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Tytuł książki

Some investigations in minimax estimation theory

Autorzy

Stanisław Trybuła

Seria

Rozprawy Matematyczne tom/nr w serii: 240 wydano: 1985

Zawartość

Pełne teksty:
rm24001.pdf

Warianty tytułu

Abstrakty

EN

CONTENTS
1. Introduction.............................................................................................................................................................................................5
2. A theorem for a multinomial population...................................................................................................................................................5
3. Estimation of frequencies of population with a hierarchic structure........................................................................................................7
4. Estimation of frequencies of multinomial population under a general quadratic loss Function..............................................................12
5. A problem of prediction.........................................................................................................................................................................15
6. Minimax estimation of distribution function............................................................................................................................................17
7. Sequential minimax estimation for stochastic processes in the case where there exists a sufficient statistic for the parameter............18
8. Sequential estimation for the multinomial process.................................................................................................................................21
9. Exponential family of processes............................................................................................................................................................23
10. Sequential estimation for a multivariate process.................................................................................................................................24
11. Sequential estimation for the Poisson process....................................................................................................................................29
12. Sequential minimax estimation in the case where the set of a priori distributions of the parameter is restricted.................................31
13. Continuation to Section 12..................................................................................................................................................................37
14. Final remarks......................................................................................................................................................................................40
References...............................................................................................................................................................................................41

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 240

Liczba stron

42

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCXL

Daty

wydano
1985

Twórcy

autor
Stanisław Trybuła
  • Politechnika Wrocławska, Instytut Matematyki, Wrocław, Polska
  • Institute of Mathematics, Technical University, Wrocław, Poland

Bibliografia

  • [1] D. Blackwell, M. A. Girshick. Theory of games and statistical decisions. New York and London 1950.
  • [2] J. R. Blum. J. Rosenblatt, Fixed precision estimation in the class of IFR distributions, Ann. Inst. Stat. Math. 21, I (1969).
  • [3] L. D. Brown. A heuristic method for determining admissibility of estimator - with applications, Ann. Stat. 7 (1979), 960-994.
  • [4] A. Dvoretzky, J. Kiefer, J. Wolfowitz, Sequential decision problems for processes with continuous time parameter. Problem of estimation, Ann. Math. Stat. 24 (1953), 403-415.
  • [5] J. Franz, W. Winkler, Über Stoppzeiten bei statistischen Problemen für homogene Prozesse mit unabhängigen Zuwachsen, Math. Nachricht. 70 (1976), 37-53.
  • [6] J. Franz, W. Winkler, Sequential estimation problems for the exponential class of processes with independent increments. Scand. Satist. 6 (1979), 129-139.
  • [7] M. A. Girshick, L. J. Savage, Boyes and minimax estimates for quadratic loss functions. Proc. Second Berkeley Symp. Math. Statist. Prob. 1 (1951), 53-74.
  • [8] J. L. Hodges, E. L. Lehmann, Some problems in minimax point estimation, Ann. Math. Stat. 21 (1950). 182-196.
  • [9] J. L. Hodges, E. L. Lehmann, Some applications of the Cramer-Rao inequality, Proc. Second Berkeley Symp. Math. Statist. Prob. I (1951), 13-22.
  • [10] J. L. Hodges, E. L. Lehmann, The use of previous experience in reaching statistical decisions, Ann. Math. Stat. 23 (1952), 376-407.
  • [11] B. Johnson McK, On admissible estimators for certain fixed sample binomial problems, Ann. Math. Stat. 42 (1971). 1579 1587.
  • [12] A. Kozek, Towards a calculus for admissibility, Ann. Stat. 10 (1982), 825-837.
  • [13] H. Kudo, On partial prior information and the property of parametric sufficiency, Proc. Fifth Berkeley Symp. Math. Statist. Prob. 1 (1967), 251-265.
  • [14] R. Magiera, On sequential minimax estimation for the exponential class of processes, Applicationes Mathematicae (Zastosowania Matematyki) 15 (1977), 445-454.
  • [15] J. Olkin, M. Sobel, Admissible and minimax estimation for the multinomial distribution and for k independent binomial distributions, Ann. Stat. 7 (1979), 284-290.
  • [16] E. S. Phadia, Minimax estimation of a cumulative distribution function, Ann. Stat. 1 (1973), 1149-1157.
  • [17] R. Różański, A modification of Sudakov's lemma and efficient sequential plans for the Ornstein Uhlenbeck process, Applicationes Mathematicae (Zastosowania Matematyki) 17, 1 (1980), 73-85.
  • [18] R. Różański,, On minimax sequential estimation of the mean value of a stationary Gaussian-Markov process, Applicationes Mathematicae (Zastosowania Matematyki) 17, 3 (1981), 25-32.
  • [19] W. N. Sudakov, O merakh opredelyayemykh markovskimi momentami. Zapiski nauchnykh seminarov LOMI im. Steklova 12, Issledovaniya po teorii sluchaynykh processov (1969), 157 164 (in Russian).
  • [20] S. Trybuła, Some problems in simultaneous minimax estimation, Ann. Math. Stat. 29 (1958), 245-53.
  • [21] S. Trybuła, On some loss function, Colloq. Math. 7 (1960), 297-305.
  • [22] S. Trybuła, Sequential estimation In processes with independent increments, Dissert. Math. 60 (1968), 1-49.
  • [23] A. Wald, Statistical decision functions, New York 1950.
  • [24] C. Stein, A necessary and sufficient condition for admissibility, Ann. Math. Statist. 26 (1955), 751-768.

Języki publikacji

EN

Uwagi

Identyfikator YADDA

bwmeta1.element.zamlynska-48fdf5f7-4764-4de6-9906-4c7a90c24b5c

Identyfikatory

ISBN
83-01-06170-7
ISSN
0012-3862

Kolekcja

DML-PL
Zawartość książki

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