| Title:
|
Towards a notion of testability (English) |
| Author:
|
Stȩpniak, Czesław |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
249-255 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The problem of testability has been undertaken many times in the context of linear hypotheses. Almost all these considerations restricted to some algebraical conditions without reaching the nature of the problem. Therefore, a general and commonly acceptable notion of testability is still wanted.
Our notion is based on a simple and natural decision theoretic requirement and is characterized in terms of the families of distributions corresponding to the null and the alternative hypothesis. Its consequences in the case of linear hypotheses are discussed. Among other it is shown that some suggestions in statistical literature are unjustified. (English) |
| Keyword:
|
general statistical hypothesis |
| Keyword:
|
strict unbiasedness |
| Keyword:
|
testability |
| Keyword:
|
linear hypotheses |
| MSC:
|
62A01 |
| MSC:
|
62C05 |
| MSC:
|
62F03 |
| MSC:
|
62J12 |
| idZBL:
|
Zbl 0781.62006 |
| idMR:
|
MR1180603 |
| DOI:
|
10.21136/AM.1992.104507 |
| . |
| Date available:
|
2008-05-20T18:43:45Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104507 |
| . |
| Reference:
|
[1] Lehmann E. L.: Testing Statistical Hypotheses.Wiley, New York, 1959. Zbl 0089.14102, MR 0107933 |
| Reference:
|
[2] Peixoto J. L.: Testable hypotheses in singular fixed linear models.Communications in Statistics -- Theory and Methods 15 (1986), 1957-1973. Zbl 0604.62059, MR 0848173 |
| Reference:
|
[3] Roy S. N. J. Roy: A note on a class of problems in normal multivariate analysis of variance.Annals of Mathematical Statistics 30 (1959), 577-581. MR 0110153, 10.1214/aoms/1177706270 |
| Reference:
|
[4] Seely J.: Estimability and linear hypotheses.American Statistician 31 (1977), 121-123. MR 0448727 |
| Reference:
|
[5] Stępniak C.: On testability of statistical hypotheses.Colloquia Mathematicae Societatis Janos Bolyai 32 (1980), 875-884, Nonparametric Statistical Inference, Budapest (Hungary). MR 0719747 |
| Reference:
|
[6] Stępniak C.: Testable hypotheses implied by a linear hypothesis.Biometrical Journal 26 (1984), 215-217. MR 0776842, 10.1002/bimj.4710260216 |
| Reference:
|
[7] Stępniak C.: A complete class for linear estimation in a general linear model.Annals of the Institute of Statistical Mathematics 39 (1987), 563-573. MR 0930530, 10.1007/BF02491490 |
| . |
