A generalization of Wishart density for the case when the inverse of the covariance matrix is a band matrix
Mathematica Bohemica (1994)
- Volume: 119, Issue: 4, page 337-346
- ISSN: 0862-7959
Access Full Article
top
Abstract
topHow to cite
topEben, Kryštof. "A generalization of Wishart density for the case when the inverse of the covariance matrix is a band matrix." Mathematica Bohemica 119.4 (1994): 337-346. <http://eudml.org/doc/29272>.
@article{Eben1994,
abstract = {In a multivariate normal distribution, let the inverse of the covariance matrix be a band matrix. The distribution of the sufficient statistic for the covariance matrix is derived for this case. It is a generalization of the Wishart distribution. The distribution may be used for unbiased density estimation and construction of classification rules.},
author = {Eben, Kryštof},
journal = {Mathematica Bohemica},
keywords = {band inverse covariance matrix; discriminant analysis; characteristic function; multivariate normal distribution; Wishart distribution; unbiased density estimation; classification rules; band inverse covariance matrix; discriminant analysis; characteristic function; multivariate normal distribution; Wishart distribution; unbiased density estimation; classification rules},
language = {eng},
number = {4},
pages = {337-346},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A generalization of Wishart density for the case when the inverse of the covariance matrix is a band matrix},
url = {http://eudml.org/doc/29272},
volume = {119},
year = {1994},
}
TY - JOUR
AU - Eben, Kryštof
TI - A generalization of Wishart density for the case when the inverse of the covariance matrix is a band matrix
JO - Mathematica Bohemica
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 119
IS - 4
SP - 337
EP - 346
AB - In a multivariate normal distribution, let the inverse of the covariance matrix be a band matrix. The distribution of the sufficient statistic for the covariance matrix is derived for this case. It is a generalization of the Wishart distribution. The distribution may be used for unbiased density estimation and construction of classification rules.
LA - eng
KW - band inverse covariance matrix; discriminant analysis; characteristic function; multivariate normal distribution; Wishart distribution; unbiased density estimation; classification rules; band inverse covariance matrix; discriminant analysis; characteristic function; multivariate normal distribution; Wishart distribution; unbiased density estimation; classification rules
UR - http://eudml.org/doc/29272
ER -
References
top- Abusev R.A., Lumelskiĭ, Ya.P., Unbiased estimators and classifìcation problems for multivariate normal populations, Theor. Prob. Appl. 25 (1980), 381-389. (1980) MR0572573
- Herz C.S, 10.2307/1969810, Ann. Math. 61 (1955), 474-523. (1955) MR0069960DOI10.2307/1969810
- Ingham A.E., An integral which occurs in statistics, Proc. Cambridge Phil. Soc. 29 (1933), 271-276. (1933) Zbl0007.00701
- Lumelskiĭ, Ya.P., Sapozhniкov P.N, 10.1137/1114048, Theor. Prob. Appl. 14 (1969), 357-365. (1969) DOI10.1137/1114048
- Muirhead R.J., Aspects of Multivariate Statistical Theory, Wiley, New York, 1982. (1982) Zbl0556.62028MR0652932
- Rao C.R., Linear Statistical Inference and Its Applications, Wiley, New York, 1965. (1965) Zbl0137.36203MR0221616
- Vapnik V.N., Estimation of Dependences Based on Empirical Data, Springer Veгlag, New Yoгk, 1982. (1982) Zbl0499.62005MR0672244
- Wishart J., Bartlett M.S., The generalised product moment distribution in a normal system, Proc. Cambridge Phil. Soc. 29 (1933), 260-270. (1933) Zbl0007.02304
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.