Reparameterized Birnbaum-Saunders regression models with varying precision

Santos‐Neto, Manoel; Cysneiros, Francisco José A.; Leiva, Víctor; Barros, Michelli

doi:10.1214/16-ejs1187

Cited by 57 publications

(46 citation statements)

References 42 publications

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“…The RVs U i are often assumed to be independent and identically distributed as gamma, inverse Gaussian, log‐normal, or Weibull, which have simple Laplace transforms and then are convenient to use. We consider a reparameterized version of the BS distribution because it allows us to mimic a property of the gamma distribution, as mentioned, traditionally used in frailty models …”

Section: Preliminariesmentioning

confidence: 99%

“…We derive local influence for the proposed model and evaluate the performance of the ML estimators by Monte Carlo (MC) simulations. In the model, the frailty follows a BS distribution with a parameterization defined in terms of the mean, whereas its variance is a quadratic function of this mean . Such a characteristic allows us to mimic a property of the highly used gamma frailty distribution.…”

Section: Introductionmentioning

confidence: 99%

“…In the model, the frailty follows a BS distribution with a parameterization defined in terms of the mean, whereas its variance is a quadratic function of this mean. 30 Such a characteristic allows us to mimic a property of the highly used gamma frailty distribution. Thus, the BS distribution appears as a new alternative to frailty modeling.…”

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confidence: 99%

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Incorporation of frailties into a cure rate regression model and its diagnostics and application to melanoma data

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Leiva

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et al. 2018

Statistics in Medicine

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Cure rate models have been widely studied to analyze time-to-event data with a cured fraction of patients. Our proposal consists of incorporating frailty into a cure rate model, as an alternative to the existing models to describe this type of data, based on the Birnbaum-Saunders distribution. Such a distribution has theoretical arguments to model medical data and has shown empirically to be a good option for their analysis. An advantage of the proposed model is the possibility to jointly consider the heterogeneity among patients by their frailties and the presence of a cured fraction of them. In addition, the number of competing causes is described by the negative binomial distribution, which absorbs several particular cases. We consider likelihood-based methods to estimate the model parameters and to derive influence diagnostics for this model. We assess local influence on the parameter estimates under different perturbation schemes. Deriving diagnostic tools is needed in all statistical modeling, which is another novel aspect of our proposal. Numerical evaluation of the considered model is performed by Monte Carlo simulations and by an illustration with melanoma data, both of which show its good performance and its potential applications. Particularly, the illustration confirms the importance of statistical diagnostics in the modeling.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Incorporation of frailties into a cure rate regression model and its diagnostics and application to melanoma data

Leão

Leiva

Saulo

et al. 2018

Statistics in Medicine

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“…() and Santos‐Neto et al. (, ). In the context of frailty models, it can be very competitive in terms of fitting. It belongs to the class of log‐symmetric distributions, such as the case of the generalized BS, LN, log‐logistic, log‐Laplace, log‐Student‐ t , log‐power‐exponential, log‐slash, and F distributions; see Vanegas and Paula (, ). The log‐symmetric class of distributions arises when an RV has the same distribution as its reciprocal or as ordinary symmetry of the distribution of the logged RV; see Jones ().…”

Section: Introductionmentioning

confidence: 99%

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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“…Bhatti (2010) suggested that (B2) might possibly: (C1) improve the model fit, since for asymmetric, heavy-tailed distributions, as occurs with TD data, the median is often considered as a better measure of central tendency than the mean; and (C2) increase the forecasting ability due to the fact that the mean is greater than the median for skew distributions. In this context, we consider two models: A first new mean-based model (BSACD1 in short) specified in terms of a time-varying conditional mean duration, as usual in ACD models, using a reparameterized version of the BS distribution (see Leiva et al, 2014a;Santos-Neto et al, 2016); and a second median-based model (BSACD2 in short) specified in terms of a time-varying conditional median duration. Thus, the primary objective of this paper is to compare both BSACD1 and BSACD2 models.…”

Section: Introductionmentioning

confidence: 99%

Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data

et al. 2017

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Modern financial markets now record the precise time of each stock trade, along with price and volume, with the aim of analysing the structure of the times between trading events -leading to a big data problem. In this paper, we propose and compare two Birnbaum-Saunders autoregressive conditional duration models specified in terms of time-varying conditional median and mean durations. These models provide a novel alternative to the existing autoregressive conditional duration models due to their flexibility and ease of estimation. Influence diagnostic tools are developed to allow goodness-of-fit assessment and to detect departures from assumptions, including the presence of outliers and influential cases. Both global and local influence tools are considered based on the parameter estimates under different perturbation schemes. A thorough Monte Carlo study is presented to evaluate the performance of the maximum likelihood estimators, and the forecasting ability of the models is assessed using the traditional and density forecast evaluation techniques. The Monte Carlo study suggests that the parameter estimators are asymptotically unbiased, consistent and normally distributed. Finally, a full analysis of a real-world financial transaction data set, from the German DAX in 2016, is presented to illustrate the proposed approach and to compare the fitting and forecasting performances with existing models in the literature. One case related to the duration time is identified as potentially influential, but its removal does not change resulting inferences demonstrating the robustness of the proposed approach. Fitting and forecasting performances favor the proposed models and, in particular, the median-based approach gives additional protection against outliers, as expected.

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Reparameterized Birnbaum-Saunders regression models with varying precision

Cited by 57 publications

References 42 publications

Incorporation of frailties into a cure rate regression model and its diagnostics and application to melanoma data

Incorporation of frailties into a cure rate regression model and its diagnostics and application to melanoma data

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

Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data

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