Browsing by Author "Galea Rojas, Manuel Jesús"

Now showing 1 - 20 of 55
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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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    Analysis of local influence in geostatistics using Student's t-distribution
    (2014) Assumpcao, R.; Uribe Opazo, M.; Galea Rojas, Manuel Jesús
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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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    Bayesian inference for the pairwise probability of agreement using data from several measurement systems
    (Taylor & Francis Inc, 2021) Castro, Mario de; Galea Rojas, Manuel Jesús
    This article deals with Bayesian inference in the comparison of measurement systems. Agreement between two systems can be evaluated using data from several measurement systems and using only data from the two systems being compared. With a measurement error model for replicated observations and the probability of agreement to compare measurement systems, we develop methods to compare measurement systems with either homoscedastic or heteroscedastic measurement errors under the Bayesian paradigm via Markov chain Monte Carlo methods. A graphical tool is described to check model adequacy. The methodology developed in the article is illustrated using a real dataset and through simulations.
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    Bayesian inference in measurement error models for replicated data
    (2013) De Castro, Mario; Bolfarine, Heleno; Galea Rojas, Manuel Jesús
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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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    Birnbaum-Saunders quantile regression and its diagnostics with application to economic data
    (2021) Sánchez, L.; Leiva, Víctor; Galea Rojas, Manuel Jesús; Saulo, H.
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    Birnbaum-Saunders quantile regression models with application to spatial data
    (2020) Sánchez, Luis; Leiva, Víctor; Galea Rojas, Manuel Jesús; Saulo, Helton
    In the present paper, a novel spatial quantile regression model based on the Birnbaum-Saunders distribution is formulated. This distribution has been widely studied and applied in many fields. To formulate such a spatial model, a parameterization of the multivariate Birnbaum-Saunders distribution, where one of its parameters is associated with the quantile of the respective marginal distribution, is established. The model parameters are estimated by the maximum likelihood method. Finally, a data set is applied for illustrating the formulated model.
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    Case-deletion diagnostics for spatial linear mixed models
    (2018) De Bastiani, Fernanda; Uribe Opazo, M. A.; Galea Rojas, Manuel Jesús; Cysneiros, A. H. M. A.
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    Diagnostic for Volatility and Local Influence Analysis for the Vasicek Model
    (2025) Galea Rojas, Manuel Jesús; Molina Núñez, Alonso Maximiliano; Beaudry, Isabelle S.
    The Ornstein–Uhlenbeck process is widely used in modeling biological systems and, in financial engineering, is commonly employed to describe the dynamics of interest rates, currency exchange rates, and asset price volatilities. As in any stochastic model, influential observations, such as outliers, can significantly influence the accuracy of statistical analysis and the conclusions we draw from it. Identifying atypical data is, therefore, an essential step in any statistical analysis. In this work, we explore a set of methods called local influence, which helps us understand how small changes in the data or model can affect an analysis. We focus on deriving local influence methods for models that predict interest or currency exchange rates, specifically the stochastic model called the Vasicek model. We develop and implement local influence diagnostic techniques based on likelihood displacement, assessing the impact of the perturbation of the variance and the response. We also introduce a novel and simple way to test whether the model’s variability stays constant over time based on the Gradient test. The purpose of these methods is to identify potential risks of reaching incorrect conclusions from the model, such as the inaccurate prediction of future interest rates. Finally, we illustrate the methodology using the monthly exchange rate between the US dollar and the Swiss franc over a period exceeding 20 years and assess the performance through a simulation study.
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    Diagnostics in Birnbaum-Saunders accelerated life models with an application to fatigue data
    (2014) Leiva, V.; Rojas, E.; Galea Rojas, Manuel Jesús; Sanhueza, A.
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    Elliptical linear mixed models with a covariate subject to measurement error
    (2020) Borssoi, J. A.; Paula, G. A.; Galea Rojas, Manuel Jesús
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    Fitting time-varying parameters to astronomical time series
    (2022) Soto Vásquez, Darlin Macarena; Motta, Giovanni; Galea Rojas, Manuel Jesús; Pontificia Universidad Católica de Chile. Facultad de Matemáticas
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    Gaussian spatial linear model of soybean yield using bootstrap methods
    (2018) Dalposso, Gustavo H.; Uribe-Opazo, Miguel A.; Johann, Jerry A.; Galea Rojas, Manuel Jesús; De Bastiani, Fernanda
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    Gaussian spatial linear models with repetitions: An application to soybean productivity
    (2017) De Bastiani, F.; Galea Rojas, Manuel Jesús; Cysneiros, A.; Uribe, M.
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    Generalized tobit models : diagnostics and application in econometrics
    (2018) Barros, Michelli; Galea Rojas, Manuel Jesús; Leiva, Víctor; Santos Neto, Manoel
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    Geostatistical modeling of soybean yield and soil chemical attributes using spatial bootstrap
    (2019) Dalposso, Gustavo H.; Uribe-Opazo, Miguel A.; Johann, Jerry A.; Bastiani, Fernanda de; Galea Rojas, Manuel Jesús
    The goal of this study was to use the spatial bootstrap method to model the spatial dependence structure of soybean yield and soil chemical attributes in an agricultural area. The study involved developing confidence intervals in probability plots to determine the probability distributions assumed by the data; determine the empirical distributions of the semivariances and model parameters, allowing to obtain statistics and confidence intervals; and to construct maps for the variables. The quantile-quantile plots indicated that the data follows a normal distribution. The confidence intervals for the semivariances helped to model the spatial dependence structure, and the descriptive statistics of the bootstrap replicates of the model parameters allowed to test the consistency of the estimates. The soil chemical attributes (calcium, potassium, and organic matter) were at levels suitable for soybean cultivation. However, the pH was below the ideal range in most of the study area, and water stress during cultivation decreased the mean yield. Therefore, according to the results, a recommendation to the farmer is to correct the soil pH to increase the yield.
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    Global and local diagnostic analytics for a geostatistical model based on a new approach to quantile regression
    (Springer, 2020) Leiva, Victor; Sánchez, Luis; Galea Rojas, Manuel Jesús; Saulo, Helton
    Data with spatial dependence are often modeled by geoestatistical tools. In spatial regression, the mean response is described using explanatory variables with georeferenced data. This modeling frequently considers Gaussianity assuming the response follows a symmetric distribution. However, when this assumption is not satisfied, it is useful to suppose distributions with the same asymmetric behavior of the data. This is the case of the Birnbaum-Saunders (BS) distribution, which has been considered in different areas and particularly in environmental sciences due to its theoretical arguments. We propose a geostatistical model based on a new approach to quantile regression considering the BS distribution. Global and local diagnostic analytics are derived for this model. The estimation of model parameters and its local influence are conducted by the maximum likelihood method. Global influence is based on the Cook distance and it is compared to local influence, in both cases to detect influential observations, whose detection and removal can modify the conclusions of a study. We illustrate the proposed methodology applying it to environmental data, which shows this situation changing the conclusions after removing potentially influential observations. A comparison with Gaussian spatial regression is conducted.
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    Gold Standard in selection of rainfall forecasting models for soybean crops region
    (Southern Cross Publishing, 2022) Oliveira, Marcio Paulo de; Uribe-Opazo, Miguel Ángel; Galea Rojas, Manuel Jesús; Johann, Jerry Adriani
    Rainfall data forecasting is essential in agricultural sciences due to impacts caused by water excess or deficit on crop growth. Our study aimed to develop a method to select rainfall forecast models using references with negligible error denoted as the gold standard. To this end, we used forecasting models from national centers such as Canadian Meteorological Center (CMC), European Center for Medium-Range Weather Forecasts (ECMWF), National Center for Environmental Prediction (NCEP), and Center for Weather Forecasting and Climate Studies (CPTEC). The study area comprised the western mesoregion of Paraná State (Brazil), and data were gathered from October to March between the soybean crop seasons of 2010/2011 and 2015/2016. Ten-day period clusters, corresponding to 240 h forecasts in the centers, were used to assess agreement with the gold standard. Our results showed that forecasting center selection must be based on rainfall value ranges and geographic locations. Selection according to the highest agreement with the gold standard was estimated at 76.9% for range 1 in CPTEC, 38.5% for range 2 and 4 in ECMWF, and 38.5% for range 3 in NCEP. In conclusion, the proposed method was efficient in selecting forecasting centers in areas of interest.
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    Inference in a structural heteroskedastic calibration model
    (2015) De Castro, M.; Galea Rojas, Manuel Jesús