Leiva, V., Saulo, H., Leao, J., & Marchant, C. (2014). A family of autoregressive conditional duration models applied to financial data. Comput. Stat. Data Anal., 79, 175–191.
Abstract: The Birnbaum-Saunders distribution is receiving considerable attention due to its good properties. One of its extensions is the class of scale-mixture Birnbaum-Saunders (SBS) distributions, which shares its good properties, but it also has further properties. The autoregressive conditional duration models are the primary family used for analyzing high-frequency financial data. We propose a methodology based on SBS autoregressive conditional duration models, which includes in-sample inference, goodness-of-fit and out-of-sample forecast techniques. We carry out a Monte Carlo study to evaluate its performance and assess its practical usefulness with real-world data of financial transactions from the New York stock exchange. (C) 2014 Elsevier B.V. All rights reserved.
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Marchant, C., Leiva, V., & Cysneiros, F. J. A. (2016). A Multivariate Log-Linear Model for Birnbaum-Saunders Distributions. IEEE Trans. Reliab., 65(2), 816–827.
Abstract: Univariate Birnbaum-Saunders models have been widely applied to fatigue studies. Calculation of fatigue life is of great importance in determining the reliability of materials. We propose and derive new multivariate generalized Birnbaum-Saunders regression models. We use the maximum likelihood method and the EM algorithm to estimate their parameters. We carry out a simulation study to evaluate the performance of the corresponding maximum likelihood estimators. We illustrate the new models with real-world multivariate fatigue data.
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Ruz, G. A., & Pham, D. T. (2012). NBSOM: The naive Bayes self-organizing map. Neural Comput. Appl., 21(6), 1319–1330.
Abstract: The naive Bayes model has proven to be a simple yet effective model, which is very popular for pattern recognition applications such as data classification and clustering. This paper explores the possibility of using this model for multidimensional data visualization. To achieve this, a new learning algorithm called naive Bayes self-organizing map (NBSOM) is proposed to enable the naive Bayes model to perform topographic mappings. The training is carried out by means of an online expectation maximization algorithm with a self-organizing principle. The proposed method is compared with principal component analysis, self-organizing maps, and generative topographic mapping on two benchmark data sets and a real-world image processing application. Overall, the results show the effectiveness of NBSOM for multidimensional data visualization.
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