×
Magiera, Ryszard

Sequential estimation for the generalized exponential hyperbolic secant process. (English) Zbl 0657.62093

Statistics 19, No. 2, 271-281 (1988).
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 plans
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.1214/aoms/1177728980 · Zbl 0051.36606 · doi:10.1214/aoms/1177728980
[2] Feller W., An Introduction to Probability Theory and its Applications, Vol II, (1971) · Zbl 0219.60003
[3] Franz J., Applicationes Mathematicae 16 pp 153– (1978)
[4] Magiera R., Applicationes Mathematicae 15 pp 445– (1977)
[5] DOI: 10.1214/aos/1176345690 · Zbl 0498.62015 · doi:10.1214/aos/1176345690
[6] Rozanski R., Applicationes Mathematicae 17 pp 73– (1980)
[7] Rozanski R., Applicationes Mathematicae 17 pp 401– (1982)
[8] Trybula S., Dissert.Math. 240 (1985)
[9] Trybuza S., Distert Math 240 (1985)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.