| Title:
|
Densities of determinant ratios, their moments and some simultaneous confidence intervals in the multivariate Gauss-Markoff model (English) |
| Author:
|
Oktaba, Wiktor |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
40 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
47-54 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The following three results for the general multivariate Gauss-Markoff model with a singular covariance matrix are given or indicated. $1^\circ $ determinant ratios as products of independent chi-square distributions, $2^\circ $ moments for the determinants and $3^\circ $ the method of obtaining approximate densities of the determinants. (English) |
| Keyword:
|
products of independent chi-squares |
| Keyword:
|
multivariate general linear Gauss-Markoff model |
| Keyword:
|
wishart distribution |
| Keyword:
|
singular covariance matrix |
| Keyword:
|
set of linear parametric functions |
| Keyword:
|
moment of determinant ratio |
| Keyword:
|
approximate simultaneous confidence interval |
| MSC:
|
62H10 |
| MSC:
|
62J05 |
| MSC:
|
62J99 |
| idZBL:
|
Zbl 0818.62055 |
| idMR:
|
MR1305648 |
| DOI:
|
10.21136/AM.1995.134277 |
| . |
| Date available:
|
2009-09-22T17:46:24Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134277 |
| . |
| Reference:
|
[1] T.W. Anderson: An Introduction to Multivariate Statistical Analysis.J. Wiley, New York, 1958. Zbl 0083.14601, MR 0091588 |
| Reference:
|
[2] G.N. Browkowicz, J.W. Linnik: A note to confidence estimation by least squares method.Teoria verojatnostej i jejo primeneniya 8 (1963), no. 2, 176. (Russian) |
| Reference:
|
[3] A.T. James: Distributions of matrix variates and latent roots derived from normal samples.Ann. Math. Stat. 35 (1964), no. 2, 475–501. Zbl 0121.36605, MR 0181057, 10.1214/aoms/1177703550 |
| Reference:
|
[4] R.J. Muirhead: Aspects of Multivariate Statistical Theory.J. Wiley, New York, 1982. Zbl 0556.62028, MR 0652932 |
| Reference:
|
[5] W. Oktaba: Estimation of the parametric functions in the multivariate general Gauss-Markoff model.XV Colloquium Metodol. Agrobiom., Pol. Acad. Sci., Warsaw 1985, pp. 178–182. (Polish) |
| Reference:
|
[6] W. Oktaba, A. Kieloch: Wishart distributions in the multivariate Gauss-Markoff model with singular covariance matrix.Appl. Math. 38 (1993), 61–66. MR 1202080 |
| Reference:
|
[7] C.R. Rao: Linear Statistical Inference and Its Applications, Sec. Ed.J. Wiley, New York, 1973. MR 0346957 |
| Reference:
|
[8] S.N. Roy: Some Aspects of Multivariate Analysis.New York, 1957. |
| Reference:
|
[9] M.S. Srivastava, G.G. Khatri: An Introduction to Multivariate Statistics.Elsevier North Holland, Inc., New York, 1979. MR 0544670 |
| Reference:
|
[10] J.K. Wani, D.G. Kabe: Generalized inverse and confidence estimation by least squares method.Trabajos De. Estadistica Y de Investigation Operativa 21, Cuadermos 1 y 2 Afio, Iberica, Tarragona 1970 vol. 34, Madrid, 1968, pp. 115–120. |
| . |
