Browsing by Author "Osorio, Felipe"

Now showing 1 - 6 of 6
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    Addressing non-normality in multivariate analysis using the t-distribution
    (2023) Osorio, Felipe; Galea Rojas, Manuel Jesús; Henríquez, Claudio; Arellano Valle, Reinaldo Boris
    The main aim of this paper is to propose a set of tools for assessing non-normality taking into consideration the class of multivariate t-distributions. Assuming second moment existence, we consider a reparameterized version of the usual t distribution, so that the scale matrix coincides with covariance matrix of the distribution. We use the local influence procedure and the Kullback–Leibler divergence measure to propose quantitative methods to evaluate deviations from the normality assumption. In addition, the possible non-normality due to the presence of both skewness and heavy tails is also explored. Our findings based on two real datasets are complemented by a simulation study to evaluate the performance of the proposed methodology on finite samples.
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    Assessment of local influence for the analysis of agreement
    (2019) Leal, Carla; Galea Rojas, Manuel Jesús; Osorio, Felipe
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    Bilinear Form Test: Theoretical Properties and Applications
    (2025) Gárate Barraza, Ángelo Fabián; Galea Rojas, Manuel Jesús; Osorio, Felipe; Pontificia Universidad Católica de Chile. Facultad de Matemáticas
    The present thesis investigates the Bilinear Form Test (BF Test) as a robust statistical tool for evaluating parameter constraints across various models. It examines the test's theoretical foundations, with a particular focus on its invariance under reparameterizations and its performance in finite-sample settings. By leveraging bilinear forms, the BF Test provides an alternative to likelihood-based methods, employing an asymptotic chi-squared distribution that simplifies hypothesis testing. Monte Carlo simulations and empirical applications—including its use in financial models like the Capital Asset Pricing Model (CAPM) and in Generalized Estimating Equations (GEE) for correlated data—demonstrate the method’s efficiency, robustness, and versatility. Key contributions of this work include a detailed exploration of the BF Test's theoretical properties, validation of its invariance across different model structures, and a comprehensive comparison with traditional testing approaches, alongside proposed extensions for future research.
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    Comparing two spatial variables with the probability of agreement
    (2024) Acosta Salazar, Jonathan Daniel; Vallejos, Ronny; Ellison, Aaron M.; Osorio, Felipe; de Castro, Mário
    Computing the agree ment betwee n 2 con tinuous sequences is of grea t interest in statistics when comparing 2 instruments or one instrument with a gold standard. The probability of agree ment quantifies the similarity between 2 variables of interest, and it is useful for determining what constitutes a practically important difference. In this article, we introduce a generalization of the PA for the treatment of spatial vari ables. Our proposal makes the PA dependent on the spatial lag. We establish the conditions for which the PA decays as a function of the distance lag for isotropic stationary and nonstationary spatial processes . Estimtion is addr essed through a first-order appr oxima tion that guarantees the asymp totic normality of the sample version of the PA. The sensitivity of the PA with respect to the covariance parame ters is studied for finite sample size. The new method is described and illustrated with real data involving autumnal changes in the green chromatic coordinate ( G cc ) , an index of “greeness ”that captures the phenological stage of tree leaves, is associ ated with carbon flux from econsys tems, and is estimated from repeated images of forest canopies.
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    Estimation in nonlinear mixed-effects models using heavy-tailed distributions
    (2012) Meza, Cristian; Osorio, Felipe; De la Cruz, Rolando
    Nonlinear mixed-effects models are very useful to analyze repeated measures data and are used in a variety of applications. Normal distributions for random effects and residual errors are usually assumed, but such assumptions make inferences vulnerable to the presence of outliers. In this work, we introduce an extension of a normal nonlinear mixed-effects model considering a subclass of elliptical contoured distributions for both random effects and residual errors. This elliptical subclass, the scale mixtures of normal (SMN) distributions, includes heavy-tailed multivariate distributions, such as Student-t, the contaminated normal and slash, among others, and represents an interesting alternative to outliers accommodation maintaining the elegance and simplicity of the maximum likelihood theory. We propose an exact estimation procedure to obtain the maximum likelihood estimates of the fixed-effects and variance components, using a stochastic approximation of the EM algorithm. We compare the performance of the normal and the SMN models with two real data sets.
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    The gradient test statistic for outlier detection in generalized estimating equations
    (2024) Osorio, Felipe; Garate, Angelo; Russo, Cibele M.
    We develop diagnostic tools for estimating equations, useful for the analysis of data with longitudinal structure. The gradient statistic introduced by Terrell (2002) is used to propose a case deletion measure, as well as a statistic for the detection of outlying observations using a mean -shift outlier model. The proposed methodology is illustrated with an example.