Geodesic
A generalization of Wishart density for the case when the inverse of the covariance matrix is a band matrix
Mathematica Bohemica, Tome 119 (1994) no. 4, pp. 337-346

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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.
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.
DOI : 10.21136/MB.1994.126118
Classification : 62H05, 62H10
Keywords: band inverse covariance matrix; discriminant analysis; characteristic function; multivariate normal distribution; Wishart distribution; unbiased density estimation; classification rules 
Eben, Kryštof. A generalization of Wishart density for the case when the inverse of the covariance matrix is a band matrix. Mathematica Bohemica, Tome 119 (1994) no. 4, pp. 337-346. doi: 10.21136/MB.1994.126118
@article{10_21136_MB_1994_126118,
     author = {Eben, Kry\v{s}tof},
     title = {A generalization of {Wishart} density for the case when the inverse of the covariance matrix is a band matrix},
     journal = {Mathematica Bohemica},
     pages = {337--346},
     year = {1994},
     volume = {119},
     number = {4},
     doi = {10.21136/MB.1994.126118},
     mrnumber = {1316585},
     zbl = {0809.62044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1994.126118/}
}
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
SP  - 337
EP  - 346
VL  - 119
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1994.126118/
DO  - 10.21136/MB.1994.126118
LA  - en
ID  - 10_21136_MB_1994_126118
ER  - 
%0 Journal Article
%A Eben, Kryštof
%T A generalization of Wishart density for the case when the inverse of the covariance matrix is a band matrix
%J Mathematica Bohemica
%D 1994
%P 337-346
%V 119
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1994.126118/
%R 10.21136/MB.1994.126118
%G en
%F 10_21136_MB_1994_126118

[1] Abusev R.A., Lumelskiĭ, Ya.P.: Unbiased estimators and classifìcation problems for multivariate normal populations. Theor. Prob. Appl. 25 (1980), 381-389. | MR

[2] Herz C.S: Bessel functions of matrix arguments. Ann. Math. 61 (1955), 474-523. | DOI | MR

[3] Ingham A.E.: An integral which occurs in statistics. Proc. Cambridge Phil. Soc. 29 (1933), 271-276. | Zbl

[4] Lumelskiĭ, Ya.P., Sapozhniкov P.N: Unbiased estimates of density functions. Theor. Prob. Appl. 14 (1969), 357-365. | DOI

[5] Muirhead R.J.: Aspects of Multivariate Statistical Theory. Wiley, New York, 1982. | MR | Zbl

[6] Rao C.R.: Linear Statistical Inference and Its Applications. Wiley, New York, 1965. | MR | Zbl

[7] Vapnik V.N.: Estimation of Dependences Based on Empirical Data. Springer Veгlag, New Yoгk, 1982. | MR | Zbl

[8] Wishart J., Bartlett M.S.: The generalised product moment distribution in a normal system. Proc. Cambridge Phil. Soc. 29 (1933), 260-270. | Zbl

Cité par Sources :