摘要:

The problem considered in this paper is to decide when to stop a sequence of the

ISSN:0747-4946    

DOI:10.1080/07474949208836241

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

Consider a fixed sample size UMP test of H0: p ≤ p0versus H1: p > p0, where p is a Bernoulli parameter. If the test is non-randomized the optimal curtailed version is well-known. If the test is randomized, the decision of a UMP test is not uniquely determined. This paper considers the problem of curtailing such tests so that the expected number of observations is minimized. A simple complete characterization of such tests is given.

ISSN:0747-4946    

DOI:10.1080/07474949208836242

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

We consider the empirical Bayes problem where the component problem is the sequential estimation of the mean of a distribution with squared error decision loss plus a sampling cost. An empirical Bayes sequential estimation procedure is exhibited which is asymptotically optimal. Asymptotic efficiency of the empirical Bayes stopping time sequence is also established. The performance of the proposed empirical Bayes procedure is studied with the help of a Monte Carlo study.

ISSN:0747-4946    

DOI:10.1080/07474949208836243

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

A new approximation method is proposed for calculating the operating characteristic function and the average sample number function of the sequential probability ratio test. This method conditions on the value of the test statistic immediately before the stopping time to produce mathematical formulas for the characteristics. An expression for the characteristic function of the stopping time is also obtained by this method. The values obtained by the proposed method are compared to a standard numerical method for the case where the underlying distribution is normal.

ISSN:0747-4946    

DOI:10.1080/07474949208836244

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

Let X1, X2... be i.i.d. observations with mean μ and variance σ2, and suppose that given a sample of size n one wishes to estimate μ by Xn, subject to the loss function Ln= A2(Xn-μ)2+n. When σ2is unknown, the optimal sample size n0for minimizing the risk Rn= E{Ln} cannotbe found. To resolve this problem, Robbins (1959) proposed a sequential procedure whenXiis normally distributed, and then the asymptotic properties have been extensively studied. In this paper, we apply Hall's three stage procedure to the problem without specifying the distribution of Xiand derive the second order asymptotic expansions of the expected sample size and the risk.

ISSN:0747-4946    

DOI:10.1080/07474949208836245

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

Central limit theorems in stochastic approximation theory often involve an integral of a limit process of the observation errors. This integral is approximated by a further stochastic iteration. Then empirical quantiles are used to construct spherical asymptotic confidence regions for the parameter to be estimated. As an example the method is applied to a recursive solution of a linear equation in a separable real Banach space.

ISSN:0747-4946    

DOI:10.1080/07474949208836246

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474949208836240

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor