摘要:

Abraham Wald developed the Sequential Probability Ratio Test in the 1940's to perform simple vs. simple hypothesis tests that would control both Type I and Type II error rates. Some applications require a test of three hypotheses. In addition, to perform a simple vs. composite two-sided test, a three-hypothesis test with all hypotheses simple has been suggested. Methods have been proposed that will test three hypotheses sequentially. They range widely in simplicity andaccuracy. In this paper,approximate probabilities of error for Armitage's (1947) test arederived. A method of adjusting the error rates used to establish the decision boundaries in order to attain the nominal error rates is developed.The procedure is compared to existing ones by Monte-Carlo simulation

ISSN:0747-4946    

DOI:10.1080/07474949408836310

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

This paper considers the problem of sequential point estimation and fixed accuracy confidence set procedures of autoregressive parameters in a ρ-th order stationary autoregressive model. The sequential estimator proposed here is based on the least squares estimator and is shown to be risk efficient as the cost of estimation error tends to infinity. Furthermore, the proposed procedure for fixed-width confidence set is shown to be both asymptotically consistent and asymptotically efficient as the width approaches zero.

ISSN:0747-4946    

DOI:10.1080/07474949408836311

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

For special pairs of parameters there is no excess over the boundary in the case ofone-sided SPRT's on Poisson, Bernoulli, and geometric parameters. Using the hitting timetheorem we find exact formulas for the distributions of the sample sizes and errorprobabilities in these cases. Applications are also given to queueing theory.

ISSN:0747-4946    

DOI:10.1080/07474949408836312

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

K treatments that yield dichotomous responses are considered in a multistage clinical trial. The total number of patients to be involved in the trial is N, which is random. The optimal length for each treatment at each stage is to be decided. The objective is to maximize the expected total number of successes of the trial. Two cases are considered: (1) Two stages. It is shown that the rate of the optimal length of the first stage is no greater than √E(N) as E(N) goes to infinity, when the distribution of N, Q, yields a regular discount sequence. The rate may be smaller than √E(N) which depends on the distribution of N and the prior distributions on the probabilities of success of the treatments. Under certain conditions, the rate is exactly √E(N). Nevertheless, the rate may be greater than E(N) without the regularity of Q. (2) r stages. It is shown that M*/E(N) converges to zero in probability as E(N) goes to infinity when Q has the regularity, where M*is the sum of the optimal lengths for the first r - 1 stages.

ISSN:0747-4946    

DOI:10.1080/07474949408836313

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

A general framework for optiinal stopping problems associated with multivariate point processes is presented. Such problems arise. for example. in finding optimal selection/detection strategies in discovering new species, error detection and job search problems. The optimal stopping problem is solved in a finite and an infinite horizon setting. and various special models are coilsidered. It turns out that in regenerative type of modlels where the interarrival time distribtutions have properties known from reliability theory. such as NBUE, IFR and DFR, the optimal stopping times have appealirig properties.

ISSN:0747-4946    

DOI:10.1080/07474949408836314

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474949408836315

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474949408836309

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor