Sequential estimation for the generalized exponential hyperbolic secant process. (English) Zbl 0657.62093
The generalized exponential hyperbolic secant (GEHS) process is introduced and its properties are studied with respect to its use in sequential analysis. For the multidimensional GEHS process and a properly weighted quadratic loss function the sequential minimax plan is determined which turns out to be a fixed time plan. For the one- dimensional GEHS process a class of sequential minimax plans is given when the set of prior distributions is restricted. Again these plans are fixed time plans. Some remarks on efficient sequential plans of that type are made at the end of the paper.
Reviewer: V.Mammitzsch
MSC:
62L12 | Sequential estimation |
62M05 | Markov processes: estimation; hidden Markov models |
62L10 | Sequential statistical analysis |
62C20 | Minimax procedures in statistical decision theory |
Keywords:
generalized exponential hyperbolic secant (GEHS) process; multidimensional GEHS process; quadratic loss; one-dimensional GEHS process; sequential minimax plans; prior distributions; fixed time plansReferences:
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