- first_name: Caroline
  full_name: Uhler, Caroline
  id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
  last_name: Uhler
  orcid: 0000-0002-7008-0216
- first_name: Donald
  full_name: Richards, Donald
  last_name: Richards
citation:
  ama: 'Zwiernik P, Uhler C, Richards D. Maximum likelihood estimation for linear
    Gaussian covariance models. <i>Journal of the Royal Statistical Society Series
    B: Statistical Methodology</i>. 2017;79(4):1269-1292. doi:<a href="https://doi.org/10.1111/rssb.12217">10.1111/rssb.12217</a>'
  apa: 'Zwiernik, P., Uhler, C., &#38; Richards, D. (2017). Maximum likelihood estimation
    for linear Gaussian covariance models. <i>Journal of the Royal Statistical Society.
    Series B: Statistical Methodology</i>. Wiley-Blackwell. <a href="https://doi.org/10.1111/rssb.12217">https://doi.org/10.1111/rssb.12217</a>'
  chicago: 'Zwiernik, Piotr, Caroline Uhler, and Donald Richards. “Maximum Likelihood
    Estimation for Linear Gaussian Covariance Models.” <i>Journal of the Royal Statistical
    Society. Series B: Statistical Methodology</i>. Wiley-Blackwell, 2017. <a href="https://doi.org/10.1111/rssb.12217">https://doi.org/10.1111/rssb.12217</a>.'
  ieee: 'P. Zwiernik, C. Uhler, and D. Richards, “Maximum likelihood estimation for
    linear Gaussian covariance models,” <i>Journal of the Royal Statistical Society.
    Series B: Statistical Methodology</i>, vol. 79, no. 4. Wiley-Blackwell, pp. 1269–1292,
    2017.'
  ista: '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.'
  mla: 'Zwiernik, Piotr, et al. “Maximum Likelihood Estimation for Linear Gaussian
    Covariance Models.” <i>Journal of the Royal Statistical Society. Series B: Statistical
    Methodology</i>, vol. 79, no. 4, Wiley-Blackwell, 2017, pp. 1269–92, doi:<a href="https://doi.org/10.1111/rssb.12217">10.1111/rssb.12217</a>.'
  short: 'P. Zwiernik, C. Uhler, D. Richards, Journal of the Royal Statistical Society.
    Series B: Statistical Methodology 79 (2017) 1269–1292.'
date_created: 2018-12-11T11:50:43Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2023-09-20T11:17:21Z
day: '01'
department:
- _id: CaUh
doi: 10.1111/rssb.12217
external_id:
  isi:
  - '000411712300012'
intvolume: '        79'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1408.5604
month: '09'
oa: 1
oa_version: Submitted Version
page: 1269 - 1292
project:
- _id: 2530CA10-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: Y 903-N35
  name: 'Gaussian Graphical Models: Theory and Applications'
publication: 'Journal of the Royal Statistical Society. Series B: Statistical Methodology'
publication_identifier:
  issn:
  - '13697412'
publication_status: published
publisher: Wiley-Blackwell
publist_id: '6142'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Maximum likelihood estimation for linear Gaussian covariance models
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 79
year: '2017'
...