| Title:
|
Variance components and an additional experiment (English) |
| Author:
|
Kubáček, Lubomír |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
391-405 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Estimators of parameters of an investigated object can be considered after some time as insufficiently precise. Therefore, an additional measurement must be realized. A model of a measurement, taking into account both the original results and the new ones, has a litle more complicated covariance matrix, since the variance components occur in it. How to deal with them is the aim of the paper. (English) |
| Keyword:
|
additional experiment |
| Keyword:
|
variance components |
| Keyword:
|
insensitivity region |
| MSC:
|
62F10 |
| MSC:
|
62H12 |
| MSC:
|
62J05 |
| idZBL:
|
Zbl 1264.62014 |
| idMR:
|
MR2984610 |
| DOI:
|
10.1007/s10492-012-0023-x |
| . |
| Date available:
|
2012-08-19T21:47:50Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142906 |
| . |
| Reference:
|
[1] Fišerová, E., Kubáček, L., Kunderová, P.: Linear Statistical Models; Regularity and Singularities.Academia Praha (2007). |
| Reference:
|
[2] Chatterjee, S., Hadi, A. S.: Sensitivity Analysis in Linear Regression.J. Wiley New York (1988). Zbl 0648.62066, MR 0939610 |
| Reference:
|
[3] Giles, D. E. A., Srivastava, V. K.: An unbiased eastimator of the covariance matrix of the mixed regression estimator.J. Am. Stat. Assoc. 86 (1991), 441-444 \MR 1137127. MR 1137127, 10.1080/01621459.1991.10475063 |
| Reference:
|
[4] Kubáček, L., Kubáčková, L., Volaufová, J.: Statistical Models with Linear Structures.Veda Bratislava (1995). |
| Reference:
|
[5] Kubáček, L., Kubáčková, L.: Nonsensitiveness regions in universal models.Math. Slovaca 50 (2000), 219-240. MR 1763121 |
| Reference:
|
[6] Kubáček, L., Kubáčková, L.: Statistics and Metrology.Publishing House of Palacký University Olomouc (2000), Czech. |
| Reference:
|
[7] Neter, J., Wassermann, W., Kutner, M. H.: Applied Linear Statistical Models, 3rd edition.Irwin Boston (1990). |
| Reference:
|
[8] Rao, C. R.: Unified theory of least squares.Commun. Stat., Part A---Theory and Methods 1 (1973), 1-8. Zbl 0252.62037, MR 0315850, 10.1080/03610927208827002 |
| Reference:
|
[9] Rao, C. R., Mitra, S. K.: Generalized Inverse of Matrices and its Applications.John Wiley & Sons New York-London-Sydney-Toronto (1971). Zbl 0236.15005, MR 0338013 |
| Reference:
|
[10] Rao, C. R.: Linear Statistical Inference and Its Applications.John Wiley & Sons New York-London-Sydney (1973); Czech translation: Academia, Praha, 1978. Zbl 0256.62002, MR 0221616 |
| Reference:
|
[11] Rao, C. R., Kleffe, J.: Estimation of Variance Components and Applications.North-Holland Amsterdam-New York-Oxford-Tokyo (1988). Zbl 0645.62073, MR 0933559 |
| Reference:
|
[12] Rao, C. R., Toutenburg, H.: Linear Models. Least Squares and Alternatives, 2nd ed.Springer New York (1999). MR 1707290 |
| Reference:
|
[13] Seber, G. A. F., Lee, A. J.: Linear Regression Analysis, 2nd ed.Wiley New York (2003) \MR 0958247. Zbl 1029.62059, MR 1958247 |
| Reference:
|
[14] Weisberg, S.: Applied Linear Regression, 3rd revised ed.John Wiley & Sons New York (1980). MR 0591462 |
| . |
