Generalized Confidence Intervals

Weerahandi, Samaradasa

doi:10.2307/2290779

Cited by 430 publications

(227 citation statements)

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“…Let X 1 , ..., X n be i.i.d. random variables from the population probability density function pdf f x x | η 1 . Also, let Y 1 , ..., Y m be iid random variables from the population pdf f y y | η 2 .…”

Section: Background and Preliminary Resultsmentioning

confidence: 99%

Equivariance and Generalized Inference in Two‐Sample Location‐Scale Families

Nkurunziza

Chen

2011

Journal of Probability and Statistics

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We are interested in-typical Behrens-Fisher problem in general location-scale families. We present a method of constructing generalized pivotal quantity GPQ and generalized P value GPV for the difference between two location parameters. The suggested method is based on the minimum risk equivariant estimators MREs , and thus, it is an extension of the methods based on maximum likelihood estimators and conditional inference, which have been, so far, applied to some specific distributions. The efficiency of the procedure is illustrated by Monte Carlo simulation studies. Finally, we apply the proposed method to two real datasets.

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Section: Background and Preliminary Resultsmentioning

confidence: 99%

Equivariance and Generalized Inference in Two‐Sample Location‐Scale Families

Nkurunziza

Chen

2011

Journal of Probability and Statistics

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“…One CI is based on the MOVER, which is a new general method, and the other CI is based on the fiducial approach. Even though the fiducial approach was introduced in 1930s, it was not a popular approach until publication of the papers [16], [7] and [8]. These authors have promoted the fiducial approach by noting fiducial solutions to problems where the standard approach fail to produce accurate results.…”

Section: Discussionmentioning

confidence: 99%

Improved Confidence Intervals for the Ratio of Coefficients of Variation of Two Lognormal Distributions

Hasan¹,

Krishnamoorthy²

2017

JSTA

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The problem of estimating the ratio of coefficients of variation of two independent lognormal populations is considered. We propose two closed-form approximate confidence intervals (CIs), one is based on the method of variance estimate recovery (MOVER), and another is based on the fiducial approach. The proposed CIs are compared with another CI available in the literature. Our new confidence intervals are very satisfactory in terms of coverage properties even for small samples, and better than other CIs for small to moderate samples. The methods are illustrated using an example.

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“…See Weerahandi [12]. To construct confidence intervals for the intraclass correlation coefficient ρ, [10] proposed the following generalized variable and Q E are independent and distributed as χ 2 S−1 , χ 2 R−1 , and χ 2 (R−1)(S−1) , respectively.…”

Section: The General Variable Approachmentioning

confidence: 99%

Modified profile likelihood approach for certain intraclass correlation coefficients

Xiao

Liu

2013

Comput Stat

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In this paper we consider the problem of constructing confidence intervals and lower bounds for the intraclass correlation coefficient in an interrater reliability study where the raters are randomly selected from a population of raters.The likelihood function of the interrater reliability is derived and simplified, and the profile likelihood based approach is readily available for computing the confidence intervals of the interrater reliability. Unfortunately, the confidence intervals computed by using the profile likelihood function are in general too narrow to have the desired coverage probabilities. From the point view of practice, a conservative approach, if is at least as precise as any existing method, is preferred since it gives the correct results with a probability higher than claimed. Under this rationale, we propose the so-called modified profile likelihoodapproach in this paper. Simulation study shows that, the proposed method in general has better performance than currently used methods. INDEX WORDS:Interrater reliability, Profile likelihood, Confidence intervals, Generalized P-values, Modified large-sample approach MODIFIED PROFILE

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Generalized Confidence Intervals

Cited by 430 publications

References 0 publications

Equivariance and Generalized Inference in Two‐Sample Location‐Scale Families

Equivariance and Generalized Inference in Two‐Sample Location‐Scale Families

Improved Confidence Intervals for the Ratio of Coefficients of Variation of Two Lognormal Distributions

Modified profile likelihood approach for certain intraclass correlation coefficients

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