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1998-1999 | 25 | 1 | 85-100
Tytuł artykułu

Information inequalities for the minimax risk of sequential estimators (with applications)

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Information inequalities for the minimax risk of sequential estimators are derived in the case where the loss is measured by the squared error of estimation plus a linear functional of the number of observations. The results are applied to construct minimax sequential estimators of: the failure rate in an exponential model with censored data, the expected proportion of uncensored observations in the proportional hazards model, the odds ratio in a binomial distribution and the expectation of exponential type random variables.
Rocznik
Tom
25
Numer
1
Strony
85-100
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-04-01
Twórcy
  • Institute of Mathematics Technical University of Łódź, ul. Żwirki 36, 90-924 Łódź, Poland
  • Institute of Mathematics Technical University of Łódź, ul. Żwirki 36, 90-924 Łódź, Poland
Bibliografia
  • M. Alvo (1977), Bayesian sequential estimation, Ann. Statist. 5, 955-968.
  • Y. S. Chow, H. Robbins and D. Siegmund (1971), Great Expectations: The Theory of Optimal Stopping, Houghton Mifflin, Boston.
  • S. Csörgő (1988), Estimation in the proportional hazards model of random censorship, Statistics 19, 437-463.
  • S. Csörgő and J. Mielniczuk (1988), Density estimation in the simple proportional hazards model, Statist. Probab. Letters 6, 419-426.
  • L. Gajek (1987), An improper Cramér-Rao lower bound, Zastos. Mat. 19, 241-256.
  • L. Gajek (1988), On minimax value in the scale model with truncated data, Ann. Statist. 16, 669-677.
  • L. Gajek and U. Gather (1991), Estimating a scale parameter under censorship, Statistics 22, 529-549.
  • J. C. Gardiner and V. Susarla (1984), Risk-efficient estimation of the mean exponential survival time under random censoring, Proc. Nat. Acad. Sci. U.S.A. 81, 5906-5909.
  • J. C. Gardiner and V. Susarla (1991), Some asymptotic distribution results in time-sequential estimation of the mean exponential survival time, Canad. J. Statist. 19, 425-436.
  • J. C. Gardiner, V. Susarla and J. van Ryzin (1986), Time sequential estimation of the exponential mean under random withdrawals, Ann. Statist. 14, 607-618.
  • J. A. Koziol and S. B. Green (1976), A Cramér-von Mises statistic for randomly censored data, Biometrika 63, 465-474.
  • E. L. Lehmann (1983), Theory of Point Estimation, Wiley, New York.
  • R. Magiera (1977), On sequential minimax estimation for the exponential class of processes, Zastos. Mat. 15, 445-454.
  • B. Mizera (1996), Lower bounds on the minimax risk of sequential estimators, Statistics 28, 123-129.
  • W. Rudin (1976), Principles of Mathematical Analysis, McGraw-Hill, New York.
  • M. Tahir (1988), Asymptotically optimal Bayesian sequential point estimation with censored data, Sequential Anal. 7, 227-237.
  • J. Wolfowitz (1947), The efficiency of sequential estimates and Wald's equation for sequential processes, Ann. Math. Statist. 19, 215-230.
  • M. Woodroofe (1982), Nonlinear Renewal Theory in Sequential Analysis, CBMS-NSF Regional Conf. Ser. Appl. Math. 39, SIAM, Philadelphia.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv25i1p85bwm
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