Bivariate quantile residual life: a characterization theorem and statistical properties

Noughabi, M. Shafaei; Kayid, Mohamed

doi:10.1007/s00362-017-0905-9

Cited by 19 publications

(8 citation statements)

References 18 publications

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“…In our data example of gastric cancer patients (Section 5.1), bivariate correlated endpoints are of great interest [55]. Correlations between responses should be employed to improve the efficiency and reduce the bias of univariate analyses [56][57][58][59][60][61][62][63][64][65] and to predict a primary outcome by the secondary outcome [66][67][68][69]. Multivariate shrinkage estimators of multivariate normal means, such as [70,71], can be considered for this extension.…”

Section: Conclusion and Future Extensionsmentioning

confidence: 99%

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

Taketomi

Konno

Chang

et al. 2021

Axioms

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Meta-analyses combine the estimators of individual means to estimate the common mean of a population. However, the common mean could be undefined or uninformative in some scenarios where individual means are “ordered” or “sparse”. Hence, assessments of individual means become relevant, rather than the common mean. In this article, we propose simultaneous estimation of individual means using the James–Stein shrinkage estimators, which improve upon individual studies’ estimators. We also propose isotonic regression estimators for ordered means, and pretest estimators for sparse means. We provide theoretical explanations and simulation results demonstrating the superiority of the proposed estimators over the individual studies’ estimators. The proposed methods are illustrated by two datasets: one comes from gastric cancer patients and the other from COVID-19 patients.

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Section: Conclusion and Future Extensionsmentioning

confidence: 99%

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

Taketomi

Konno

Chang

et al. 2021

Axioms

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“…However, it is not trivial to extend this prediction method under competing risks. This risk prediction scheme is equivalent to dynamic prediction [48][49][50][51][52][53]. Moreover, the accelerated life test plans may be considered including the case of one-shot devices with competing risks [54,55].…”

Section: Discussionmentioning

confidence: 99%

Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies

Michimae

Emura

2022

Mathematics

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Survival and reliability analyses deal with incomplete failure time data, such as censored and truncated data. Recently, the classical left-truncation scheme was generalized to analyze “field data”, defined as samples collected within a fixed period. However, existing competing risks models dealing with left-truncated field data are not flexible enough. We propose copula-based competing risks models for latent failure times, permitting a flexible parametric form. We formulate maximum likelihood estimation methods under the Weibull, lognormal, and gamma distributions for the latent failure times. We conduct simulations to check the performance of the proposed methods. We finally give a real data example. We provide the R code to reproduce the simulations and data analysis results.

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“…Denote the th element of this vector bỹ(x). We generalize the -BQRL function proposed by Shafaei Noughabi and Kayid [16] to define the -MQRL given bỹ…”

Section: Preliminariesmentioning

confidence: 99%

“…Recently, Shafaei Noughabi and Kayid [16] proposed a bivariate -QRL ( -BQRL) function which characterizes the underlying distribution properly. Although this function is useful and applicable in statistics and reliability fields, it is nondynamic.…”

Section: Introductionmentioning

confidence: 99%

“…At arbitrary time , he/she may observe that (i) all belts may be safely working or (ii) one or more of them may fail at . The bivariate -QRL ( -BQRL) function introduced by Shafaei Noughabi and Kayid [16] does not support histories of type (ii). This motivates us to extend the univariate -quantile residual life function to multivariate setting preserving its dynamic feature.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Multivariate Quantile Residual Life in Reliability Theory

Noughabi

Kayid

Abouammoh

2018

Mathematical Problems in Engineering

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We extend the univariate α-quantile residual life function to multivariate setting preserving its dynamic feature. Principal attributes of this function are derived and their relationship to the dynamic multivariate hazard rate function is discussed. A corresponding ordering, namely, α-quantile residual life order, for random vectors of lifetimes is introduced and studied. Based on the proposed ordering, a notion of positive dependency is presented. Finally, a discussion about conditions characterizing the class of decreasing multivariate α-quantile residual life functions is pointed out.

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Bivariate quantile residual life: a characterization theorem and statistical properties

Cited by 19 publications

References 18 publications

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies

Dynamic Multivariate Quantile Residual Life in Reliability Theory

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