摘要:

The sum of observations from a population is an important statistic. However its distribution in a sequential analysis is usually mathematically untractable when the stopping rule depends on the observed outcomes, which makes statistical analyses difficult. To overcome the difficulty, a new method is proposed to obtain absorption probability distributions of random paths on any boundaries or barrier sets, where the random path is a sequence of partial sums of observations from the population. By this method, sanlple spaces for sequential rules are interpreted as partitions of a common sample space. The absorption probability on the boundary is the product of a latent function and the likelihood function of the random path, where the latent function is defined as the conditional absorption probability. Latent functions for a variety of stopp~ng rules are given as iterative convolutions over boundaries. Though this method is general, our discussion is focused on finite populations. Advantages of the method are demonstrated through several applications.

ISSN:0747-4946    

DOI:10.1080/07474949608836347

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

It is shown that the Renewal Theorem holds uniformly with respect to the step distribution F when the latter is restricted

ISSN:0747-4946    

DOI:10.1080/07474949608836348

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

For the mean vector of a multivariate normal distribution, a fixed width confidence region is given when the covariance matrix is a linear combination of known symmetric matrices but the combining coefficients are unknown. It is shown that several models considered in the literature are special cases of this model.

ISSN:0747-4946    

DOI:10.1080/07474949608836349

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

An accelerated sequential procedure for estimating the mean p in the class of the natural exponential family of distributions having power variance function (NEF-PVF), is proposed. The accelerated procedure is conducted under a combined loss of weighted squared estimation error and sarnpling cost. A class of bias-corrected estimators, which are natural for this suggested accelerated sampling scheme is proposed. The asymptotic properties of the suggested estimators are provided. In particular, one realizes the impact of acceleration on the regret and the tradeoff between bias reduction and regret reduction.

ISSN:0747-4946    

DOI:10.1080/07474949608836350

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

We consider the problem of providing a fixed width confidence interval for the difference of two normal means when the variances are unknown and unequal. We propose a two-stage procedure that differs from those of Chapman (1950) and Ghosll (1975). The procedure provides the desired confidence, subject to the restriction on the width, for certain values of the design parameter h. Values of h are given by the Monte Carlo rnethod for various combinations of first stage sample size and confidence level. Finally, it is shown that the procedure is asymptotically more efficient than those of Chapmail and Ghosh with respect to total sample size, as the width of the interval approaches zero.

ISSN:0747-4946    

DOI:10.1080/07474949608836351

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474949608836346

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor