Estimation of a Common Mean and Weighted Means Statistics

Rukhin, Andrew L.; Vangel, Mark

doi:10.2307/2669626

Cited by 54 publications

(67 citation statements)

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“…The visual averaging library program includes unweighted and weighted averages as well as the limitation of relative statistical weights (LWM) [25], normalized residual (NRM) [26], Rajeval technique (RT) [27], the Expected Value (EVM) [28], bootstrap and Mandel-Paule (MP) [29] statistical methods to calculate averages of experimental data with uncertainties. In our evaluation, we generally adopted the weighted average, using NRM in some discrepant cases.…”

Section: Adopted Valuesmentioning

confidence: 99%

Tables of E2 transition probabilities from the first 2+ states in even–even nuclei

Pritychenko

Birch

Singh

et al. 2016

Atomic Data and Nuclear Data Tables

420

184

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Section: Adopted Valuesmentioning

confidence: 99%

Tables of E2 transition probabilities from the first 2+ states in even–even nuclei

Pritychenko

Birch

Singh

et al. 2016

Atomic Data and Nuclear Data Tables

420

184

View full text Add to dashboard Cite

show abstract

“…For example see Jordan and Krishnamoorthy (1996), Yu et al (1999), Rukhin and Vangel (1998), and Vangel and Rukhin (1999). We consider two of them, i.e.…”

Section: Applicationsmentioning

confidence: 99%

“…We consider two of them, i.e. Rukhin and Vangel (1998), and Vangel and Rukhin (1999), with the purpose to illustrate the estimation of the variance components.…”

Section: Applicationsmentioning

confidence: 99%

“…The earliest work in this area is due to Cochran (1937Cochran ( , 1954. Other notable works are due to Rao (1977), Hartley and Rao (1978), Rao, Kaplan and Cochran (1981), Harville (1977), Vangel and Rukhin (1999), and Rukhin and Vangel (1998). Some related works are reported in Fairweather (1972), Jordan and Krishnamoorthy (1996) and Yu, Sun and Sinha (1999).…”

Section: Introductionmentioning

confidence: 99%

“…, σ 2 k are known as the intralaboratory (within) variances. There are several papers dealing with the estimation of the mean µ (see Rukhin and Vangel (1998) and Vangel and Rukhin (1999)). Our interest in this paper is in the improved estimation of the between and within laboratory variances: σ 2 τ , σ 2 1 , .…”

Section: Introductionmentioning

confidence: 99%

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Non-negative estimation of variance components in heteroscedastic one-way random-effects ANOVA models

et al. 2010

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There is considerable amount of literature dealing with inference about the parameters in a heteroscedastic one-way random effects ANOVA model. In this paper we primarily address the problem of improved quadratic estimation of the random effect variance component. It turns out that such estimators with a smaller MSE compared to some standard unbiased quadratic estimators exist under quite general conditions. Improved estimators of the error variance components are also established.

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Discussion on ‘Five examples of assessment and expression of measurement uncertainty’ by Antonio Possolo

Gleser

2013

Appl Stoch Models Bus & Ind

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The five examples in this paper present a varied and interesting collection of contexts in which models and methods for assessing measurement uncertainty are used. Consistent with Dr. Possolo's assertion that 'probability distributions are well suited to express measurement uncertainty', his paper presents and advocates the use of probability models to guide simulations whose variability expresses the uncertainty connected with a measurement.Actually, although this is not always clear in Dr. Possolo's discussion, there is more than one kind of uncertainty involved with measurement. We must differentiate between pre-data uncertainty and post-data uncertainty. I say more about this distinction in Section 2 of this discussion, and this distinction serves as a guiding theme for my comments on Dr. Possolo's examples (and the methodology used in these examples) in Section 3. Section 4 concludes with some remarks about the question of how best to communicate information about uncertainty of measurement. Pre-data uncertainty and post-data uncertaintyPre-data uncertainty is concerned with the variability about the true value of the measurand of the values produced by a particular method of measurement-it is uncertainty about the accuracy of the measurement methodology. In statistics, indices of variability of point estimators or coverage probabilities of confidence intervals are used in the frequentist paradigm of inference to select procedures that will give the most accurate measurement, resulting in minimal uncertainty. Distributions of the point estimators provide not only these indices but also more detailed insight into the performance of the measurement method. Examples of such an approach in Dr. Possolo's paper are the arsenic-in-oyster-tissue example of Section 3 and the viscosity example of Section 4. In the arsenic-in-oyster-tissue example, the parametric bootstrap is used to estimate the distribution of the maximum likelihood estimator of the consensus value under the assumption that has the value O attained by the maximum likelihood estimator. One could instead simulate the exact distribution of the estimator when a particular value of the measurand holds. If the value specified for the measurand is correct, the distribution will be the correct pre-data uncertainty of measurement. The bootstrap distribution thus estimates the correct pre-data distribution of the measurement rather than giving it exactly. There is an unfortunate tendency in the literature to regard this bootstrap distribution as a post-data expression of uncertainty because the data are involved in choosing which distribution to simulate, but this is not the case-what is obtained is an estimate of the correct pre-data distribution of values for the measurement.When expressed in terms of distributions, post-data uncertainty commonly takes the form of a distribution for the measurand (not the measurement) conditional upon observed measurement values. To obtain such a distribution, we start with a prior distribution for the measurand that express...

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Estimation of a Common Mean and Weighted Means Statistics

Cited by 54 publications

References 0 publications

Tables of E2 transition probabilities from the first 2+ states in even–even nuclei

Tables of E2 transition probabilities from the first 2+ states in even–even nuclei

Non-negative estimation of variance components in heteroscedastic one-way random-effects ANOVA models

Discussion on ‘Five examples of assessment and expression of measurement uncertainty’ by Antonio Possolo

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