摘要:

We consider a class of invariant sequential procedures for constructing one sided and two sided confidence sets for a parameter γ in Rk, with the property that they have a coverage probability at least 1 ‒a and probability of covering a certain set of false values at most β. The asymptotic properties of the stopping time are studied and the limiting values of the error probabilities are found as the parameter approaches the boundary points. Applications are made to the problem of simultaneous confidence sets for the mean and variance of a normal random vari¬able and for its multivariate analogue.

ISSN:0747-4946    

DOI:10.1080/07474948908836165

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

In response to a recent critique of a sequential clinical trials model, a version of the model is described for which the optimal stopping rule is explicitly soluble. The paper seeks to further the dialogue between practitioners and theoretician by describing, with the use of concrete formulas and graphics, a wide variety of the model's operating characteristics. Some should be of particular interest to practitioners and others should be of interest to theoreticians.

ISSN:0747-4946    

DOI:10.1080/07474948908836166

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

When a control chart is used to detect changes in a process the usual practice is to take samples from the process using a fixed sampling interval between samples. This paper considers the properties of Shewhart control charts when the sampling interval used after each sample is not tixed but instead depends on what is observed in the sample. The basic rationale is that the sampling interval should be short if there is some indication of a change in the process and long if there is no indication of a change. If the indication of a change is strong enough then the chart signals in the same way as the fixed sampling interval Shewhart chart. The result is that samples will be taken more frequently when there is a change in the process, and this process change can be detected much more quickly than when fixed sampling intervals are used. Expressions for properties such as the average time to signal and the average number of samples to signal are developed. It is shown that if the sampling interval must be chosen from a range of possible sampling intervals then the optimal control chart for detecting a specified process change uses only the shortest possible interval and the longst possible interval. The chart is optimal in the sense that it mini¬mizes the average time to signal and the average number of samples to signal when the process has changed, subject to constraints on the false alarm rate and the sampling rate when the process has not changed.

ISSN:0747-4946    

DOI:10.1080/07474948908836167

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

In sequential analysis, Bayes stopping rules are often difficult to determine explicitly. Bickel and Yahav (1967, Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, VI, pp 401 413) provided an attractive large sample approximation to sequential Bayes rules which they called "asymptotically pointwise optimal" (A.P.O.) rules. The present paper proposes A.P.O. rules for certain hierarchical and empirical Bayes models. These rules are shown to be asymptotically "non deficient" in the sense of Woodroofe (1981, Zeitschrift fiir Wahrscheinlich keitstheorie und Verwandte Gebiete, pp 331 341).

ISSN:0747-4946    

DOI:10.1080/07474948908836168

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

It is well known how to combine the significance levels observed in a number of independent experiments. When this number is a random variable determined by a stopping rule, the observed significance level can still be calculated if there is an acceptable ordering of the points in the extended sample space. But what can be said if the stopping time is ill defined This paper obtains explicit lower bounds on the level of significance by considering orderings based on a family of alternative hypotheses. These bounds give some measure of the effect of failing to specify the stopping rule in advance.

ISSN:0747-4946    

DOI:10.1080/07474948908836169

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474948908836170

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474948908836164

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor