Browsing by Author "Arellano Valle, RB"

Now showing 1 - 16 of 16
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    A Gibbs sampling scheme to the product partition model: an application to change-point problems
    (PERGAMON-ELSEVIER SCIENCE LTD, 2003) Loschi, RH; Cruz, FRB; Iglesias, PL; Arellano Valle, RB
    This paper extends previous results for the classical product partition model applied to the identification of multiple change points in the means and variances of time series. Prior distributions for these two parameters and for the probability p that a change takes place at a particular period of time are considered and a new scheme based on Gibbs sampling to estimate the posterior relevances of the model is proposed. The resulting algorithm is applied to the analysis of two Brazilian stock market data. The computational experiments seem to indicate that the algorithm runs fast in common PC-like machines and it may be a useful tool for analyzing change-point problems.
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    A new class of skew-normal distributions
    (TAYLOR & FRANCIS INC, 2004) Arellano Valle, RB; Gomez, HW; Quintana, FA
    We introduce a new family of asymmetric normal distributions that contains Azzalini's skew-normal (SN) distribution as a special case. We study the main properties of this new family, showing in particular that it may be generated via mixtures on the SN asymmetry parameter when the mixing distribution is normal. This property provides a Bayesian interpretation of the new family.
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    Bartlett and Bartlett-type corrections for testing linear restrictions
    (ROUTLEDGE, 1999) Arellano Valle, RB; Ferrari, SLP; Cribari Neto, F
    This letter shows how to extend a number of published results on Bartlett and Bartlett-type corrections to likelihood ratio and score test for the test of linear restrictions in regression models. A few applications and simulation results are also presented.
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    Bayesian analysis of the calibration problem under elliptical distributions
    (ELSEVIER SCIENCE BV, 2000) Branco, M; Bolfarine, H; Iglesias, P; Arellano Valle, RB
    In this paper we discuss calibration problems under dependent and independent elliptical family of distributions. In the dependent case, it is shown that the posterior distribution of the quantity of interest is robust with respect to the distributions in the elliptical family. In particular, the results obtained by Hoadley (1970. J. Amer. Statist. 65, 356-369) showing that the inverse estimator is a Bayes estimator under normal models with a Student-t prior also holds under the dependent elliptical family of distributions. In the independent case, the use of the elliptical family allows the consideration of models which provide protection against possible outliers in the data. The multivariate calibration problem is also considered, where some results given in Brown (1993. Measurement, Regression and Calibration. Oxford University Press, Oxford) are extended. Finally, the results of the paper are applied to a real data problem, showing that the Student-t model can be a valid alternative to normality. (C) 2000 Elsevier Science B.V. All rights reserved.
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    Bayesian inference in spherical linear models: robustness and conjugate analysis
    (ELSEVIER INC, 2006) Arellano Valle, RB; del Pino, G; Iglesias, P
    The early work of Zellner on the multivariate Student-t linear model has been extended to Bayesian inference for linear models with dependent non-normal error terms, particularly through various papers by Osiewalski, Steel and coworkers. This article provides a full Bayesian analysis for a spherical linear model. The density generator of the spherical distribution is here allowed to depend both on the precision parameter phi and on the regression coefficients beta. Another distinctive aspect of this paper is that proper priors for the precision parameter are discussed.
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    Bayesian sensitivity analysis in elliptical linear regression models
    (ELSEVIER SCIENCE BV, 2000) Arellano Valle, RB; Galea Rojas, M; Zuazola, PI
    Bayesian influence measures for linear regression models have been developed mostly for normal regression models with noninformative prior distributions for the unknown parameters. In this work we extend existing results in several directions. First, we review influence measures for the ordinary normal regression model under conjugate prior distributions in unified framework. Second, we consider elliptical regression models with noninformative prior distributions for the model parameters and investigate the influence of a given subset of observations on the posterior distributions of the location and scale parameters. We found that these influence measures are Bayesian versions of classical counterparts to identify outliers or influential observations. Finally, we show that departures from normality within the multivariate elliptical family of distributions only affect the posterior distribution of the scale parameter. (C) 2000 Elsevier Science B.V. All rights reserved.
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    Definition and probabilistic properties of skew-distributions
    (ELSEVIER, 2002) Arellano Valle, RB; del Pino, G; San Martin, E
    The univariate, and multivariate skew-normal distributions have a number of intriguing properties. It is shown here that these hold for a general class of distributions, defined in terms of independence conditions on signs and absolute values. For this class, two stochastic representations become equivalent, one using conditioning on the positivity of a random vector and the other employing a vector of absolute values. General methods for computing moments and for obtaining the density function of a general skew-distribution are given. The case of spherical and elliptical distributions is briefly discussed. (C) 2002 Published by Elsevier Science B.V.
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    Elliptical functional models
    (ACADEMIC PRESS INC, 1998) Vilca Labra, F; Arellano Valle, RB; Bolfarine, H
    In this paper, functional models with not replications are investigated within the class of the elliptical distributions. Emphasis is placed on the special case of the Student-t distribution. Main results encompasses consistency and asymptotic normality of the maximum likelihood estimators. Due to the presence of incidental parameters. standard maximum likelihood methodology cannot be used to obtain the main results, which require extensions of some existing results related to elliptical distributions. Asymptotic relative efficiencies an reported which show that the generalized least squares estimator can be highly inefficient when compared with the maximum likelihood estimator under nonnormality. (C) 1998 Academc Press.
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    Measurement error models with nonconstant covariance matrices
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2002) Arellano Valle, RB; Bolfarine, H; Gasco, L
    In this paper we consider measurement error models when the observed random vectors are independent and have mean vector and covariance matrix changing with each observation. The asymptotic behavior of the sample mean vector and the sample covariance matrix are studied for such models. Using the derived results, we study the case of the elliptical multiplicative error-in-variables models, providing formal justification for the asymptotic distribution of consistent slope parameter estimators. The model considered extends a normal model previously considered in the literature. Asymptotic relative efficiencies comparing several estimators are also reported. (C) 2002 Elsevier Science (USA).
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    On fundamental skew distributions
    (ELSEVIER INC, 2005) Arellano Valle, RB; Genton, MG
    A new class of multivariate skew-normal distributions, fundamental skew-normal distributions and their canonical version, is developed. It contains the product of independent univariate skew-normal distributions as a special case. Stochastic representations and other main properties of the associated distribution theory of linear and quadratic forms are considered. A unified procedure for extending this class to other families of skew distributions such as the fundamental skew-symmetric, fundamental skew-elliptical, and fundamental skew-spherical class of distributions is also discussed. (c) 2004 Published by Elsevier Inc.
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    On score tests in structural regression models
    (GORDON BREACH SCI PUBL LTD, 1998) Arellano Valle, RB; Bolfarine, H
    In this paper we investigate the distribution of the score statistics for testing hypothesis about the slope parameter in a simple structural regression model. It is shown that for two of the most common ways of making the model identifiable, the distribution of the score statistics under the null hypothesis can be found exactly as an increasing function of an F statistics, providing thus exact test statistics for testing hypothesis about the slope parameter. It is unknown if such results hold in general for the likelihood ratio statistics. Use is made of orthogonal parameterizations obtained in the literature. Generalizations to an elliptical structural model are also investigated.
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    On some characterizations of spherical distributions
    (ELSEVIER SCIENCE BV, 2001) Arellano Valle, RB
    A characterization for each spherical (symmetric) distribution is presented. Moreover, a representation as a scale mixture of the Pearson type II distribution is obtained. Some extensions to the multivariate case are also considered. (C) 2001 Elsevier Science BN, All rights reserved.
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    Predictivistic characterizations of multivariate student-t models
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2003) Loschi, RH; Iglesias, PL; Arellano Valle, RB
    De Finetti style theorems characterize models (predictive distributions) as mixtures of the likelihood function and the prior distribution, beginning from some judgment of invariance about observable quantities. The likelihood function generally has its functional form identified from invariance assumptions only. However, we need additional conditions on observable quantities (typically, assumptions on conditional expectations) to identify the prior distribution. In this paper, we consider some well-known invariance assumptions and establish additional conditions on observable quantities in order to obtain a predictivistic characterization of the multivariate and matrix-variate Student-t distributions as well as for the Student-t linear model. As a byproduct, a characterization for the Pearson type 11 distribution is provided. (C) 2003 Elsevier Science (USA). All rights reserved.
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    Skew normal measurement error models
    (ELSEVIER INC, 2005) Arellano Valle, RB; Ozan, S; Bolfarine, H; Lachos, VH
    In this paper we define a class of skew normal measurement error models, extending usual symmetric normal models in order to avoid data transformation. The likelihood function of the observed data is obtained, which can be maximized by using existing statistical software. Inference on the parameters of interest can be approached by using the observed information matrix, which can also be computed by using existing statistical software, such as the Ox program. Bayesian inference is also discussed for the family of asymmetric models in terms of invariance with respect to the symmetric normal distribution showing that early results obtained for the normal distribution also holds for the asymmetric family. Results of a simulation study and an analysis of a real data set analysis are provided. (c) 2004 Elsevier Inc. All rights reserved.
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    Statistical inference for a general class of asymmetric distributions
    (ELSEVIER SCIENCE BV, 2005) Arellano Valle, RB; Gomez, HW; Quintana, FA
    We consider a general class of asymmetric univariate distributions depending on a real-valued parameter a, which includes the entire family of univariate symmetric distributions as a special case. We discuss the connections between our proposal and other families of skew distributions that have been studied in the statistical literature. A key element in the construction of such families of distributions is that they can be stochastically represented as the product of two independent random variables. From this representation we can readily derive theoretical properties, easy-to-implement simulation schemes as well as extensions to the multivariate case. We also study statistical inference for this class based on the method of moments and maximum likelihood. We give special attention to the skew-power exponential distribution, but other cases like the skew-t distribution are also considered. Finally, the statistical methods are illustrated with 3 examples based on real datasets. (C) 2004 Elsevier B.V. All rights reserved.
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    Weak nondifferential measurement error models
    (ELSEVIER SCIENCE BV, 1998) Bolfarine, H; Arellano Valle, RB
    In this note we consider the class of weak nondifferential measurement error models, which as a special case, contains the class of the nondifferential measurement error models (Carroll et al., 1995). Examples of measurement error models which are in this class and that are not nondifferential models are considered. Only simple linear regression models are used to illustrate the approach but as indicated it can be generalized to more complex situations. Some characterization results are also reported. (C) 1998 Elsevier Science B.V. All rights reserved.