Coverage of generalized confidence intervals

Bose, Arup

doi:10.1016/j.jmva.2008.12.001

Cited by 8 publications

(6 citation statements)

References 30 publications

(52 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Unlike the traditional test of average bioequivalence, the explicit equivalence limit (EL) is not available for every endpoint measured in a field study (Hothorn and Oberdoerfer, 2006). Furthermore, varieties of non‐GM conventional crops possess a considerable amount of natural variation (Reynolds et al, 2005; van der Voet et al, 2011) and a single non‐GM variety would not suffice to serve as the reference. Recently, the GMO panel of EFSA mandated each field site to include an assortment of commercial non‐GM reference varieties with a proven history of safe consumption (EFSA, 2010).…”

mentioning

confidence: 99%

Statistical Analysis in the Safety Evaluation of Genetically‐Modified Crops: Equivalence Tests

Kang

Vahl

2014

Crop Science

View full text Add to dashboard Cite

Risk assessment is an important step in the process of deregulating a genetically modified (GM) crop and its derived products for food and feed. The European Food Safety Authority (EFSA) evaluates safety by testing for the average equivalence between the GM crop and a group of commercial non‐GM reference varieties representing a population of crops with a history of safe use. This paper defines the equivalence tests described by EFSA in terms of parameters in the mixed model. A basic strategy for the equivalence tests is proposed. Generalized inference is employed to overcome two challenges in testing equivalences: the unconventional parameter of interest and the limited number of reference varieties. Balanced or partially balanced incomplete designs are recommended in equivalence testing. Simulation indicates this new method maintains the desired type I error rate and holds good power under practical designs. An illustrative data example is used to demonstrate the execution of the proposed method in SAS. Finally, issues associated with the equivalence tests and suggested topics for future research are discussed.

show abstract

mentioning

confidence: 99%

Statistical Analysis in the Safety Evaluation of Genetically‐Modified Crops: Equivalence Tests

Kang

Vahl

2014

Crop Science

View full text Add to dashboard Cite

show abstract

“…Although it can be seen that the simulated coverage probabilities are satisfactory according to the above simulation results, we think that the application of the method proposed by Roy and Bose (2009) in this problem can improve the accuracy further, and this will be one topic of our future research.…”

Section: Accepted Manuscriptmentioning

confidence: 83%

“…Almost at the same time, Li et al (2007) and Xu and Li (2006) also found this connection and gave another general method to construct generalized pivotal quantity. Roy and Bose (2009) provided theoretical explanation of the observed empirical behavior of the generalized intervals and suggested several ways to improve the finite sample performance of the generalized intervals.…”

Section: A Brief Review Of Generalized Fiducial Inferencementioning

confidence: 99%

“…Additionally, Roy and Bose (2009) pointed out that in general the generalized confidence intervals are not first order accurate, i.e., accurate only up to the n 1/2 term, and they suggest a modification to make the intervals first order accurate and hence, improve the coverage of the intervals significantly in many applications. Although it can be seen that the simulated coverage probabilities are satisfactory according to the above simulation results, we think that the application of the method proposed by Roy and Bose (2009) in this problem can improve the accuracy further, and this will be one topic of our future research.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

See 1 more Smart Citation

A new generalized confidence interval for the among-group variance in the heteroscedastic one-way random effects model

Liu

Yu-qin

2015

Communications in Statistics - Simulation and Computation

View full text Add to dashboard Cite

Based on the generalized inference idea, a new kind of generalized confidence intervals are derived for the among-group variance component in the heteroscedastic one-way random effects model. We construct structure equations of all variance components in the model based on their minimal sufficient statistics, meanwhile, the fiducial generalized pivotal quantity can be obtained through solving an implicit equation of the parameter of interest. Then the confidence interval is derived naturally from the fiducial generalized pivotal quantity. Simulation results demonstrate that the new procedure performs very well in terms of both empirical coverage probability and average interval length.

show abstract

“…Asymptotic properties of the CI based on the GPQs have been discussed by Hanning et al . and Roy and Bose . The present article exploits this technique for interval estimation of R , when X 1 and X 2 are independently distributed members of the exponentiated scale family, also known as resilience or frailty parameter family (Marshall and Olkin):

G ((), \frac{x}{λ}, α) = F^{α} ((), \frac{x}{λ}) Resilience family o r

\overset{G}{true} ((), \frac{x}{λ}, α) = {\overset{F}{true}}^{α} ((), \frac{x}{λ}), x ε normalR, λ, α > 0 Frailty family,

where λ and α are the scale and resilience (frailty) parameters, respectively and F (.)…”

Section: Introductionmentioning

confidence: 99%

On the Interval Estimation of Stress–Strength Reliability for Exponentiated Scale Family of Distributions

Patil

Kulkarni

2017

Quality & Reliability Eng

View full text Add to dashboard Cite

The stress-strength reliability R D P.X 1 < X 2 / where X 1 and X 2 represent the stress applied and strength of an equipment, respectively, plays a crucial role in setting warranty periods while launching new brands of a product. The paper addresses the issue of estimating R when X 1 and X 2 belong to the exponentiated scale family, which includes the popular EED that has proven to be an excellent model for lifetime distributions. The cases of known/unknown and equal/unequal scale parameters are handled separately. For known scale parameter, a generalized pivot quantity for the shape parameter and R are developed. The interval estimates of R based on the proposed generalized pivot quantity exhibited uniformly best performance. For an unknown scale parameter, a maximum scale invariant likelihood estimator of the shape and an allied estimator of the scale are introduced. The parametric bootstrap interval estimates of R based on a proposed maximum scale invariant likelihood estimator of the shape parameter exhibited best performance among others. An application in setting warranty periods is illustrated based on two real data sets.

show abstract

Coverage of generalized confidence intervals

Cited by 8 publications

References 30 publications

Statistical Analysis in the Safety Evaluation of Genetically‐Modified Crops: Equivalence Tests

Statistical Analysis in the Safety Evaluation of Genetically‐Modified Crops: Equivalence Tests

A new generalized confidence interval for the among-group variance in the heteroscedastic one-way random effects model

On the Interval Estimation of Stress–Strength Reliability for Exponentiated Scale Family of Distributions

Contact Info

Product

Resources

About