Multilevel maximum likelihood estimation with application to covariance matrices

0486424 - ÚI 2020 RIV US eng J - Journal Article
Turčičová, Marie - Mandel, Jan - Eben, Kryštof
Multilevel maximum likelihood estimation with application to covariance matrices.
Communications in Statistics - Theory and Methods. Roč. 48, č. 4 (2019), s. 909-925. ISSN 0361-0926. E-ISSN 1532-415X
R&D Projects: GA ČR GA13-34856S
Institutional support: RVO:67985807
Keywords : Fisher information * High dimension * Hierarchical maximum likelihood * Nested parameter spaces * Spectral diagonal covariance model * Sparse inverse covariance model
OECD category: Statistics and probability
Impact factor: 0.612, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1080/03610926.2017.1422755

The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of covariance models to the sample, which is important in data assimilation. The hierarchical maximum likelihood approach is applied to the spectral diagonal covariance model with different parameterizations of eigenvalue decay, and to the sparse inverse covariance model with specified parameter values on different sets of nonzero entries. It is shown computationally that using smaller sets of parameters can decrease the sampling noise in high dimension substantially.
Permanent Link: http://hdl.handle.net/11104/0281241