| Title:
|
Strange Design Points in Linear Regression (English) |
| Author:
|
Pázman, Andrej |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
103-110 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss, partly on examples, several intuitively unexpected results in a standard linear regression model. We demonstrate that direct observations of the regression curve at a given point can not be substituted by observations at two very close neighboring points. On the opposite, we show that observations at two distant design points improve the variance of the estimator. In an experiment with correlated observations we show somewhat unexpected conditions under which a design point gives no or very little information about the estimated parameters, and so can be excluded from the design. For completeness we repeat briefly known conditions under which a design point is sensitive to the presence of outliers. (English) |
| Keyword:
|
singular models |
| Keyword:
|
optimal design |
| Keyword:
|
correlated observations |
| MSC:
|
62J05 |
| MSC:
|
62K05 |
| idZBL:
|
Zbl 1244.62101 |
| idMR:
|
MR2920712 |
| . |
| Date available:
|
2011-12-16T14:52:44Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141758 |
| . |
| Reference:
|
[1] Fišerová, E., Kubáček, L., Kunderová, P.: Linear Statistical Models: Regularity and Singularities. Academia, Praha, 2007. |
| Reference:
|
[2] Harville, D. A.: Matrix Algebra from a Statistician’s Perspective. Springer, New York, 1997. Zbl 0881.15001, MR 1467237 |
| Reference:
|
[3] Näther, W.: Exact designs for regression models with correlated errors. Statistics 16 (1985), 479–484. MR 0803486, 10.1080/02331888508801879 |
| Reference:
|
[4] Pázman, A.: Foundations of Optimum Experimentsl Design. Kluwer, Dordrecht, 1986. |
| Reference:
|
[5] Pázman, A.: Information contained in design points of experiments with correlated observations. Kybernetika 46 (2010), 769–781. Zbl 1201.62105, MR 2722100 |
| Reference:
|
[6] Pázman, A., Pronzato, L.: On the irregular behavior of LS estimators for asymptotically singular designs. Statistics and Probability Letters 76 (2006), 1089–1096. Zbl 1090.62076, MR 2269278, 10.1016/j.spl.2005.12.010 |
| Reference:
|
[7] Pukelsheim, F.: Optimal Design of Experiments. Wiley, New York, 1993. Zbl 0834.62068, MR 1211416 |
| Reference:
|
[8] Zvára, K.: Regresní analýza. Academia, Praha, 1989. |
| . |
