Multilevel maximum likelihood estimation with application to covariance matrices

Abstract

The asymptotic variance of the maximum likelihood estimate is proved to\ndecrease when the maximization is restricted to a subspace that contains the\ntrue parameter value. Maximum likelihood estimation allows a systematic fitting\nof covariance models to the sample, which is important in data assimilation.\nThe hierarchical maximum likelihood approach is applied to the spectral\ndiagonal covariance model with different parameterizations of eigenvalue decay,\nand to the sparse inverse covariance model with specified parameter values on\ndifferent sets of nonzero entries. It is shown computationally that using\nsmaller sets of parameters can decrease the sampling noise in high dimension\nsubstantially.\n