Showing papers in "Sequential Analysis in 1986"
TL;DR: In this paper, fixed-size confidence regions for the mean vector of a multinormal distribution were used to measure the confidence of a multi-scale distribution in fixed-sized confidence regions.
Abstract: Fixed-Size confidence regions for the mean vector of A multinormal distribution، للحصول على النص الكامل يرجى زيارة مكتبة الحسين بن طلال في جامعة اليرموك او زيارة موقعها الالكتروني
25 citations
TL;DR: In this paper, the existence problem of bounded risk estimators for scale families is considered and it is shown that there does not exist such an estimator if the sample size is fixed.
Abstract: The paper considers the existence problem of bounded risk estimators for scale families. It is shown that there does not exist such an estimator if the sample size is fixed. Two–stage procedures are considered to solve the problem.
18 citations
TL;DR: In this article, the problem of constructing a fixed size ellipsoidal confidence region for the difference of the mean vectors of two independent multinormal populations has been studied and two stage and sequential procedures for each problem and study various exact and asymptotic properties of these procedures through several theorems.
Abstract: The present paper deals with the problem of constructing a fixed size ellipsoidal confidence region for the difference of the mean vectors of two independent multinormal populations.We have assumed that the covariance matrices of the first and second populations are respectively given by σ2 1H and σ2 2 H, where σ2 1 and σ2 2 are both unknown. Here H is assumed to be a known positive definite matrix. The two cases, namely,(i)σ1 = σ2 and equal sample sizes and (ii)σ1 ≠ σ2 and unequal sample sizes have been dealt with separately. We propose both two stage and sequential procedures for each problem and study various exact and asymptotic Properties of these procedures through several theorems. Moderate samplesize performances of our proposed sampling rules have also been studied and these are found to be very satisfactory.
12 citations
TL;DR: The Bahadur type representation of linear combination of order statistics with possibly discontinuous weight function J is established in this article, and an analogous representation up to Op(n-1) is derived for a Studentized estimator.
Abstract: The Bahadur type representation of linear combination of order statistics with possibly discontinuous weight function J is established. The order of the remainder term depends on the smoothness of J. An analogous representation up to Op(n-1) is derived for a Studentized estimator. The representations are incorporated into the study of asymptotic relations of L- and M-estimators which could be equivalent up to the order Op(n-1) under some conditions.
10 citations
TL;DR: In this paper, new approximations are developed for boundary crossing probabilities, which are used to construct approxiamtions for the expected waiting time and the variance of the waiting time for crossing the boundary.
Abstract: In this paper new approximations are developed for boundary crossing probabilities. In turn, these results are used to construct approxiamtions for the expected waiting time and the variance of the waiting time for crossing the boundary. Applicatons to sequential tests are discussed and numerical results are presented. The new approximations appear to be remarkable accurate in the case of an early crossing of the boundary, thus complementing the classical asymptotic approximations that have been developed for these problems.
10 citations
TL;DR: This work presents an efficient recursive method for computing m that is linear in m, does no accumulate round off errors, and produces the mallest conservative value of m.
Abstract: Existing methods for character izing truncated sequential probability rtio test are either a) conservative, in that they may produce a truncation point m that is larger than that neede to guarantee given α and β values; b) inefficient in that the computational effort needed to find m is proportional to m3 or c) subject ot considerable round off errors as m increases. We present an efficient recursive method for computing m that is linear in m, does no accumulate round off errors, and produces the mallest conservative value of m. An example is given for i.i.d normal observations.
9 citations
TL;DR: In this article, the orthonormal Legendre polynomial system is incorporated in the formulation of signed rank statistics for asymptotic efficient testing and estimation procedures for the location parameter (or the intercept parameter in a linear model).
Abstract: The orthonormal Legendre polynomial system is incorporated in the formulationf of signed rank statistics for asymptoticaly efficient testing and estimation procedures for the location parameter (or the intercept parameter in a linear model). A well defined stopping rule relates to an adaptive, sequential procedure for the choice of a finite set of terms and the related score function. Some refined asymptotic linearity results( in location as well as regression parameters) on signed rank staistics (with reference to the Legendre polynomial system) are established, and their role in the proposed (sequentially adaptive) procedure is thoroughly discussed.
9 citations
TL;DR: In this paper, a class of test statistics is introduced to test the null hypothesis that a life distribution is exponential against the alternative that it is new better than used in expectation, but not exponential.
Abstract: Under a random censorship model, a class of test statistics is introduced to test the null hypothesis that a life distribution is exponential against the alternative that it is new better than used in expectation, but not exponential. The statistics are constructed by using the Kaplan–Meier estimator with a weight function and are shown to be asymptotically normal under some regurality conditions. Furthermore an asymptonatic test is derived by using a consistent estimator of the null asymptotic variance. The efficiencies in the proportional censoring model are computed against some alternatives and we discuss optimal tests in the Pitman sense.
8 citations
TL;DR: In this paper, the exact calculation of the decision boundaries for sequential probability ratio test for simple hypotheses and alternatives in the case of an exponential or a Pareto distribution is discussed.
Abstract: This paper deals with the exact calculation of the decision boundaries for sequential probability ratio test for simple hypotheses and alternatives in the case of an exponential or a Pareto distribution. The calculations also enable one to give some idea of the mean sample size for the sequential test.
6 citations
TL;DR: In this paper, the authors give a proof of asymptotic normality of test statistics under contiguous sequence of alternatives by using a counting-process approach and show that the optimal test statistic in this class is seen to lead a locally most powerful tests for contiguous sequences of particular parametric alternatives.
Abstract: Kumazawa (1986) introduced a class of test statistics for testing whether a life distribution is new better than used in expectation under a random censorship model. The purpose of this paper is to give a proof of asymptotic normality of test statistics under contiguous sequence of alternatives by using a counting-process approach. For uncensored case the optimal test statistic in this class is seen to lead a locally most powerful tests for contiguous sequence of particular parametric alternatives.
4 citations
TL;DR: Optimal Bayesian sequential sampling schemes for choosing the better of two binomial populations are presented in this article, where signle observation sequential, group sequential and fixed sample size schemes are used.
Abstract: Optimal Bayesian sequential Sampling schemes for choosing the better of two binomial populations are presented. Signle observation sequential, group sequential and fixed sample size schemes are com...
TL;DR: In this paper, a class of test statistics for testing the null hypothesis that a life distribution is exponential against the alternative that it is new better than used in expectation, but not exponential, on the basis of incomplete observations is presented.
Abstract: We present a class of test statistics for testing the null hypothesis that a life distribution is exponential against the alternative that it is new better than used in expectation, but not exponential, on the basis of incomplete observations. This class includes the statistic proposed in Koul and Susarla (1980) as a special case. Asymptotic normality of the statistics in this class under fixed distribution and contiguous sequence of alternatives is obtained by using martingale weak convergence theorems and counting process theory. Locally most powerful tests for contiguous sequence of alternatives under proportional censoring models are discussed.
TL;DR: In this paper, the authors studied the rate of convergence to normality for U-statistics with a random summation index Ln/n → τ where may τ be either a constant or a random variable.
Abstract: In this work the rate of convergence to normality is studied for U–statistics with a random summation index Ln. The result applies to the situation that Ln/n → τ where may τ be either a constant or a random variable. The obtained order of convergence cannot be improved in general. In the independent case a stronger result holds. The study includes and extends previous work on the order of convergence for random sums by Landers and Rogge (1977) and for random U–statistics by Ghosh and DasGupta (1980) and Cśenki (1981). It also leads to a sharpening of the moment condition in the central limit theorem for random U–statistics proved by Sproule (1974). Specializing the random summation index to a fixed one, we obtain an extension of a theoerem by Helmers and van Zwet (1982) to U–statistics having a projection with finite absolute moment larger than 2. From this result we infer that the central limit theorem proved by Hoeffding (1948)1948) can be formulated under a weaker moment condition.
TL;DR: In this article, the authors compare the performance characteristics of various allocation rules that have been mentioned in the literature, and seek to correlate the structure of these and other allocation rules with their performance characteristics.
Abstract: The risk in trial to compare two meical treatments is borne by patients who receive the inferior treatment during the experimental phase and by those remaining after the experiment who will all receive the inferior treatment if the results are misleading. An allocation rule s task is to balance these competing risks by deciding, during the course of the trial, when the experimental phase should be terminated. This paper compares the performance characteristics of various allocation rules that have been mentioned in the literature, and it seekds to correlate the structure of these and other allocation rules with their performance characteristics. Much use is made of computer based graphical techniques.
TL;DR: In this paper, the authors considered multistage point estimation with a loss function that includes a cost for each stage of sampling, as well as a cost of each observation, and showed that there exists an optimal policy when the loss function and prior satisfy certain mild conditions.
Abstract: Multistage point estimation, with a loss function that includes a cost for each stage of sampling, as well as a cost for each observation, is considered. It is shown that there exists an optimal (Bayes) policy when the loss function and prior satisfy certain mild conditions. For the case when the loss consists of squared error, fixed cost per observation and fixed cost per stage, the observations have density belonging to a one–parameter exponential family, the natural parameter has a conjugate prior distribution, and the estimand is the (conditional) mean of the observations, a one–stage look–ahead policy is proposed. Its asymptotic performance relative to the optimal policy is evaluated for the exponential and (two–para–meter) normal cases.
TL;DR: In this article, the authors studied the asymptotic behavior of the regret for the sequential procedure developed by Wang (1980) for the point estimation of the mean of a multinormal population.
Abstract: Asymptotic behaviour of the regret is studied for the sequential procedure developed by Wang (1980) for the point estimation of the mean of a multinormal population. A condition on the initial sample size is also provided for which the regret is bounded.
TL;DR: In this paper, the authors consider a broad class of distributions of the white noise process, which consists of i.i.d. random variables, and prove locally asymptotic Wiener (LAW) structure in extension of local normality (LAN) for their model.
Abstract: We consider testing problems for the parameters of autoregressive moving average (ARMA)-processes. For a broad class of distributions of the white noise process, which consists of i.i.d.random variables,we prove locally asymptotic Wiener (LAW) structure in extension of locally asymptotic normality (LAN) for our model. On this basis invariance principles can be established in a very convenient way. We are able to give asymptotic results for the proposed repeated significance test(RST) procedure under hypothesis as well as under contiguous alternatives.Finally we introduce RST-procedures with estimated scores
TL;DR: In this article, the problem of constructing a fixed width confidence interval for the mean of a normal distribution with unknown variance was dealt with and it was shown that a Bayesian approach leads to Stein's two stage sampling scheme and that within a certain class of fixed-width confidence intervals at a level 1-β it yields minimal cost of observation for large values of the variance.
Abstract: This paper deals with the problem of constructing a fixed width confidence interval for the mean of a normal distribution with unknown variance. It is shown that a Bayesian approach leads to Stein's two stage sampling scheme and that within a certain class of fixed width confidence intervals at a level 1- β it yields minimal cost of observation for large values of the variance.
TL;DR: In this article, an optimal stopping problem for stochastic processes of the form A+B was studied, where A is a submartingale and B a super martingale, and by the Doob Meyer decomposition, A = C+N and B = V+M, where N and M are local martingales, C is an increasing and V a decreasing predictable process.
Abstract: Bayesian sequential decision problems can be reduced to an optimal stopping problem for a stochastic process of the form A+B, where A is a submartingale and B a supermartingale, and by the Doob Meyer decomposition, A = C+N and B = V+M, where N and M are local martingales, C is an increasing and V a decreasing predictable process If N and M are uniformly integrable, then we have an equivalent optimal stopping problem for the process C+V Often, C and V do not only have continuous but also "differentiable" paths The stopping time T of first horizontal tangent is suggested as an approximation of an optimal stopping time Often, T leads to a problem of curved boundary crossing for a basic observable process, where the boundary may be non random or random