Diagnostics in multivariate generalized Birnbaum-Saunders regression models

Marchant, Carolina; Leiva, Víctor; Cysneiros, Francisco José A.; Vivanco, Juan

doi:10.1080/02664763.2016.1148671

Cited by 55 publications

(46 citation statements)

References 39 publications

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“…() and Marchant et al. (, ). Work on some of these issues is currently in progress and we hope to report some findings in a future paper.…”

Section: Discussion Conclusion and Future Researchmentioning

confidence: 98%

“…The introduced methodology may also be extended to the correlated frailty case, where the nature of the heterogeneity and the dependence are explicitly specified, and are of main importance; see Petersen (1998). Finally, the inclusion of multivariate aspects in frailty models, as well as spatial components, can also be considered; see Garcia-Papani et al (2016) and Marchant et al (2016aMarchant et al ( , 2016b. Work on some of these issues is currently in progress and we hope to report some findings in a future paper.…”

Section: Discussion Conclusion and Future Researchmentioning

confidence: 99%

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Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data

et al. 2017

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In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum-Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum-likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real-world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.

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“…() and Marchant et al. (, ). Work on some of these issues is currently in progress and we hope to report some findings in a future paper.…”

Section: Discussion Conclusion and Future Researchmentioning

confidence: 98%

Section: Discussion Conclusion and Future Researchmentioning

confidence: 99%

Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data

et al. 2017

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“…Note that it is not possible to utilize the MD as a criterion for detecting outliers when there are more variables than data (cases). In addition, observe that the MD is useful to test goodness of fit in regression models (Marchant, Leiva, Cysneiros, & Vivanco, b). However, sometimes outliers do not have a large MD, which is known as masking effect.…”

Section: A Standard Methodologymentioning

confidence: 99%

Monitoring urban environmental pollution by bivariate control charts: New methodology and case study in Santiago, Chile

et al. 2018

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Particulate matter (PM) pollution is a serious environmental problem. Santiago of Chile is one of the most polluted cities in the world in terms of PM2.5 and PM10. Monitoring of environmental risk is useful for detecting and preventing adverse effects on human health in highly polluted cities. In this paper, we propose a methodology for monitoring PM pollution in Santiago based on bivariate quality control charts and an asymmetric distribution. A simulation study is carried out to evaluate performance of the proposed methodology. A case study with PM pollution real‐world data from Santiago is provided, which shows that the methodology is suitable to alert early episodes of extreme air pollution. The results are in agreement with the critical episodes reported with the current model used by the Chilean health authority.

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“…Furthermore, acceptance regions for goodness of fit based on L-moments are also an important issue to be considered [52]. Incorporation of censored data, multivariate versions of value extreme Birnbaum-Saunders distributions, and their modeling and diagnostics are also of interest [39,40] in the context of L-moments. As future research, all of these issues are being explored by the authors.…”

Section: Discussionmentioning

confidence: 99%

L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data

Lillo

Leiva

Nicolis

et al. 2016

Journal of Applied Statistics

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Understanding patterns in the frequency of extreme natural events, such as earthquakes, is important as it helps in the prediction of their future occurrence and hence provides better civil protection. Distributions describing these events are known to be heavy tailed and positive skew making standard distributions unsuitable for such a situation. The Birnbaum-Saunders distribution and its extreme value version have been widely studied and applied due to their attractive properties. We derive L-moment equations for these distributions and propose novel methods for parameter estimation, goodness-of-fit assessment and model selection. A simulation study is conducted to evaluate the performance of the L-moment estimators, which is compared to that of the maximum likelihood estimators, demonstrating the superiority of the proposed methods. To illustrate these methods in a practical application, a data analysis of real-world earthquake magnitudes, obtained from the global centroid moment tensor catalogue during 1962-2015, is carried out. This application identifies the extreme value Birnbaum-Saunders distribution as a better model than classic extreme value distributions for describing seismic events.

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Diagnostics in multivariate generalized Birnbaum-Saunders regression models

Cited by 55 publications

References 39 publications

Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data

Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data

Monitoring urban environmental pollution by bivariate control charts: New methodology and case study in Santiago, Chile

L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data

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