Sample size for maximum-likelihood estimates of Gaussian model depending on dimensionality of pattern space. (July 2019)

• Record Type: Journal Article
• Authors: Psutka, Josef V.; Psutka, Josef
• Is Part Of: Pattern recognition. Volume 91(2019:Jul.)
• Page Start: 25
• Page End: 33
• Publication Date: 2019-07
• Subjects: Maximum-likelihood estimate -- Likelihood function -- Gaussian model -- Gaussian mixture model -- Sample size -- Dimensionality -- Pattern space -- Heteroscedastic data.; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2019.01.046
• Languages: English
• ISSNs: 0031-3203

Abstract

Highlights: The paper attempts to answer the question - What is the indicative pattern size required to estimate the parameters of the Gaussian model with the defined accuracy? Obtained results provide useful recommendations for researchers working on pattern statistical models. The recommended values of the sample size are easy to remember. We assume that presented results could aid in applications wherein statistical pattern modeling and statistical pattern recognition based on Gaussian modeling are involved. Abstract: 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.