摘要:

In this paper, sequential and fixed sampling schemes are combined to estimate the parameters and quantiles of a two parameter binary response model. In the first stage of the proposed procedure, samples are sequentially observed to estimate two particular quantiles. Additional responses are then observed in the second stage at these two quantile estimates. Maximum likelihood estimators of the parameters and quantiles of the model are than produced using the combined samples from both stages. The asymptotic distributions of the estimators are derived. Asymptotic comparisons are made between the proposed procedure and a strictly sequential estimation procedure. A Monte-Carlo study is performed to assess the effectivness of the proposed procedure for finite samples. Recommendations are made concerning the number of observations to collect in each stage.

ISSN:0747-4946    

DOI:10.1080/07474949708836384

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

Stochastic approximation aims to estimate efficiently level crossing or extermal points of a nonparametric regression function in a parametric or nonparametric manner. For bundle strength of parallel filaments (with stochastic length, cross section etc.,) and in some other problems, one has an extended statistical functionalwhere ψ is a suitable function andG(x|y)stands for a conditional distribution function of X, the dependent variate, given the independent variateY=y. For a compact setCchosen from extraneous considerations, the problem of interest is to locate an optimaly0∈C, in the sense that. Nonparametric estimation of the conditional distributionG(.|y), nonlinear nature of the functionalθ(·), and the fact thatyis in continuum inCadd complexity to possible statistical resolutions and create impasses for a direct application of the well known Bechhofer-Gupta-Sobel methodology. General asympotics for the selection procedures arising in this context are considered with due emphasis on a stochatic iteration scheme.

ISSN:0747-4946    

DOI:10.1080/07474949708836385

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

It is well known that maximum likelihood (ML) estimation results in biased estimates when estimating parameters following a sequential test. Existing bias correction methods rely on explicit calculations of the bias that are often difficult to derive. We suggest a simple alternative to the existing methods. The new approach relies on approximating the bias of the estimate using a bootstrap method. It requires bootstrapping the sequential testing process by resampling observations from a distribution based on the ML estimate. Each bootstrap process will give a new ML estimate, and the corresponding bootstrap mean can be used to calibrate the estimate. An advantage of the new method over the existing methods is that the same procedure can be used under different stopping rules and different study designs. Simulation results suggest that this method performs competitively with existing methods.

ISSN:0747-4946    

DOI:10.1080/07474949708836386

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

In this paper, we considerkhypergeometric populationsπi= π(Mi,mi,si),i=1,…,k,whereMiis the number of units in populationπi,miis the number of units selected fromπi,andsiis the number of defective units inπi. Let. A populationπiwithis considered as a best population. We are interested in selecting the best population and the best population compared with a control. It is assumed that the unknown parameteressii = 1,…,k, follow some binomial prior distribution with unknown hyperparameters. Under the hypergeometric-binomial model, two empirical Bayes selection rules are studied according to the different selection problems. It is shown that for each empirical Bayes selection rule, the corresponding Bayes risk tends to the minimum Bayes risk with a rate of convergence of orderO(exp(-cn))for some positive constantc, where the value ofcvaries depending on the rule andnis the number of accumulated past observations.

ISSN:0747-4946    

DOI:10.1080/07474949708836387

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

In this paper the distribution of a concomitant statistic in a Gaussian sequential setting is characterized. It is shown that the distribution of such a statistic, conditional on the value of the stopping time, can be represented as a convolution of a normal random variable with a stochastic integral of the monitoring process of the trial. For continuous sequential designs the characteristic function of this stochastic integral is shown to satisfy an integral equation. The tools developed here are relevant for secondary inference problems in sequential clinical trials.

ISSN:0747-4946    

DOI:10.1080/07474949708836388

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474949708836383

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor