Log-symmetric regression models under the presence of non-informative left- or right-censored observations

Vanegas, Luis Hernando; Paula, Gilberto A.

doi:10.1007/s11749-016-0517-z

Cited by 16 publications

(10 citation statements)

References 23 publications

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“…Boston crime data were studied by Vanegas and Paula . Medeiros and Ferrari developed a Bartlett‐type correction for these models, whereas Vanegas and Paula analyzed the presence of noninformative left or right censored data. Despite the high density and volatility, high‐frequency financial data were well fitted by a log‐symmetric duration model .…”

Section: Introductionmentioning

confidence: 99%

“…[3][4][5][6][7][8] Log-symmetric regressions provide a solution for describing data when the assumption of normality is not valid. 9 In addition, these regression models allow either the median or skewness of the response variable (response hereafter) to be formulated. Both measures are important when modeling variables with asymmetric distributions.…”

Section: Introductionmentioning

confidence: 99%

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Log‐symmetric regression models: information criteria and application to movie business and industry data with economic implications

Ventura

Saulo

Leiva

et al. 2019

Appl Stoch Models Bus & Ind

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This work deals with log‐symmetric regression models, which are particularly useful when the response variable is continuous, strictly positive, and following an asymmetric distribution, with the possibility of modeling atypical observations by means of robust estimation. In these regression models, the distribution of the random errors is a member of the log‐symmetric family, which is composed by the log‐contaminated‐normal, log‐hyperbolic, log‐normal, log‐power‐exponential, log‐slash and log‐Student‐t distributions, among others. One way to select the best family member in log‐symmetric regression models is using information criteria. In this paper, we formulate log‐symmetric regression models and conduct a Monte Carlo simulation study to investigate the accuracy of popular information criteria, as Akaike, Bayesian, and Hannan‐Quinn, and their respective corrected versions to choose adequate log‐symmetric regressions models. As a business application, a movie data set assembled by authors is analyzed to compare and obtain the best possible log‐symmetric regression model for box offices. The results provide relevant information for model selection criteria in log‐symmetric regressions and for the movie industry. Economic implications of our study are discussed after the numerical illustrations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Log‐symmetric regression models: information criteria and application to movie business and industry data with economic implications

Ventura

Saulo

Leiva

et al. 2019

Appl Stoch Models Bus & Ind

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“…The proof is quite analogous to the one given in appendix of Vanegas and Paula (2017). Hence, the asymptotic variance-covariance matrix ofθ takes the form…”

Section: Asymptotic Statementsmentioning

confidence: 83%

“…To study the limit behavior of the penalized maximum likelihood estimatorŝ θ under censoring, we adopt the approach of Vanegas and Paula (2017) and the assumptions of regularity given in Bagdonavicius and Nikulin (2001). This approach consists in assuming the number of knots fixed, which means that the penalty matrices and the sizes of γ 1 , · · · , γ k are not functions of the sample size n. Some additional conditions are necessary to guarantee the consistency and asymptotic normality of the estimators, given by…”

Section: Asymptotic Statementsmentioning

confidence: 99%

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Semi-parametric generalized log-gamma regression models

Delgado¹

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2 DedicationTo my mom María Antonia for her unconditional love and wisedom. To share with me the passion about knowledge.To my wife Sandra, a great support point over these years. To my kids, Juan David and Ana María, my best examples of how to learn of the life and don't surrender. i AcknowledgementsTo me is obvious that this work is a crystallization of countless hints, moments and subtle ideas that many people share with me. So, I would like to thank all of you. A special mention to:• Gilberto A. Paula for the opportunity to work under his guidance, his continuous challenges and his confidence.• Viviana Giampaoli and Eliane Pinheiros because their observations in my qualify exam help me to improve this work.• Luis H. Vanegas his illuminating conversations about classic statistics and semi-parametric models were essentials for this project.• Liliana Blanco C. and Rodrigo de Castro K. for their excellence teaching, full of precision and clarity. These qualities shaped my mind.• Yuri M. Suhov and Anatoli Iambartsev for let me know a little bit about information theory and quantum statistical mechanics.• My fellows, Alejandro Roldán, Kishor K. Ramavarmaraja and Rogério de Assis Medeiros because always had time to discuss mathematical and cultural ideas.• Finally, I would like to thank IME-USP, a great place to learn.ii The central objective of this work is to develop statistical tools for semiparametric regression models with generalized log-gamma errors under the presence of censored and uncensored observations. The estimates of the parameters are obtained through the multivariate version of Newton-Raphson algorithm and an adequate combination of Fisher Scoring and Backffitting algorithms. Through analytical tools and using simulations the properties of the penalized maximum likelihood estimators are studied. Some diagnostic techniques such as quantile and deviance-type residuals as well as local influence measures are derived. The methodologies are implemented in the statistical computational environment R. The package sglg is developed. Finally, we give some applications of the models to real data.Keywords: censored observations, generalized log-gamma distribution, maximum penalized likelihood estimation, natural cubic spline, P-splines, skewness, semi-parametric models.iii O objetivo central do trabalhoé proporcionar ferramentas estatísticas para modelos de regressão semiparamétricos quando os erros seguem distribução loggamma generalizada na presença de observações censuradas ou não censuradas. A estimacão paramétrica e não paramétrica são realizadas através dos procedimentos Newton -Raphson, escore de Fisher e Backfitting (Gauss -Seidel). As propriedades assintóticas dos estimadores de máxima verossimilhança penalizada são estudadas em forma analítica, bem como através de simulações. Alguns procedimentos de diagnóstico são desenvolvidos, tais como resíduos tipo componente do desvio e resíduo quantílico, bem como medidas de influência local sob alguns esquemas usuais de perturbacão. Os principais procediment...

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Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Balakrishnan

Kundu

2018

Appl Stoch Models Bus & Ind

110

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Birnbaum and Saunders introduced a two-parameter lifetime distribution to model the fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate, and matrix-variate cases. More than 200 papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and, at the same time, indicate several open problems that could be considered for further research. KEYWORDSBayes estimators, EM algorithm, Fisher information matrix, hazard function, length-biased distribution, moments and inverse moments, probability density function, stochastic orderings, TP 2 property 4

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Log-symmetric regression models under the presence of non-informative left- or right-censored observations

Cited by 16 publications

References 23 publications

Log‐symmetric regression models: information criteria and application to movie business and industry data with economic implications

Log‐symmetric regression models: information criteria and application to movie business and industry data with economic implications

Semi-parametric generalized log-gamma regression models

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

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