 Minimax sequential estimation plans for exponential-type processesRyszard Magiera Statistics & Probability Letters, 1990, vol. 9, issue 2, 179-185 Abstract: The study of the theory of sequential estimation for continuous-time stochastic processes was initiated by Dvoretzky, Kiefer and Wolfowitz (1953). They proved that for the Poisson, negative-binomial, gamma and Wiener processes the minimax sequential plan reduces to a fixed-time plan if a weighted quadratic loss function is used. Their results were generalized by Magiera (1977) to an exponential class of processes with stationary independent increments and by Trybula (1985) in case of the n-dimensional processes. It turns out, however, that for a certain class of processes there exist truly sequential minimax plans. It was showed by Trybula (1985) that for the Poisson process an inverse plan is minimax. Wilczynski (1985) has obtained an analogous result for the multinomial process. In this paper we consider a class of exponential-type processes and for this class we prove that, with a properly weighted quadratic loss function, the inverse plans are minimax in the class of all sequential plans having finite risk. Examples illustrating the derived result are also presented. Keywords: Sequential; estimation; minimax; plan; inverse; plan; exponential-type; process (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:9:y:1990:i:2:p:179-185 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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