Fiducial inference on the largest mean of a multivariate normal distribution

Wandler, Damian V.; Hannig, Jan

doi:10.1016/j.jmva.2010.08.003

Cited by 18 publications

(11 citation statements)

References 11 publications

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“…Generalized fiducial techniques have been applied to quantized random variables and propagation of errors, [11][12][13][14] nonparametric problems, 7,[15][16][17] prediction and tolerance intervals, 18,19 simultaneous confidence intervals, 3,[20][21][22] and model selection. 7,23,24 The generalized fiducial framework has connections to many other areas of research including Dempster-Shafer Calculus, [25][26][27] generalized p values, 28 and generalized confidence intervals. 5 In fact, the development of generalized fiducial inference can be traced back to a series of papers related to generalized confidence intervals.…”

Section: A Brief Historymentioning

confidence: 99%

“…Primarily, generalized fiducial inference provides a useful recipe for constructing confidence intervals, as well as tools for proving that these intervals have asymptotically correct coverage. Generalized fiducial techniques have been applied to quantized random variables and propagation of errors, nonparametric problems, prediction and tolerance intervals, simultaneous confidence intervals, and model selection …”

Section: Introductionmentioning

confidence: 99%

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Generalized fiducial inference

Iverson

2014

WIREs Computational Stats

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Generalized Fiducial Inference provides a recipe for constructing confidence intervals as well as tools for establishing the asymptotically correct coverage of many of these intervals. Confidence intervals based on the generalized fiducial framework have been applied to a wide range of problems, many of which lack exact pivots, and these intervals have exhibited excellent asymptotic and small sample performance. Generalized fiducial inference has also been used for model selection and simultaneous inference. In this article, the generalized fiducial framework is presented along with important results and applications. In the process, simple examples are used to illustrate the intuition behind and the application of the framework and its tools. WIREs Comput Stat 2014, 6:132–143. doi: 10.1002/wics.1291 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

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Section: A Brief Historymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized fiducial inference

Iverson

2014

WIREs Computational Stats

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“…Based on these realizations, GFI was proposed and well‐defined by Hannig 35 . Until now, GFI has been successfully applied in many important statistical problems, such as variance components, 36,37 reliability assessment, 38–40 maximum mean of a multivariate normal distribution, 41 multiple comparisons, 42 extreme value estimation, 43 wavelet regression, 44 logistic regression and binary response models, 45 ultrahigh‐dimensional regression, 46 nonparametric inference, 47–50 and many others 51,52 …”

Section: Introductionmentioning

confidence: 99%

Hypothesis testing of process capability index Cpk from the perspective of generalized fiducial inference

Meng

Yang

Huang

2020

Quality & Reliability Eng

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Hypothesis testing of Cpk is an essential part for decision making on process capability. The difficulty to test the hypothesis of Cpk is the complexity of the natural estimator Ĉpk distribution even under the normal distribution. Thus, traditional methods of the hypothesis testing of Cpk based on the natural estimator Ĉpk only give the approximate test method under the normal distribution and seldom discuss the hypothesis testing under some commonly used but complex non‐normal distributions. The emerging generalized fiducial inference (GFI) in recent years is an effective method for statistical inference on complex statistics. Thus, we first propose a novel hypothesis testing method for Cpk based on generalized p‐value. For application, the mathematic expression of the proposed method for the commonly used normal distribution, Gamma distribution, Weibull distribution, and two‐parameter exponential distribution is derived in detail. Next, to study the performance of the proposed method in terms of the frequency property, the real probabilities of Type I error and Type II error are calculated through simulation. The calculated results show that the proposed method has satisfactory performance for different distributions. Finally, the implementation of the proposed method is illustrated by two real examples.

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“…with ρ ∈ (−1, 1) is the Pearson correlation coefficient. Following the steps of the method described above, Wandler and Hannig (2011) obtained the GFD for θ θ…”

Section: Estimation By Using the Generalized Fiducial Distributionmentioning

confidence: 99%

“…Since there are five parameters, it is necessary to have the same number of generating equations to determinate each term in (ii). To find that, Wandler and Hannig (2011) used the following five data generating equations using the first three samples, i.e., U 11 , U 21 , U 12 , U 22 and U 23 . Moreover, in this case, J contains the n 2,1,n−3 p-tuples of indices j j j = (1 ≤ j 1 < .…”

Section: Estimation By Using the Generalized Fiducial Distributionmentioning

confidence: 99%

Some extensions in measurement error models

Tomaya¹,

Yanet²

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In this dissertation, we approach three different contributions in measurement error model (MEM). Initially, we carry out maximum penalized likelihood inference in MEM's under the normality assumption. The methodology is based on the method proposed by Firth (1993), which can be used to improve some asymptotic properties of the maximum likelihood estimators. In the second contribution, we develop two new estimation methods based on generalized fiducial inference for the precision parameters and the variability product under the Grubbs model considering the two-instrument case. One method is based on a fiducial generalized pivotal quantity and the other one is built on the method of the generalized fiducial distribution. Comparisons with two existing approaches are reported. Finally, we propose to study inference in a heteroscedastic MEM with known error variances. Instead of the normal distribution for the random components, we develop a model that assumes a skew-t distribution for the true covariate and a centered Student's t distribution for the error terms. The proposed model enables to accommodate skewness and heavy-tailedness in the data, while the degrees of freedom of the distributions can be different. We use the maximum likelihood method to estimate the model parameters and compute them via an EM-type algorithm. All proposed methodologies are assessed numerically through simulation studies and illustrated with real datasets extracted from the literature.

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Fiducial inference on the largest mean of a multivariate normal distribution

Cited by 18 publications

References 11 publications

Generalized fiducial inference

Generalized fiducial inference

Hypothesis testing of process capability index Cpk from the perspective of generalized fiducial inference

Some extensions in measurement error models

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