Optimal sequentially planned decision procedures. With the assistance of Günter Duscha, Josef Lübbert and Thomas Meyerthole.

*(English)*Zbl 0771.62057
Lecture Notes in Statistics (Springer). 79. New York: Springer-Verlag. xii, 207 p. (1993).

It is pointed out that in spite of its nice property of minimizing the expected sample sizes at certain parameter values, the Wald sequential probability ratio test is rarely used in practice. The reason suggested for this is that the sample size by itself is not a good indicator of the actual costs of sampling: such factors as set-up costs, the length of time required for agricultural experiments, and the penalties for continuing to use inferior treatments in clinical trials, must also be considered.

To take account of such factors, a class of highly adaptive sequential statistical decision procedures is described and analyzed. A main feature of these procedures is that the number of observations to be taken at any given stage of the experiment may depend upon the previous observations. The existence of optimal procedures is proved under various conditions, and algorithms are given for constructing such procedures. Computer programs for the computation of the operating characteristic curve and the expected sampling cost curve are included in an appendix.

To take account of such factors, a class of highly adaptive sequential statistical decision procedures is described and analyzed. A main feature of these procedures is that the number of observations to be taken at any given stage of the experiment may depend upon the previous observations. The existence of optimal procedures is proved under various conditions, and algorithms are given for constructing such procedures. Computer programs for the computation of the operating characteristic curve and the expected sampling cost curve are included in an appendix.

Reviewer: L.Weiss (Ithaca)

##### MSC:

62L10 | Sequential statistical analysis |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

62L05 | Sequential statistical design |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |