Browsing by Author "Leiva, Victor"

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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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    On a logistic regression model with random intercept : diagnostic analytics, simulation and biological application
    (2020) Tapia, A.; Leiva, Victor; Galea Rojas, Manuel Jesús; Werneck, R.
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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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    Robust autoregressive modeling and its diagnostic analytics with a COVID-19 related application
    (2024) Liu, Yonghui; Wang, Jing; Leiva, Victor; Tapia, Alejandra; Tan, Wei; Liu, Shuangzhe
    Autoregressive models in time series are useful in various areas. In this article, we propose a skew-t autoregressive model. We estimate its parameters using the expectation-maximization (EM) method and develop the influence methodology based on local perturbations for its validation. We obtain the normal curvatures for four perturbation strategies to identify influential observations, and then to assess their performance through Monte Carlo simulations. An example of financial data analysis is presented to study daily log-returns for Brent crude futures and investigate possible impact by the COVID-19 pandemic.