Browsing by Author "Arellano-Valle, Reinaldo B."

Now showing 1 - 18 of 18
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    2021 International Statistical Institute Mahalanobis Award: A Tribute to Heleno Bolfarine
    (2021) Ruggeri, Fabrizio; Bolfarine, Henrique; Bazan, Jorge Luis; Arellano-Valle, Reinaldo B.; Lachos Davila, Victor Hugo; Castro, Mario
    The Government of India sponsors the Mahalanobis International Award, which, managed by the International Statistical Institute, is presented every other year at the International Statistical Institute World Statistics Congress. The Mahalanobis Award recognises an individual for lifetime achievements in statistics in a developing country or region. This article celebrates the 2021 winner, Prof. Heleno Bolfarine, who, unfortunately, passed away a few days before the award ceremony.
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    A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers
    (2022) Bevilacqua, Moreno; Caamano-Carrillo, Christian; Arellano-Valle, Reinaldo B.; Gomez, Camilo
    In this paper, we propose a new class of non-Gaussian random fields named two-piece random fields. The proposed class allows to generate random fields that have flexible marginal distributions, possibly skewed and/or heavy-tailed and, as a consequence, has a wide range of applications. We study the second-order properties of this class and provide analytical expressions for the bivariate distribution and the associated correlation functions. We exemplify our general construction by studying two examples: two-piece Gaussian and two-piece Tukey-h random fields. An interesting feature of the proposed class is that it offers a specific type of dependence that can be useful when modeling data displaying spatial outliers, a property that has been somewhat ignored from modeling viewpoint in the literature for spatial point referenced data. Since the likelihood function involves analytically intractable integrals, we adopt the weighted pairwise likelihood as a method of estimation. The effectiveness of our methodology is illustrated with simulation experiments as well as with the analysis of a georeferenced dataset of mean temperatures in Middle East.
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    A flexible two-piece normal dynamic linear model
    (2023) Aliverti, Emanuele; Arellano-Valle, Reinaldo B.; Kahrari, Fereshteh; Scarpa, Bruno
    We construct a flexible dynamic linear model for the analysis and prediction of multivariate time series, assuming a two-piece normal initial distribution for the state vector. We derive a novel Kalman filter for this model, obtaining a two components mixture as predictive and filtering distributions. In order to estimate the covariance of the error sequences, we develop a Gibbs-sampling algorithm to perform Bayesian inference. The proposed approach is validated and compared with a Gaussian dynamic linear model in simulations and on a real data set.
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    A multivariate modified skew-normal distribution
    (2024) Mondal, Sagnik; Arellano-Valle, Reinaldo B.; Genton, Marc G.
    We introduce a multivariate version of the modified skew-normal distribution, which contains the multivariate normal distribution as a special case. Unlike the Azzalini multivariate skew-normal distribution, this new distribution has a nonsingular Fisher information matrix when the skewness parameters are all zero, and its profile log-likelihood of the skewness parameters is always a non-monotonic function. We study some basic properties of the proposed family of distributions and present an expectation-maximization (EM) algorithm for parameter estimation that we validate through simulation studies. Finally, we apply the proposed model to the univariate frontier data and to a trivariate wind speed data, and compare its performance with the Azzalini skew-normal model.
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    An invariance property of quadratic forms in random vectors with a selection distribution, with application to sample variogram and covariogram estimators
    (2010) Arellano-Valle, Reinaldo B.; Genton, Marc G.
    We study conditions under which an invariance property holds for the class of selection distributions. First, we consider selection distributions arising from two uncorrelated random vectors. In that setting, the invariance holds for the so-called C-class and for elliptical distributions. Second, we describe the invariance property for selection distributions arising from two correlated random vectors. The particular case of the distribution of quadratic forms and its invariance, under various selection distributions, is investigated in more details. We describe the application of our invariance results to sample variogram and covariogram estimators used in spatial statistics and provide a small simulation study for illustration. We end with a discussion about other applications, for example such as linear models and indices of temporal/spatial dependence.
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    Comparing growth curves with asymmetric heavy-tailed errors: Application to the southern blue whiting (Micromesistius australis)
    (2014) Contreras-Reyes, Javier E.; Arellano-Valle, Reinaldo B.; Mariella Canales, T.
    Von Bertalanffy growth models (VBGMs) have been used in several studies of age, growth and natural mortality. Assuming that the residuals about this growth model are normal is, however, questionable. Here, we assume that these residuals are heteroskedastic and follow a log-skew-t distribution, a flexible distribution that is asymmetric and heavy-tailed. We apply the proposed methodology to length-at-age data for the southern blue whiting (Micromesistius australis) collected from Chilean austral continental waters between 1997 and 2010. The estimates of the VBGM parameters were L-infinity = 57.042 cm, K = 0.173 yr(-1), t(0) = -2.423 yr for males, and L-infinity= 61.318 cm, K = 0.163 yr(-1), t(0) = -2.253 yr for females. The BIC criteria suggest that females grow significantly faster than males and that length-at-age for both sexes exhibits significant heteroskedasticity and asymmetry. (C) 2014 Elsevier B.V. All rights reserved.
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    Flexible cloglog links for binomial regression models as an alternative for imbalanced medical data
    (2023) Alves, Jessica S. B.; Bazan, Jorge L.; Arellano-Valle, Reinaldo B.
    The complementary log-log link was originally introduced in 1922 to R. A. Fisher, long before the logit and probit links. While the last two links are symmetric, the complementary log-log link is an asymmetrical link without a parameter associated with it. Several asymmetrical links with an extra parameter were proposed in the literature over last few years to deal with imbalanced data in binomial regression (when one of the classes is much smaller than the other); however, these do not necessarily have the cloglog link as a special case, with the exception of the link based on the generalized extreme value distribution. In this paper, we introduce flexible cloglog links for modeling binomial regression models that include an extra parameter associated with the link that explains some unbalancing for binomial outcomes. For all cases, the cloglog is a special case or the reciprocal version loglog link is obtained. A Bayesian Markov chain Monte Carlo inference approach is developed. Simulations study to evaluate the performance of the proposed algorithm is conducted and prior sensitivity analysis for the extra parameter shows that a uniform prior is the most convenient for all models. Additionally, two applications in medical data (age at menarche and pulmonary infection) illustrate the advantages of the proposed models.
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    Kullback-Leibler Divergence Measure for Multivariate Skew-Normal Distributions
    (2012) Contreras-Reyes, Javier E.; Arellano-Valle, Reinaldo B.
    The aim of this work is to provide the tools to compute the well-known Kullback-Leibler divergence measure for the flexible family of multivariate skew-normal distributions. In particular, we use the Jeffreys divergence measure to compare the multivariate normal distribution with the skew-multivariate normal distribution, showing that this is equivalent to comparing univariate versions of these distributions. Finally, we applied our results on a seismological catalogue data set related to the 2010 Maule earthquake. Specifically, we compare the distributions of the local magnitudes of the regions formed by the aftershocks.
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    Likelihood Based Inference and Bias Reduction in the Modified Skew-t-Normal Distribution
    (2023) Arrue, Jaime; Arellano-Valle, Reinaldo B.; Calderin-Ojeda, Enrique; Venegas, Osvaldo; Gomez, Hector W.
    In this paper, likelihood-based inference and bias correction based on Firth's approach are developed in the modified skew-t-normal (MStN) distribution. The latter model exhibits a greater flexibility than the modified skew-normal (MSN) distribution since it is able to model heavily skewed data and thick tails. In addition, the tails are controlled by the shape parameter and the degrees of freedom. We provide the density of this new distribution and present some of its more important properties including a general expression for the moments. The Fisher's information matrix together with the observed matrix associated with the log-likelihood are also given. Furthermore, the non-singularity of the Fisher's information matrix for the MStN model is demonstrated when the shape parameter is zero. As the MStN model presents an inferential problem in the shape parameter, Firth's method for bias reduction was applied for the scalar case and for the location and scale case.
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    Multiplicative errors-in-variables beta regression
    (2023) Carrasco, Jalmar M. F.; Ferrari, Silvia L. P.; Arellano-Valle, Reinaldo B.
    This paper deals with beta regression models with a covariate that is not directly observed; instead, it is replaced by a surrogate covariate that underpredicts its actual value. We propose a multiplicative errors-invariables model tailored for this situation and develop calibration regression and pseudo-likelihood-based inference for the unknown parameters. The impact of ignoring the measurement error and the performance of the inference methods are evaluated through simulations and a real data illustration.
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    Multivariate unified skew-t distributions and their properties
    (2024) Wang, Kesen; Karling, Maicon J.; Arellano-Valle, Reinaldo B.; Genton, Marc G.
    The unified skew-t (SUT) is a flexible parametric multivariate distribution that accounts for skewness and heavy tails in the data. A few of its properties can be found scattered in the literature or in a parameterization that does not follow the original one for unified skew- normal (SUN) distributions, yet a systematic study is lacking. In this work, explicit properties of the multivariate SUT distribution are presented, such as its stochastic representations, moments, SUN-scale mixture representation, linear transformation, additivity, marginal distribution, canonical form, quadratic form, conditional distribution, change of latent dimensions, Mardia measures of multivariate skewness and kurtosis, and non-identifiability issue. These results are given in a parameterization that reduces to the original SUN distribution as a sub- model, hence facilitating the use of the SUT for applications. Several models based on the SUT distribution are provided for illustration.
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    On a new type of Birnbaum-Saunders models and its inference and application to fatigue data
    (2020) Arrue, Jaime; Arellano-Valle, Reinaldo B.; Gomez, Hector W.; Leiva, Victor
    The Birnbaum-Saunders distribution is a widely studied model with diverse applications. Its origins are in the modeling of lifetimes associated with material fatigue. By using a motivating example, we show that, even when lifetime data related to fatigue are modeled, the Birnbaum-Saunders distribution can be unsuitable to fit these data in the distribution tails. Based on the nice properties of the Birnbaum-Saunders model, in this work, we use a modified skew-normal distribution to construct such a model. This allows us to obtain flexibility in skewness and kurtosis, which is controlled by a shape parameter. We provide a mathematical characterization of this new type of Birnbaum-Saunders distribution and then its statistical characterization is derived by using the maximum-likelihood method, including the associated information matrices. In order to improve the inferential performance, we correct the bias of the corresponding estimators, which is supported by a simulation study. To conclude our investigation, we retake the motivating example based on fatigue life data to show the good agreement between the new type of Birnbaum-Saunders distribution proposed in this work and the data, reporting its potential applications.
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    On the non-identifiability of unified skew-normal distributions
    (2023) Wang, Kesen; Arellano-Valle, Reinaldo B.; Azzalini, Adelchi; Genton, Marc G.
    We investigate the non-identifiability of the multivariate unified skew-normal distribution under permutation of its latent variables. We show that the non-identifiability issue also holds with other parameterizations and extends to the family of unified skew-elliptical distributions and more generally to selection distributions. We provide several suggestions to make the unified skew-normal model identifiable and describe various sub-models that are identifiable.
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    Robust finite mixture modeling of multivariate unrestricted skew-normal generalized hyperbolic distributions
    (2019) Maleki, Mohsen; Wraith, Darren; Arellano-Valle, Reinaldo B.
    In this paper, we introduce an unrestricted skew-normal generalized hyperbolic (SUNGH) distribution for use in finite mixture modeling or clustering problems. The SUNGH is a broad class of flexible distributions that includes various other well-known asymmetric and symmetric families such as the scale mixtures of skew-normal, the skew-normal generalized hyperbolic and its corresponding symmetric versions. The class of distributions provides a much needed unified framework where the choice of the best fitting distribution can proceed quite naturally through either parameter estimation or by placing constraints on specific parameters and assessing through model choice criteria. The class has several desirable properties, including an analytically tractable density and ease of computation for simulation and estimation of parameters. We illustrate the flexibility of the proposed class of distributions in a mixture modeling context using a Bayesian framework and assess the performance using simulated and real data.
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    Some properties of the unified skew-normal distribution
    (2022) Arellano-Valle, Reinaldo B.; Azzalini, Adelchi
    For the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present contribution aims at filling some of the missing gaps. Specifically, the moments up to the fourth order are obtained, and from here the expressions of the Mardia's measures of multivariate skewness and kurtosis. Other results concern the property of log-concavity of the distribution, closure with respect to conditioning on intervals, and a possible alternative parameterization.
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    Student-t censored regression model: properties and inference
    (2012) Arellano-Valle, Reinaldo B.; Castro, Luis M.; Gonzalez-Farias, Graciela; Munoz-Gajardo, Karla A.
    In statistical analysis, particularly in econometrics, it is usual to consider regression models where the dependent variable is censored (limited). In particular, a censoring scheme to the left of zero is considered here. In this article, an extension of the classical normal censored model is developed by considering independent disturbances with identical Student-t distribution. In the context of maximum likelihood estimation, an expression for the expected information matrix is provided, and an efficient EM-type algorithm for the estimation of the model parameters is developed. In order to know what type of variables affect the income of housewives, the results and methods are applied to a real data set. A brief review on the normal censored regression model or Tobit model is also presented.
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    Sub-dimensional Mardia measures of multivariate skewness and kurtosis
    (2022) Chowdhury, Joydeep; Dutta, Subhajit; Arellano-Valle, Reinaldo B.; Genton, Marc G.
    The Mardia measures of multivariate skewness and kurtosis summarize the respective characteristics of a multivariate distribution with two numbers. However, these mea-sures do not reflect the sub-dimensional features of the distribution. Consequently, test-ing procedures based on these measures may fail to detect skewness or kurtosis present in a sub-dimension of the multivariate distribution. We introduce sub-dimensional Mar-dia measures of multivariate skewness and kurtosis, and investigate the information they convey about all sub-dimensional distributions of some symmetric and skewed families of multivariate distributions. The maxima of the sub-dimensional Mardia measures of multivariate skewness and kurtosis are considered, as these reflect the maximum skewness and kurtosis present in the distribution, and also allow us to identify the sub-dimension bearing the highest skewness and kurtosis. Asymptotic distributions of the vectors of sub-dimensional Mardia measures of multivariate skewness and kurtosis are derived, based on which testing procedures for the presence of skewness and of deviation from Gaussian kurtosis are developed. The performances of these tests are compared with some existing tests in the literature on simulated and real datasets. (c) 2022 Elsevier Inc. All rights reserved.
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    Tractable Bayes of skew-elliptical link models for correlated binary data
    (2023) Zhang, Zhongwei; Arellano-Valle, Reinaldo B.; Genton, Marc G.; Huser, Raphael
    Correlated binary response data with covariates are ubiquitous in longitudinal or spatial studies. Among the existing statistical models, the most well-known one for this type of data is the multivariate probit model, which uses a Gaussian link to model dependence at the latent level. However, a symmetric link may not be appropriate if the data are highly imbalanced. Here, we propose a multivariate skew-elliptical link model for correlated binary responses, which includes the multivariate probit model as a special case. Furthermore, we perform Bayesian inference for this new model and prove that the regression coefficients have a closed-form unified skew-elliptical posterior with an elliptical prior. The new methodology is illustrated by an application to COVID-19 data from three different counties of the state of California, USA. By jointly modeling extreme spikes in weekly new cases, our results show that the spatial dependence cannot be neglected. Furthermore, the results also show that the skewed latent structure of our proposed model improves the flexibility of the multivariate probit model and provides a better fit to our highly imbalanced dataset.