Browsing by Author "Lachos, Victor H."

Now showing 1 - 7 of 7
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    Bayesian Modeling of Censored Partial Linear Models using Scale-Mixtures of Normal Distributions
    (AMER INST PHYSICS, 2012) Castro, Luis M.; Lachos, Victor H.; Ferreira, Guillermo P.; Arellano Valle, Reinaldo B.; Stern, JM; Lauretto, MD; Polpo, A; Diniz, MA
    Regression models where the dependent variable is censored (limited) are usually considered in statistical analysis. Particularly, the case of a truncation to the left of zero and a normality assumption for the error terms is studied in detail by [1] in the well known Tobit model. In the present article, this typical censored regression model is extended by considering a partial linear model with errors belonging to the class of scale mixture of normal distributions. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. The likelihood function is utilized to compute not only some Bayesian model selection measures but also to develop Bayesian case-deletion influence diagnostics based on the q-divergence measures. We evaluate the performances of the proposed methods with simulated data. In addition, we present an application in order to know what type of variables affect the income of housewives.
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    Influence diagnostics for censored regression models with autoregressive errors
    (2018) Schumacher, Fernanda L.; Lachos, Victor H.; Vilca‐Labra, Filidor E.; Castro Cepero, Luis Mauricio
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    LIKELIHOOD BASED INFERENCE FOR SKEW-NORMAL INDEPENDENT LINEAR MIXED MODELS
    (STATISTICA SINICA, 2010) Lachos, Victor H.; Ghosh, Pulak; Arellano Valle, Reinaldo B.
    Linear mixed models with normally distributed response are routinely used in longitudinal data. However, the accuracy of the assumed normal distribution is crucial for valid inference of the parameters We present a new class of asymmetric linear mixed models that provides for an efficient estimation of the parameters in the analysis of longitudinal data We assume that, marginally. the random effects follow a multivariate skew-normal/independent distribution (Branco and Dey (2001)) and that the random errors follow a symmetric normal/independent distribution (Lange and Sinsheimer (1993)), providing an appealing robust alternative to the usual symmetric normal distribution in linear mixed models Specific distributions examined include the skew-normal, the skew-t, the skew-slash, and the skew-contaminated normal distribution We present all efficient EM-type algorithm algorithm for the computation of maximum likelihood estimation of parameters The technique for the prediction of future responses under this class of distributions is also investigated The methodology is illustrated through an applications to Framingham cholesterol data and a. simulation study.
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    Likelihood-based inference for linear mixed-effects models using the generalized hyperbolic distribution
    (John Wiley and Sons Inc, 2023) Lachos, Victor H.; Galea Rojas, Manuel Jesús; Zeller, Camila; Prates, Marcos O.
    In this paper, we develop statistical methodology for the analysis of data under nonnormal distributions, in the context of mixed effects models. Although the multivariate normal distribution is useful in many cases, it is not appropriate, for instance, when the data come from skewed and/or heavy-tailed distributions. To analyse data with these characteristics, in this paper, we extend the standard linear mixed effects model, considering the family of generalized hyperbolic distributions. We propose methods for statistical inference based on the likelihood function, and due to its complexity, the EM algorithm is used to find the maximum likelihood estimates with the standard errors and the exact likelihood value as a by-product. We use simulations to investigate the asymptotic properties of the expectation-maximization algorithm (EM) estimates and prediction accuracy. A real example is analysed, illustrating the usefulness of the proposed methods.
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    Moments of the doubly truncated selection elliptical distributions with emphasis on the unified multivariate skew-t distribution
    (ELSEVIER INC, 2022) Galarza, Christian E.; Matos, Larissa A.; Castro, Luis M.; Lachos, Victor H.
    In this paper, we compute doubly truncated moments for the selection elliptical class of distributions, including some multivariate asymmetric versions of well-known elliptical distributions, such as the normal, Student's t, slash, among others. We address the moments for doubly truncated members of this family, establishing neat formulation for high-order moments and its first two moments. We establish sufficient and necessary conditions for the existence of these truncated moments. Further, we propose optimized methods to handle the extreme setting of the parameters, partitions with almost zero volume or no truncation, which are validated with numerical studies. All results have been particularized to the unified skew-t distribution, a complex multivariate asymmetric heavy-tailed distribution which includes the extended skew-t, extended skew-normal, skew-t, and skew-normal distributions as particular and limiting cases. (C) 2021 Elsevier Inc. All rights reserved.
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    Partially linear censored regression models using heavy-tailed distributions: A Bayesian approach
    (ELSEVIER SCIENCE BV, 2014) Castro, Luis M.; Lachos, Victor H.; Ferreira, Guillermo P.; Arellano Valle, Reinaldo B.
    Linear regression models where the response variable is censored are often considered in statistical analysis. A parametric relationship between the response variable and covariates and normality of random errors are assumptions typically considered in modeling censored responses. In this context, the aim of this paper is to extend the normal censored regression model by considering on one hand that the response variable is linearly dependent on some covariates whereas its relation to other variables is characterized by nonparametric functions, and on the other hand that error terms of the regression model belong to a class of symmetric heavy-tailed distributions capable of accommodating outliers and/or influential observations in a better way than the normal distribution. We achieve a fully Bayesian inference using pth-degree spline smooth functions to approximate the nonparametric functions. The likelihood function is utilized to compute not only some Bayesian model selection measures but also to develop Bayesian case-deletion influence diagnostics based on the q-divergence measures. The newly developed procedures are illustrated with an application and simulated data. (C) 2013 Elsevier B.V. All rights reserved.
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    The skew-t censored regression model: parameter estimation via an EM-type algorithm
    (KOREAN STATISTICAL SOC, 2022) Lachos, Victor H.; Bazan, Jorge L.; Castro, Luis M.; Park, Jiwon
    The skew-t distribution is an attractive family of asymmetrical heavy-tailed densities that includes the normal, skew-normal and Student's-t distributions as special cases. In this work, we propose an EM-type algorithm for computing the maximum likelihood estimates for skew-t linear regression models with censored response. In contrast with previous proposals, this algorithm uses analytical expressions at the E-step, as opposed to Monte Carlo simulations. These expressions rely on formulas for the mean and variance of a truncated skew-t distribution, and can be computed using the R library MomTrunc. The standard errors, the prediction of unobserved values of the response and the log-likelihood function are obtained as a by-product. The proposed methodology is illustrated through the analyses of simulated and a real data application on Letter-Name Fluency test in Peruvian students.