# 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

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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

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- 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
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- 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

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