Multilevel maximum likelihood estimation with application to covariance matrices

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.

Multivariate Multilevel Modelling to Assess Factors Affecting the Quality of Vocational High Schools in South Sulawesi Province

“…Multilevel maximum likelihood estimation (MLE) is the model's chosen strategy for parameter estimation [17]. The specification of the model used is the intercept only (MVMM.0) multilevel model, which means the multivariate multilevel model without involving the independent/explanatory variables at the school level and regency level, the school-level multivariate multilevel model (MVMM1.…”