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1998-1999 | 25 | 1 | 1-18
Tytuł artykułu

On minimax sequential procedures for exponential families of stochastic processes

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The problem of finding minimax sequential estimation procedures for stochastic processes is considered. It is assumed that in addition to the loss associated with the error of estimation a cost of observing the process is incurred. A class of minimax sequential procedures is derived explicitly for a one-parameter exponential family of stochastic processes. The minimax sequential procedures are presented in some special models, in particular, for estimating a parameter of exponential families of diffusions, for estimating the mean or drift coefficients of the class of Ornstein-Uhlenbeck processes, for estimating the drift of a geometric Brownian motion and for estimating a parameter of a family of counting processes. A class of minimax sequential rules for a compound Poisson process with multinomial jumps is also found.
Rocznik
Tom
25
Numer
1
Strony
1-18
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-04-14
poprawiono
1997-01-25
Twórcy
  • Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
  • Barndorff-Nielsen, O. (1978), Information and Exponential Families, Wiley, New York.
  • Black, F. and Scholes, M. (1973), The pricing of options and corporate liabilities, J. Political Economy 81, 637-654.
  • Brown, L. (1986), Fundamentals of Statistical Exponential Families, IMS, Hayward, Calif.
  • Döhler, R. (1981), Dominierbarkeit und Suffizienz in der Sequentialanalyse, Math. Operationsforsch. Statist. Ser. Statist. 12, 101-134.
  • Dvoretzky,, A. Kiefer, J. and Wolfowitz, J. (1953), Sequential decision problems for processes with continuous time parameter. Problems of estimation, Ann. Math. Statist. 24, 403-415.
  • Franz, J. (1985), Special sequential estimation problems in Markov processes, in: Sequential Methods in Statistics, R. Zieliński (ed.), Banach Center Publ. 16, PWN-Polish Sci. Publ., Warszawa, 95-114.
  • Küchler, U. and Sørensen, M. (1994), Exponential families of stochastic processes and Lévy processes, J. Statist. Plann. Inference 39, 211-237.
  • Le Breton, A. and Musiela, M. (1985), Some parameter estimation problems for hypoelliptic homogeneous Gaussian diffusions, in: Sequential Methods in Statistics, R. Zieliński (ed.), Banach Center Publ. 16, PWN-Polish Sci. Publ., Warszawa, 337-356.
  • Liptser, R. S. and Shiryaev, A. N. (1978), Statistics of Random Processes, Vol. 2, Springer, Berlin.
  • Magiera, R. (1977), On sequential minimax estimation for the exponential class of processes, Zastos. Mat. 15, 445-454.
  • Magiera, R. (1990), Minimax sequential estimation plans for exponential-type processes, Statist. Probab. Lett. 9, 179-185.
  • Magiera, R. and Wilczyński, M. (1991), Conjugate priors for exponential-type processes, ibid. 12, 379-384.
  • Rhiel, R. (1985), Sequential Bayesian and minimax decisions based on stochastic processes, Sequential Anal. 4, 213-245.
  • Różański, R. (1982), On minimax sequential estimation of the mean value of a stationary Gaussian Markov process, Zastos. Mat. 17, 401-408.
  • Trybuła, S. (1985), Some investigations in minimax estimation theory, Dissertationes Math. (Rozprawy Mat.) 240.
  • Wilczyński, M. (1985), Minimax sequential estimation for the multinomial and gamma processes, Zastos. Mat. 18, 577-595.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv25i1p1bwm
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