摘要:

We derive the joint distribution of the sequence of estimates of the parameter vector θ in a normal general linear model when data accumulate over a series of analyses. This seclllerlce of estimates has a remarkably simple covariance structure, even when observations are correlated, allowing standard group sequential tests to be applied in very general settings. If observations variaices and covariances depend on an unknown scale factor σ2, the joint distribution of the sequence of estimates of θ σ2has a simple form. again even in the case of correlated observations. From these results, we establish a general treatment of group sequential t,χ2and F-tests.

ISSN:0747-4946    

DOI:10.1080/07474949708836390

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

The problem of Bayes sequential point estimation without using the prior information is considered. Two sequential procedures of the type of Bickel and Yahav (1967, 1968), for the scale exponential and location normal families respectively, are proposed. It is shown in the present paper that the proposed procedures are asymptotically pointwise optimal (A.P.O.) in the sense of Bickel and Yahav (1967) and the second order approximation of the Bayes risk is established for a large class of prior distributions.

ISSN:0747-4946    

DOI:10.1080/07474949708836391

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

We consider Brownian motion with drift and stopping boundaries: linear upper and lower boundaries, and possibly a vertical boundary at a truncation point, all under conditions assuring a finite stopping time. T. W. Anderson (Ann. Math. Statist. 31, 1960) derived formulas for the distributions of the stopped process along these boundaries and for the associated expected stopping times. We present simpler formulas, and briefer derivations.

ISSN:0747-4946    

DOI:10.1080/07474949708836392

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

We consider the problenl of const,ructing a fixed-size confidence region for a linear functioll of mean vectors of k multinormal populations. The covariance matrices are assunlcd to be known except for the unknown scalar multipliers. A two-stage procedure is proposed to derive such a confidence region. We also discuss the asylnptotic efficiency of the procedure.

ISSN:0747-4946    

DOI:10.1080/07474949708836393

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

The exact formulas of Bayes stopping times are often difficult to derive. Bickel and Yahav (1965) had provided the large sample approximation known as the "Asymptotically pointwise optimal" (A.P.O.) rule. The A.P.O. rule for the problem of the mean of a multivariate normal distribution, for a completely unknown covariance matrix , has been developed by the present author. This paper gives the A.P.O. rule of the mean of a multivariate normal ditribution for a covariance matrix with some structure. Also the result is shown to be asymptotically" non-deficient" in the sence of Woodroofe.

ISSN:0747-4946    

DOI:10.1080/07474949708836394

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474949708836389

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor