| Title:
|
A generalization of Wishart density for the case when the inverse of the covariance matrix is a band matrix (English) |
| Author:
|
Eben, Kryštof |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
119 |
| Issue:
|
4 |
| Year:
|
1994 |
| Pages:
|
337-346 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
band inverse covariance matrix |
| Keyword:
|
discriminant analysis |
| Keyword:
|
characteristic function |
| Keyword:
|
multivariate normal distribution |
| Keyword:
|
Wishart distribution |
| Keyword:
|
unbiased density estimation |
| Keyword:
|
classification rules |
| MSC:
|
62H05 |
| MSC:
|
62H10 |
| idZBL:
|
Zbl 0809.62044 |
| idMR:
|
MR1316585 |
| DOI:
|
10.21136/MB.1994.126118 |
| . |
| Date available:
|
2009-09-24T21:06:27Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126118 |
| . |
| Reference:
|
[1] Abusev R.A., Lumelskiĭ, Ya.P.: Unbiased estimators and classifìcation problems for multivariate normal populations.Theor. Prob. Appl. 25 (1980), 381-389. MR 0572573 |
| Reference:
|
[2] Herz C.S: Bessel functions of matrix arguments.Ann. Math. 61 (1955), 474-523. MR 0069960, 10.2307/1969810 |
| Reference:
|
[3] Ingham A.E.: An integral which occurs in statistics.Proc. Cambridge Phil. Soc. 29 (1933), 271-276. Zbl 0007.00701 |
| Reference:
|
[4] Lumelskiĭ, Ya.P., Sapozhniкov P.N: Unbiased estimates of density functions.Theor. Prob. Appl. 14 (1969), 357-365. 10.1137/1114048 |
| Reference:
|
[5] Muirhead R.J.: Aspects of Multivariate Statistical Theory.Wiley, New York, 1982. Zbl 0556.62028, MR 0652932 |
| Reference:
|
[6] Rao C.R.: Linear Statistical Inference and Its Applications.Wiley, New York, 1965. Zbl 0137.36203, MR 0221616 |
| Reference:
|
[7] Vapnik V.N.: Estimation of Dependences Based on Empirical Data.Springer Veгlag, New Yoгk, 1982. Zbl 0499.62005, MR 0672244 |
| Reference:
|
[8] Wishart J., Bartlett M.S.: The generalised product moment distribution in a normal system.Proc. Cambridge Phil. Soc. 29 (1933), 260-270. Zbl 0007.02304 |
| . |
