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Author Barros, M.; Galea, M.; Leiva, V.; Santos-Neto, M. pdf  doi
openurl 
  Title Generalized Tobit models: diagnostics and application in econometrics Type
  Year 2018 Publication Journal Of Applied Statistics Abbreviated Journal J. Appl. Stat.  
  Volume 45 Issue 1 Pages 145-167  
  Keywords Cook distance; elliptically contoured distributions; labor supply data; local influence method; maximum likelihood method; R software; residuals; Student-t distribution  
  Abstract The standard Tobit model is constructed under the assumption of a normal distribution and has been widely applied in econometrics. Atypical/extreme data have a harmful effect on the maximum likelihood estimates of the standard Tobit model parameters. Then, we need to count with diagnostic tools to evaluate the effect of extreme data. If they are detected, we must have available a Tobit model that is robust to this type of data. The family of elliptically contoured distributions has the Laplace, logistic, normal and Student-t cases as some of its members. This family has been largely used for providing generalizations of models based on the normal distribution, with excellent practical results. In particular, because the Student-t distribution has an additional parameter, we can adjust the kurtosis of the data, providing robust estimates against extreme data. We propose a methodology based on a generalization of the standard Tobit model with errors following elliptical distributions. Diagnostics in the Tobit model with elliptical errors are developed. We derive residuals and global/local influence methods considering several perturbation schemes. This is important because different diagnostic methods can detect different atypical data. We implement the proposed methodology in an R package. We illustrate the methodology with real-world econometrical data by using the R package, which shows its potential applications. The Tobit model based on the Student-t distribution with a small quantity of degrees of freedom displays an excellent performance reducing the influence of extreme cases in the maximum likelihood estimates in the application presented. It provides new empirical evidence on the capabilities of the Student-t distribution for accommodation of atypical data.  
  Address [Barros, Michelli; Santos-Neto, Manoel] Univ Fed Campina Grande, Dept Stat, Campina Grande, Brazil, Email: victorleivasanchez@gmail.com  
  Corporate Author Thesis  
  Publisher Taylor & Francis Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0266-4763 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000415929600011 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 781  
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Author Leiva, V.; Liu, S.Z.; Shi, L.; Cysneiros, F.J.A. pdf  doi
openurl 
  Title Diagnostics in elliptical regression models with stochastic restrictions applied to econometrics Type
  Year 2016 Publication Journal Of Applied Statistics Abbreviated Journal J. Appl. Stat.  
  Volume 43 Issue 4 Pages 627-642  
  Keywords computational statistics; elliptically contoured distributions; generalized least squares; local influence method; maximum-likelihood method; mixed estimation  
  Abstract We propose an influence diagnostic methodology for linear regression models with stochastic restrictions and errors following elliptically contoured distributions. We study how a perturbation may impact on the mixed estimation procedure of parameters in the model. Normal curvatures and slopes for assessing influence under usual schemes are derived, including perturbations of case-weight, response variable, and explanatory variable. Simulations are conducted to evaluate the performance of the proposed methodology. An example with real-world economy data is presented as an illustration.  
  Address [Leiva, Victor] Univ Adolfo Ibanez, Fac Sci & Engn, Vina Del Mar, Chile, Email: victorleivasanchez@gmail.com  
  Corporate Author Thesis  
  Publisher Taylor & Francis Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0266-4763 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000368584400003 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 575  
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Author Lillo, C.; Leiva, V.; Nicolis, O.; Aykroyd, R.G. pdf  doi
openurl 
  Title L-moments of the Birnbaum-Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data Type
  Year 2018 Publication Journal Of Applied Statistics Abbreviated Journal J. Appl. Stat.  
  Volume 45 Issue 2 Pages 187-209  
  Keywords GCMT catalogue; Generalized extreme value distributions; goodness-of-fit methods; maximum likelihood and moment estimation; Monte Carlo simulation; R software  
  Abstract 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 modelling the frequency of such events. 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.  
  Address [Lillo, Camilo; Leiva, Victor] Univ Adolfo Ibanez, Fac Sci & Engn, Vina Del Mar, Chile, Email: victorleivasanchez@gmail.com  
  Corporate Author Thesis  
  Publisher Taylor & Francis Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0266-4763 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000417787500001 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 780  
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Author Marchant, C.; Leiva, V.; Cysneiros, F.J.A.; Vivanco, J.F. pdf  doi
openurl 
  Title Diagnostics in multivariate generalized Birnbaum-Saunders regression models Type
  Year 2016 Publication Journal Of Applied Statistics Abbreviated Journal J. Appl. Stat.  
  Volume 43 Issue 15 Pages 2829-2849  
  Keywords Birnbaum-Saunders distributions; global and local influence; goodness-of-fit; multivariate data analysis; R software  
  Abstract Birnbaum-Saunders (BS) models are receiving considerable attention in the literature. Multivariate regression models are a useful tool of the multivariate analysis, which takes into account the correlation between variables. Diagnostic analysis is an important aspect to be considered in the statistical modeling. In this paper, we formulate multivariate generalized BS regression models and carry out a diagnostic analysis for these models. We consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption. We also consider the local influence approach and study how a perturbation may impact on the estimation of model parameters. We implement the obtained results in the R software, which are illustrated with real-world multivariate data to show their potential applications.  
  Address [Marchant, Carolina; Cysneiros, Francisco Jose A.] Univ Fed Pernambuco, Dept Stat, Recife, PE, Brazil, Email: victorleivasanchez@gmail.com  
  Corporate Author Thesis  
  Publisher Taylor & Francis Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0266-4763 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000384263000009 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 662  
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