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Abstract and Applied Analysis
Volume 2014, Article ID 542985, 8 pages
Research Article

Likelihood Inference of Nonlinear Models Based on a Class of Flexible Skewed Distributions

1School of Science, Huzhou Teachers’ College, Huzhou 313000, China
2School of Management, Chongqing Jiaotong University, Chongqing 400074, China

Received 28 August 2014; Accepted 28 September 2014; Published 3 December 2014

Academic Editor: Jinde Cao

Copyright © 2014 Xuedong Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with the issue of the likelihood inference for nonlinear models with a flexible skew-t-normal (FSTN) distribution, which is proposed within a general framework of flexible skew-symmetric (FSS) distributions by combining with skew-t-normal (STN) distribution. In comparison with the common skewed distributions such as skew normal (SN), and skew-t (ST) as well as scale mixtures of skew normal (SMSN), the FSTN distribution can accommodate more flexibility and robustness in the presence of skewed, heavy-tailed, especially multimodal outcomes. However, for this distribution, a usual approach of maximum likelihood estimates based on EM algorithm becomes unavailable and an alternative way is to return to the original Newton-Raphson type method. In order to improve the estimation as well as the way for confidence estimation and hypothesis test for the parameters of interest, a modified Newton-Raphson iterative algorithm is presented in this paper, based on profile likelihood for nonlinear regression models with FSTN distribution, and, then, the confidence interval and hypothesis test are also developed. Furthermore, a real example and simulation are conducted to demonstrate the usefulness and the superiority of our approach.