Multilevel maximum likelihood estimation with application to covariance matrices. Issue 4 (16th February 2019)

• Record Type: Journal Article
• Authors: Turčičová, Marie; Mandel, Jan; Eben, Kryštof
• Is Part Of: Communications in statistics. Volume 48:Issue 4(2019)
• Page Start: 909
• Page End: 925
• Publication Date: 2019-02-16
• Subjects: Fisher information -- High dimension -- Hierarchical maximum likelihood -- Nested parameter spaces -- Spectral diagonal covariance model -- Sparse inverse covariance model; 62H12 -- 62F12; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1422755
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: 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.