On minimal pairwise sufficient statistic

• Autorzy: Kuśmierek, A.
• Języki publikacji: EN

Abstrakty

EN

Each statistic, which is pairwise sufficient and (in a natural sense) countably complete, is a minimal pairwise sufficient statistic. The Basu theorem for pairwise sufficient statistic is also obtained.

Słowa kluczowe

PL

pary wystarczającej statystyki; minimalne pary wystarczającej statystyki; pełna statystyka; pomocnicze statystyki

EN

pairwise sufficient statistic; minimal pairwise sufficient statistic; complete statistic; ancillary statistic

• Czasopismo: Journal of Applied Analysis
• Rocznik: 2001
• Tom: Vol. 7, nr 2
• Strony: 285-292
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Kuśmierek, A.

• Faculty of Mathematics University of Łódź Banacha 22 90-238 Łódź, Poland

Bibliografia

• [1] Bahadur, R. R., Statistics and subfields, Ann. Math. Statist. 26 (1955), 490-497.
• [2] Bahadur, R. R., Sufficiency and statistical decision functions, Ann. Math. Statist. 25 (1954), 423-462.
• [3] Basu, D. and Ghosh, J. K., Sufficient statistics in sampling from a finite universe, Proc. 36th Session Internat. Statist. Inst, (in ISI Bulletin) (1969), 850-859.
• [4] Billingsley, P., Probability and Measure, John Wiley & Sons, New York, 1979.
• [5] Burkholder, D. L., Sufficiency in the undominated case, Ann. Math. Statist. 32 (1961), 1191-1200.
• [6] Fisher, R. A. , On the mathematical foundation of theoretical statistics, Philos. Trans. Roy. Soc. London Ser. A 222 (1922), 309-368
• [7] Ghosh, J. K., Morimoto, H. and Yamada, S., Neyman factorization and minimality of pairwise sufficient subfields, Ann. Statist. 9 (1981), 514-530.
• [8] Halmos, P. R., Savage, L. J., Application of the Radon-Nikodym theorem of the theory of sufficient statistics, Ann. Math. Statist. 20 (1949), 225-241.
• [9] Heyer, H. and Yamada, S., On an extended notion of common conditional probability, Probab. Math. Statist. 15 (1995), 353-363.
• [10] Le Cam, L., Sufficiency and approximate sufficiency, Ann. Math. Statist. 35 (1964), 1419-1455.
• [11] Schervish, M. J., Theory of Statistics, Springer-Verlag, New York, 1995.
• [12] Siebert, E., Pairwise sufficiency, Z. Wahrsch. Verw. Gebiete 46 (1979), 237-246.
• [13] Yamada, S., Pivotal Measures in Statistical Experiments and Sufficiency, Springer- Verlag, New York, 1994.