Sample size for maximum-likelihood estimates of Gaussian model depending on dimensionality of pattern space

The significant properties of the maximum likelihood (ML) estimate are consistency, normality, and efficiency. While it has been proven that these properties are valid when the sample size approaches infinity, the behavior of an ML estimator when working with small sample sizes is largely unknown. However, in real tasks, we usually do not have sufficient data to completely fulfill the conditions of an optimal ML estimate. The question arises as to what amount of data is required to be able to estimate a Gaussian model that provides sufficiently accurate likelihood estimates. This issue is addressed with respect to the number of dimensions of the pattern space. (C) 2019 Elsevier Ltd. All rights reserved.