Araya, H., & Plaza-Vega, F. (2023). Parameter estimation for fractional power type diffusion: A hybrid Bayesian-deep learning approach. Commun. Stat.-Theory Methods, Early Access.
Abstract: In this article, we consider the problem of parameter estimation in a power-type diffusion driven by fractional Brownian motion with Hurst parameter in (1/2,1). To estimate the parameters of the process, we use an approximate bayesian computation method. Also, a particular case is addressed by means of variations and wavelet-type methods. Several theoretical properties of the process are studied and numerical examples are provided in order to show the small sample behavior of the proposed methods.
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Khosravi, M., Leiva, V., Jamalizadeh, A., & Porcu, E. (2016). On a nonlinear Birnbaum-Saunders model based on a bivariate construction and its characteristics. Commun. Stat.-Theory Methods, 45(3), 772–793.
Abstract: The Birnbaum-Saunders (BS) distribution is an asymmetric probability model that is receiving considerable attention. In this article, we propose a methodology based on a new class of BS models generated from the Student-t distribution. We obtain a recurrence relationship for a BS distribution based on a nonlinear skew-t distribution. Model parameters estimators are obtained by means of the maximum likelihood method, which are evaluated by Monte Carlo simulations. We illustrate the obtained results by analyzing two real data sets. These data analyses allow the adequacy of the proposed model to be shown and discussed by applying model selection tools.
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