On an equivariant estimate of the density of a matrix normal distribution
Point and Interval Estimation
- 18 Downloads
- 1 Citations
Abstract
An optimal equivariant Bayes estimate of the density of a matrix normal distribution is obtained. This estimate is applied to the construction of the optimal Bayes group classification rule.
Keywords
Normal Distribution Group Classification Classification Rule Equivariant Estimate Matrix Normal Distribution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.J. Aitchison, “Goodness of prediction fit,”Biometrika,62, 547–554 (1975).MATHMathSciNetGoogle Scholar
- 2.G. D. Murray, “A note on the estimation of probability density functions,”Biometrika,64, 150–152 (1977).MATHMathSciNetGoogle Scholar
- 3.N. V. Ming, “On the estimation of parametric density functions,”Biometrika,67, 505–506 (1980).MathSciNetGoogle Scholar
- 4.W. Wertz, “Ueber ein nichtparametrisches Schaetzproblem,”Metrika,26, 157–167 (1979).MATHMathSciNetGoogle Scholar
- 5.G. P. Klimov,Invariant Inference in Statistics [in Russian], Moscow State Univ. Press, Moscow (1973).Google Scholar
- 6.V. M. Kondakov and P. N. Sapozhnikov, “Kuhlback-Leibler Informational Measure in the distribution density estimating problem,”J. Sov. Math.,56, No. 3, 2415–2418 (1991).Google Scholar
- 7.V. M. Kondakov,On an Equivariant Estimate of the Density of a Multivariate Normal Distribution, Dep. VINITI, No. 8113, Moscow (1984).Google Scholar
- 8.V. M. Kondakov,On a Group Classification Rule [in Russian], Dep. VINITI, No. 5066, Moscow (1988).Google Scholar
- 9.V. M. Kondakov,On a Group Classification Rule for Populations with Matrix Normal Distributions [in Russian], Dep. VINITI, No. 7650, Moscow (1989).Google Scholar
- 10.R. A. Abusev and Ya. P. Lumel'skii,Statistical Group Classification [in Russian], Perm Univ. Press, Perm (1987).Google Scholar
- 11.G. Ryzin, “Bayes risk consistency of classification procedures using density estimation,”Sankhya, Ser. A,28, 261 (1966).MATHMathSciNetGoogle Scholar
- 12.P. Horn and C. Johnson,Matrix Analysis [Russian translation], Mir, Moscow (1989).Google Scholar
Copyright information
© Plenum Publishing Corporation 1995