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About 10,000 papers for “Sequential estimation”

Sequential Estimation

Malay Ghosh, Nitis Mukhopadhyay, Pranab K. Sen · Wiley series in probability and statistics · 1997

Cited by 319

Sequential Estimation

F. J. Anscombe · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1953

Summary The literature on sequential estimation is reviewed, with special reference to inverse binomial sampling, double sampling, and asymptotic theory. An approximate distribution for the sample size is found for a certain type of sequential sampling rule, in which a cumulative sum of independent random variables all having the same continuous distribution is plotted against their number until a fixed boundary is first reached or crossed. Approximate methods are given for solving a number of particular problems, including (i) estimating the mean of a normal population by a confidence interval of prescribed width and coefficient, when the population variance is unknown, and (ii) estimating the parameters of a simple birth-death process so that the difference between the birth rate and the death rate is estimated with prescribed standard error. The possible usefulness of sequential estimation procedures is discussed.

Cited by 189

Sequential Estimation

Adam T. Martinsek, Malay Ghosh, Nitis Mukhopadhyay et al. · Journal of the American Statistical Association · 1998

Cited by 28

Sequential estimation.

Jerrad Hampton (122900), Manuel E. Lladser (122903) · Figshare · 2015

Cited by 0Open access

Sequential Factorial Estimation

J. Stuart Hunter · Technometrics · 1964

Through the use of a “predictor-corrector” equation an experimenter may quickly determine the least squares estimates of all the coefficients in a polynomial model after the conclusion of each run, given that an initial set of orthogonal estimates of the coefficients is available. The analysis of variance may similarly be constructed at the conclusion of each added run. The predictor-corrector equation is subject to mild restrictions which are fully met in the usual application of the 2 k and 2 k–p factorial designs. Adaptation of the predictor-corrector equation to the case of complimentary blocks of two runs each is described. Examples are given.

Cited by 13

10. Sequential Estimation

Michael Woodroofe · Society for Industrial and Applied Mathematics eBooks · 1982

10.1. Point estimation. Let Y1,Y2,⋯ be i.i.d. normally distributed random variables with unknown mean μ, −∞<μ<∞ , and unknown variance σ2>0 , and letμ^n=Y¯n,σ^n2=1n−1∑i=1n(Yi−Y¯n)2,n≧2denote the unbiased estimators of μ and σ2 .

Cited by 0

Sequential shrinkage estimation

Nickerson, David MacLeod, 1958- ( Dissertant ), Malay, Ghosh ( Thesis advisor ), Varma, Arun K. ( Reviewer ) et al. · University of Florida Digital Collections (University of Florida) · 1985

Cited by 0

Sequential Estimation and Closed Sequential Decision Procedures

Edward Paulson · The Annals of Mathematical Statistics · 1964

In Chapter 10 of his classical work on sequential analysis [8], Wald started a program for dealing with multiple decision problems based on sequential estimation, and this work was to some extent further developed by Stein [7]. However, as far as the present writer is aware, this program was never completed. In a recent paper [6] a sequential procedure for estimating the mean of a normal distribution was given and the results applied to the problem of deciding which of $k$ non-overlapping intervals contains the mean. In the present paper, the main results of [6] are first derived in a different manner, using a slight modification of a procedure given by Wald (see Chapter 10 of [8]). This new derivation lends itself to dealing with other situations, and sequential confidence limits are worked out explicitly for two other cases, namely, for the variance and for the ratio of variances of normal distributions. These results are then applied to get closed decision procedures for a number of decision problems, including (1) testing a hypothesis regarding the mean of a normal distribution against either one-sided or two-sided alternatives; (2) comparing the means of $k$ experimental categories with a standard or control; (3) testing a hypothesis about the variance of a normal distribution; (4) deciding which of $k$ non-overlapping intervals contains the variance; (5) testing a hypothesis about the ratio of variances; (6) comparing the variances of $k$ experimental categories with a standard or control. In addition, a brief discussion of "mixed" problems, where we are concerned with finding a confidence interval for the parameter after a decision has been reached is given in Sections 3.1 and 3.3. In some of these problems open sequential solutions (in which there is no upper bound to the number of measurements required to reach a decision) are already known which have some optimum properties. However, for administrative and other reasons it is often desirable to restrict consideration to closed sequential procedures, so as to have an upper bound to the time or cost of an experiment. This has recently been emphasized by Armitage in connection with medical applications [2]. All the sequential procedures of the present paper are closed, but the point of closure in Section 3 depends on $s^2$ if $\sigma^2$ is unknown.

Cited by 16Open access

Distributed Sequential Federated Estimation

Zhanfeng Wang, Xinyu Zhang, Yuan‐chin Ivan Chang · Statistica Sinica · 2026

When analyzing data stored across multiple sites, concerns about data security and communication arise.Federated learning, which avoids centralizing data, offers a p r omising s o lution t o a d dress t h ese c o ncerns.H o wever, integrating information from separate local sites in a statistically sound manner is crucial, as common averaging methods may lead to information loss due to data non-homogeneity and incomparable results among sites.By applying sequential methods in federated learning, integration can be facilitated and the analysis process can be accelerated, particularly within a distributed computing framework.We propose an efficient da ta -driven me th od th at ma intains th e principles of classical sequential adaptive design.Numerical studies and an application to COVID-19 data from 32 hospitals in Mexico, using a regression model, illustrate the effectiveness o f o u r approach.

Cited by 0Open access

Estimation following sequential tests

David Siegmund · Biometrika · 1978

SUMMARY A method is given for obtaining confidence intervals following sequential tests. It involves defining an order relation among points on the stopping boundary and computing the probability of a deviation more extreme in this order relation than the observed one. Particular attention is given to the case of a normal mean with known or unknown variance. A comparison with the customary fixed sample size interval based on the same data is given. The purpose of this paper is to describe a method for obtaining confidence intervals following sequential tests. An order relation is defined among the points on the stopping boundary of the test. The confidence limits are determined by finding those values of the unknown parameter for which the probabilities of more extreme deviations in the order relation than the one observed have prescribed values. To facilitate understanding the proposed procedures, most of the paper is restricted to estimating the mean of a normal population with known variance following the class of sequential tests recommended by Armitage (1975) for clinical trials. The case of unknown variance is discussed briefly in ? 4. It is easy to see that the proposed method is valid more generally, although the probability calculations required to implement it depend on the specific parent distribution and stopping rule. A closely related method was proposed by Armitage (1958), who studied the case of binomial data numerically by enumeration of sample paths. Let xl, x2, ... be independent and normally distributed with unknown mean ,u and known variance cr2. Let sn =x1 + .. . + xn, and for given b > 0 consider the stopping rule

Cited by 145