Bayesian inference for sinh-normal/independent nonlinear regression models |
| |
Authors: | Filidor Vilca N Balakrishnan |
| |
Institution: | 1. Department of Statistics, State University of Campinas S?o Paulo, Brazil;2. Department of Mathematics and Statistics, McMaster University, Hamilton, Canada |
| |
Abstract: | Sinh-normal/independent distributions are a class of symmetric heavy-tailed distributions that include the sinh-normal distribution as a special case, which has been used extensively in Birnbaum–Saunders regression models. Here, we explore the use of Markov Chain Monte Carlo methods to develop a Bayesian analysis in nonlinear regression models when Sinh-normal/independent distributions are assumed for the random errors term, and it provides a robust alternative to the sinh-normal nonlinear regression model. Bayesian mechanisms for parameter estimation, residual analysis and influence diagnostics are then developed, which extend the results of Farias and Lemonte Bayesian inference for the Birnbaum-Saunders nonlinear regression model, Stat. Methods Appl. 20 (2011), pp. 423-438] who used the Sinh-normal/independent distributions with known scale parameter. Some special cases, based on the sinh-Student-t (sinh-St), sinh-slash (sinh-SL) and sinh-contaminated normal (sinh-CN) distributions are discussed in detail. Two real datasets are finally analyzed to illustrate the developed procedures. |
| |
Keywords: | Birnbaum–Saunders distribution sinh-normal distribution Bayesian inference robust estimation normal/independent distribution generalized inverse Gaussian distribution |
|
|