| Title:
|
Ridge Estimator Revisited (English) |
| Author:
|
Kubáček, Lubomír |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
73-86 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Bad conditioned matrix of normal equations in connection with small values of model parameters is a source of problems in parameter estimation. One solution gives the ridge estimator. Some modification of it is the aim of the paper. The behaviour of it in models with constraints is investigated as well. (English) |
| Keyword:
|
linear model |
| Keyword:
|
ridge estimator |
| Keyword:
|
constraints |
| MSC:
|
62J05 |
| MSC:
|
62J07 |
| idZBL:
|
Zbl 06204932 |
| idMR:
|
MR3058875 |
| . |
| Date available:
|
2012-11-26T10:19:20Z |
| Last updated:
|
2014-03-12 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143069 |
| . |
| Reference:
|
[1] Fišerová, E., Kubáček, L., Kunderová, P.: Linear Statistical Models: Regularity and Singularities. Academia, Praha, 2007. |
| Reference:
|
[2] Harville, D. A.: Matrix Algebra for a Statistician’s Perspective. Springer, New York– Berlin–Heidelberg–Barcelona–Hong Kong–London–Milan–Paris–Singapore–Tokyo, 1997. MR 1467237 |
| Reference:
|
[3] Hoerl, A. E., Kennard, R. W.: Ridge regression: Biased eastimation for nonorthogonal problems. Technometrics 12 (1970), 55–67. 10.1080/00401706.1970.10488634 |
| Reference:
|
[4] Hoerl, A. E., Kennard, R. W.: Ridge regression: Application to nonorthogonal problems. Technometrics 12 (1970), 69–82. 10.1080/00401706.1970.10488635 |
| Reference:
|
[5] Goldstein, M., Smith, A. F. M.: Ridge–type estimators for regression analysis. Journal of the Royal Statistical Society, Series B 36 (1974), 284–291 Zbl 0287.62036, MR 0418342 |
| Reference:
|
[6] Rao, C. R., Mitra, S. K.: Generalized Inverse of Matrices and its Applications. Wiley, New York–London–Sydney–Toronto, 1971. Zbl 0236.15005, MR 0338013 |
| Reference:
|
[7] Theobald, C. M.: Generalizations of mean square error applied to ridge regression. Journal of the Royal Statistical Society, Series B 36 (1974), 103–106. Zbl 0282.62055, MR 0368328 |
| . |
