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.
This paper was supported by the project no. P103/12/G084 of the Grant Agency of the Czech Republic.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Long, J.S.: Regression Models for Categorical and Limited Dependent Variables, 282p. SAGA Publications, Thousand Oaks (1997)
Long, J.S., Freese, J.: Regression Models for Categorical Dependent Variables Using Stata, p. 589. Stata Press, College Station (2014)
Jackson, D.L.: Revising Sample Size and Number of Parameter Estimates: Some Support for the N: q Hypothesis. Structural Equation Modeling: A Multidisciplinary journal 10(1), 128–141 (2003)
Bartlett, J.E., Kotrlik, J.W., Higgins, C.C.: Organizational Research: Determining Appropriate Sample Size in Survey Research. Information Technology, Learning, and Performance Journal 19(1). Spring (2001)
Shafarevich, I.R., Remizov, A.O.: Linear Algebra and Geometry, 530p. Springer-Verlag, Berlin 2013)
Strang, G.: Linear Algebra and Its Applications, 495p. Hardcover (2005)
Leon, S.L.: Linear Algebra with Applications, 523p. Prentice Hall (2005)
Smithson, M.: Confidence Intervals, 128p. SEGE Publications Inc. (2003)
Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins, Baltimore (1996)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Psutka, J.V., Psutka, J. (2015). Sample Size for Maximum Likelihood Estimates of Gaussian Model. In: Azzopardi, G., Petkov, N. (eds) Computer Analysis of Images and Patterns. CAIP 2015. Lecture Notes in Computer Science(), vol 9257. Springer, Cham. https://doi.org/10.1007/978-3-319-23117-4_40
Download citation
DOI: https://doi.org/10.1007/978-3-319-23117-4_40
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23116-7
Online ISBN: 978-3-319-23117-4
eBook Packages: Computer ScienceComputer Science (R0)