Estimation and diagnostic for skew-normal partially linear models

Ferreira, Clécio S.; Paula, Gilberto A.

doi:10.1080/02664763.2016.1267124

Cited by 17 publications

(8 citation statements)

References 41 publications

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“…in which the superscript (k) indicates the estimate of the related parameter at stage k of the algorithm and E θ (k) is the conditional expectation of the complete penalized loglikelihood function given the current estimate θ = θ (k) . Like [16] and [7], we consider the following penalty function:…”

Section: Parameter Estimation Via An Ecme Algorithmmentioning

confidence: 99%

“…In additive models, the Akaike information criterion (AIC) can be applied to select an appropriate α. Following [7], the AIC for PLR models is defined by:…”

Section: Estimation Of Smoothing Parameter αmentioning

confidence: 99%

“…For instance, [16] developed diagnostic measures for PLR models using the Student-t distribution, [30] derived an iterative estimation process and some diagnostic procedures in PLR with AR(1) symmetrical errors. [7] proposed a PLR model allowing the errors to follow a skew-normal [2] distribution. In the context of partial linear censored regression (PCR) models, [31] proposed the log-symmetric regression model, where the presence of non-informative censored observations is admitted.…”

Section: Introductionmentioning

confidence: 99%

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Estimation and diagnostics for partially linear censored regression models based on heavy-tailed distributions

Lemus

Lachos

Galarza

et al. 2021

Statistics and Its Interface

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In many studies, limited or censored data are collected. This occurs, in several practical situations, for reasons such as limitations of measuring instruments or due to experimental design. So, the responses can be either left, interval or right censored. On the other hand, partially linear models are considered as a flexible generalizations of linear regression models by including a nonparametric component of some covariates in the linear predictor. In this paper, we discuss estimation and diagnostic procedures in partially linear censored regression models with errors following a scale mixture of normal (SMN) distributions. This family of distributions contains a group of well-known heavy-tailed distributions that are often used for robust inference of symmetrical data, such as Student-t, slash and contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum penalized likelihood (MPL) estimates of the parameters is presented. To examine the performance of the proposed model, case-deletion and local influence techniques are developed to show its robustness against outlying and influential observations. This is performed by sensitivity analysis of the maximum penalized likelihood estimates under some usual perturbation schemes, either in the model or in the data, and by inspecting some proposed diagnostic graphs. We evaluate the finite sample performance of the algorithm and the asymptotic properties of the MPL estimates through empirical experiments. An application to a real dataset is presented to illustrate the effectiveness of the proposed methods. Both estimation procedure and diagnostic tools were implemented in the R PartCensReg package.

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Section: Parameter Estimation Via An Ecme Algorithmmentioning

confidence: 99%

“…In additive models, the Akaike information criterion (AIC) can be applied to select an appropriate α. Following [7], the AIC for PLR models is defined by:…”

Section: Estimation Of Smoothing Parameter αmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimation and diagnostics for partially linear censored regression models based on heavy-tailed distributions

Lemus

Lachos

Galarza

et al. 2021

Statistics and Its Interface

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“…Thus, it seems that asymmetric errors are more appropriate for modelling log(Cost). Another possible comparison would be between partially linear under generalized loggamma errors models and skew-normal errors Ferreira and Paula (2017). Figure 7.6: Index plot based on the contribution of individual basic perturbation E i to the eigenvector e max which gives the maximum conformal normal curvature (left) and of B i (right) under the case-weight perturbation scheme from the partially linear generalized log-gamma model fitted to the drg2000 data.…”

Section: The Modelmentioning

confidence: 99%

“…Ibacache-Pulgar and Paula (2011) extended the work by Kim et al (2002) on diagnostic methods in partially linear normal models to the Student-t class, Vanegas and Paula (2016) discussed semi-parametric models under log-symmetric distributions, whereas Relvas and Paula (2016) developed an iterative process as well as diagnostic procedures in partially linear models with first order auto-regressive symmetric errors. More recently, Ferreira and Paula (2017) developed estimation and diagnostic procedures in skew-normal partially linear models.…”

Section: Introductionmentioning

confidence: 99%

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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