Sample size for maximum likelihood estimates of gaussian model

Abstract

Significant properties of maximum likelihood (ML) estimate are consistency, normality and efficiency. However, it has been proven that these properties are valid when the sample size approaches infinity. Many researches warn that a behavior of ML estimator working with the small sample size is largely unknown. But, in real tasks we usually do not have enough data to completely fulfill the conditions of optimal ML estimate. The question, which we discuss in the article is, how much data we need to be able to estimate the Gaussian model that provides sufficiently accurate likelihood estimates. This issue is addressed with respect to the dimension of space and it is taken into account possible property of ill conditioned data.