Browsing by Author "Bolfarine, H"

Now showing 1 - 9 of 9
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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 calibration under a student-t model
    (SPRINGER HEIDELBERG, 1998) Branco, M; Bolfarine, H; Iglesias, P
    In this paper we consider linear calibration problems in regressions models with independent errors distributed according to the Student-t distribution. The approach followed is Bayesian, thus, involving the need for the specification of prior distributions for the model parameters. It is shown that the problem is equivalent to considering an heteroscedastic regression model with an appropriate prior distributions on the model variances. By considering this alternative construction for the Student-t calibration model it is possible to use the Gibbs sampler to estimate the marginal posterior distributions. Simulation studies are reported which illustrate the performance of the approach proposed. An application to a data set analyzed by Smith and Corbett (1987) on measuring marathon courses is considered by using the approach developed in the paper.
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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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    Elliptical structural models
    (MARCEL DEKKER INC, 1996) ArellanoValle, RB; Bolfarine, H
    In this paper we consider structural measurement error models within the elliptical family of distributions. We consider dependent and independent elliptical models, each of which requires special treatment methodology. We discuss in each case estimation and hypothesis testing using maximum likelihood theory. As shown, most of the developments obtained under normal theory carries through to the dependent case. In the independent case, emphasis is placed on the t-distribution, an important member of the elliptical family. Correcting likelihood ratio statistics in both cases is also of major interest.
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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 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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    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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    Ultrastructural elliptical models
    (CANADIAN JOURNAL STATISTICS, 1996) ArellanoValle, RB; Bolfarine, H; VilcaLabra, F
    Dolby's (1976) ultrastructural model with no replications is investigated within the class of the elliptical distributions. General asymptotic results are given for the sample covariance matrix S in the presence of incidental parameters. These results are used to study the asymptotic behaviour of some estimators of the slope parameter, unifying and extending existing results in the literature. In particular, under some regularity conditions they are shown to be consistent and asymptotically normal. For the special case of the structural model, some asymptotic relative efficiencies are also reported which show that generalized least squares and the method of moment estimators can be highly inefficient under nonnormality.
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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.