Towards a notion of testability
Applications of Mathematics (1992)
- Volume: 37, Issue: 4, page 249-255
- ISSN: 0862-7940
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topStępniak, Czesław. "Towards a notion of testability." Applications of Mathematics 37.4 (1992): 249-255. <http://eudml.org/doc/15713>.
@article{Stępniak1992,
abstract = {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.},
author = {Stępniak, Czesław},
journal = {Applications of Mathematics},
keywords = {general statistical hypothesis; strict unbiasedness; testability; linear hypotheses; general statistical hypothesis; strict unbiasedness; testability; linear hypotheses},
language = {eng},
number = {4},
pages = {249-255},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Towards a notion of testability},
url = {http://eudml.org/doc/15713},
volume = {37},
year = {1992},
}
TY - JOUR
AU - Stępniak, Czesław
TI - Towards a notion of testability
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 4
SP - 249
EP - 255
AB - 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.
LA - eng
KW - general statistical hypothesis; strict unbiasedness; testability; linear hypotheses; general statistical hypothesis; strict unbiasedness; testability; linear hypotheses
UR - http://eudml.org/doc/15713
ER -
References
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- Roy S. N. J. Roy, 10.1214/aoms/1177706270, Annals of Mathematical Statistics 30 (1959), 577-581. (1959) MR0110153DOI10.1214/aoms/1177706270
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- Stępniak C., On testability of statistical hypotheses, Colloquia Mathematicae Societatis Janos Bolyai 32 (1980), 875-884, Nonparametric Statistical Inference, Budapest (Hungary). (1980) MR0719747
- Stępniak C., 10.1002/bimj.4710260216, Biometrical Journal 26 (1984), 215-217. (1984) MR0776842DOI10.1002/bimj.4710260216
- Stępniak C., 10.1007/BF02491490, Annals of the Institute of Statistical Mathematics 39 (1987), 563-573. (1987) MR0930530DOI10.1007/BF02491490
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