摘要:

Let X1,X2,...,Xn,... be iid N(μ,σ2) random variables with an unknown mean μ and known σ, and let Xn=(X1+...+Xn)/n . For a given d > 0 and 0 < α < 1 we determine a suitable m such thatso that{Xn± d, n ≥ m} is a fixed-width confidences sequences for μ . The sample size m is compared with the optimum sample size m*in the usual fixed-width confidence interval with the same coverage probability 1 - α. An almost power one test for μis also briefly discussed. A similar problem is considered for the binomial probability p, and a suitable m is determined to achievewhere [Pcirc]n, is the usual estimator for p.

ISSN:0747-4946    

DOI:10.1080/07474949808836409

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

In this paper we use simulation to examine the small sample behavior of a series of increasingly complicated stopping rules in the context of sequential estimation of a multivariate mean/regression parameter vector.This is done under a set ot hierarchical bayes models. some.but not all.of the rules are known to be he non-deficient [Ghosh and Hoekstra ('89, '95)] Thus.this study extends the work of those papers to finite sample number behavior.

ISSN:0747-4946    

DOI:10.1080/07474949808836410

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Suppose that {Xn} is a strongly mixing process with unknow marginal density f(x) and that we estimate f(x) by a kernel estimator [fcirc]n(x|hn)and want to achive the MISE no larger than some preassigned postive number w. However,the appropriate sample size n*depends on a functional of the unknow density function. Therefore some sequential procedure is required and we adopt a fully sequential procedure. In this paper we investigate the asymptotic properties of the procedure and show that the producure is asymptotically efficient in a certain sense as w→0. The results are almost the same in the i.i.d. setting. our result extend a class of models to which the methodology can be applied. For example economic variable,experiments on a single subject in which obervation are not indepent, and so on.

ISSN:0747-4946    

DOI:10.1080/07474949808836411

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

This paper is concerned with sequential estimation of the probability of a random variable falling a specified number of standard deviations away from the mean, when the mean, the standard deviation and the underlying distribution are unknown. We consider both point and interval estimation of tail probability under some broad assumptions on the underlying distribution,we establish asymptotic collsistency of the sequential fixed-width interval procedure and risk-efficiency of the sequential point-estimation procedure. We also carry out a simulation study for the fixed-width interval estimation when the underlying distribution is normal or exponential.

ISSN:0747-4946    

DOI:10.1080/07474949808836412

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

We present a nonlinear renewel theory for lattice Markov random walks with pertmbation and obtain limit theorems forandas a → ∞ through the coset v + λZ, where Znis a perturbed Markov random walk related to a finite Markov chain ynand Ta=inf{n > 0 : Zn> a}

ISSN:0747-4946    

DOI:10.1080/07474949808836413

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Suppose F and G are unknow continuous distributions and one can observe sequential a series of independent random vectors (X1,Y1),(X2,Y2),...such that (Xi,Yi)'s initially have distribution F×F and at some unknow time their distribution may become F×G. Namely,a change in the distribution of the Y observations may occur for some reason, while the X observation maintain their distribution. We coinsider the case where the X observation maintain their distribution We consider the case where the post-change distribution is a Lehmann alternative of F, i.e.., G = Fδfor some δ > 0. The problem is to detect the change as soon as possible after its occurrence, subject to constriant on the rate of false alarms Let Ankdenote the likehood ratio of the ranks of the combined data(X1,...,Xn,Y1,...,Yn) for the test of no change versus na change to a Lehmann alternative at k+1 in the Y sequence. We consider the nonparmetric Shiryaev-Roberts stopping rule based on Ankand compute its average run length to dectection by decoupling method

ISSN:0747-4946    

DOI:10.1080/07474949808836414

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

During his investigations of the modified kiefer-weiss problem Lorden (1980) considered the (auxiliary) problem of minimizing a weighted sum of the error Probabilites and the expected sample size. He derived a compiete solution for one-parameter exponential famlies and "inner" parameter points. Here we treat the remaining case of external points. It turns out that the optimal stopping rules fail to be finite a.s.. An additional example shows that this may happen also for other types of distributions.

ISSN:0747-4946    

DOI:10.1080/07474949808836415

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474949808836408

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor