Fiducial approach for assessing agreement between two instruments

Wang, Chih–Ming; Iyer, Hariharan

doi:10.1088/0026-1394/45/4/006

Cited by 12 publications

(12 citation statements)

References 16 publications

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“…It was noted in Hannig that inference involving discretized random variables is common in the area of metrology and generalized fiducial inference has been applied to problems such as assessing the uncertainty due to instrumentation, propagation of uncertainties, , and assessing the agreement between instruments , . A simulation study by Witkovsk and Wimmer compared many methods for interval estimation for quantized data and those presented in Hannig et al were deemed the most successful.…”

Section: The Fiducial Argumentmentioning

confidence: 99%

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: The Fiducial Argumentmentioning

confidence: 99%

Generalized fiducial inference

Iverson

2014

WIREs Computational Stats

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“…It is fairly widely known that ordinary least squares (OLS) (or weighted least squares (WLS) if σ yi depends on y i ) estimates of β 0 and β 1 , which ignore the errors in x are biased due to the observation errors in x meas [1][2][3][4][5][6][7]. However, it appears to be less widely known that if the main inference goal is prediction, using future x to predict future Y , then bias in OLS estimates is of little or no concern.…”

Section: Correspondence: Tburr@lanlgovmentioning

confidence: 99%

“…In Example 1, there could be interest in whether β 0 = 0 and β 1 = 1, which would provide insight regarding relation between the two temperature measurement options [7]. In an example in [14], β 1 is the parameter of interest.…”

Section: Predictionmentioning

confidence: 99%

“…Similarly to this MCMC-based numerical Bayesian approach, Wang and Iyer [7] presented a "fiducial inference" numerical option for estimating cov(β 0 ,β 1 ) and for testing whether β 0 = 1 and β 1 = 1. In our example 1, there is also interest in whether β 0 = 1 and β 1 = 1 because x and y are two options for measuring the same temperature.…”

Section: Numerical Bayesian Alternativementioning

confidence: 99%

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Least-squares fitting with errors in the response and predictor

Burr

Croft

Reed

2012

Int. J. Metrol. Qual. Eng.

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Abstract. Least squares regression is commonly used in metrology for calibration and estimation. In regression relating a response y to a predictor x, the predictor x is often measured with error that is ignored in analysis. Practitioners wondering how to proceed when x has non-negligible error face a daunting literature, with a wide range of notation, assumptions, and approaches. For the model ytrue = β0 + β1 xtrue, we provide simple expressions for errors in predictors (EIP) estimatorsβ0,EIP for β0 andβ1,EIP for β1 and for an approximation to covariance (β0,EIP,β1,EIP). It is assumed that there are measured data x = xtrue + ex, and y = ytrue + ey with errors ex in x and ey in y and the variances of the errors ex and ey are allowed to depend on xtrue and ytrue, respectively. This paper also investigates the accuracy of the estimated cov(β0,EIP,β1,EIP) and provides a numerical Bayesian alternative using Markov Chain Monte Carlo, which is recommended particularly for small sample sizes where the approximate expression is shown to have lower accuracy than desired.

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“…Recent works have showed an improvement in the interval estimation when the generalized fiducial inference is adopted. For example, in measurement error models, Wang and Iyer (2008) provided procedures for constructing uncertainty regions for the intercept and slope parameters using a FGPQ. Moreover, Yan, Wang and Xu (2017a), Yan, Wang and Xu (2017b) and Yan and Xu (2017) proposed two confidence intervals based on FGPQ and GFD for the slope parameter with good empirical frequentist properties.…”

Section: Introductionmentioning

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 approach for assessing agreement between two instruments

Cited by 12 publications

References 16 publications

Generalized fiducial inference

Generalized fiducial inference

Least-squares fitting with errors in the response and predictor

Some extensions in measurement error models

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