Homogeneity diagnostics for skew-normal nonlinear regression models

Xie, Fei; Wei, Bo‐Cheng; Lin, Jin-Guan

doi:10.1016/j.spl.2008.11.001

Cited by 32 publications

(10 citation statements)

References 17 publications

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“…, which corresponds to considering that the distribution of Z i is heteroscedastic (Xie et al 2009). In this case, we have that…”

Section: Perturbation Of the Scale Matrixmentioning

confidence: 99%

“…However, the method proposed here can be used to test for homogeneity of any parameter involved in the variance, as discussed by Xie et al (2009).…”

Section: Perturbation Of the Scale Matrixmentioning

confidence: 99%

“…This section concentrates on this problem in SMSN-MEM. Following Xie et al (2009), we suppose that the skewness parameter can be modeled bȳ…”

Section: In the Smsn-mem The Variance Of The Ith Observation Ismentioning

confidence: 99%

“…To examine the performances and properties of the score test, formal simulations studies under several situations need to be carried out, as discussed in Xie et al (2009), which will be reported in a follow-up paper. Due to recent advances in computational technology, it is worthwhile also to carry out Bayesian treatments via Markov chain Monte Carlo (MCMC) sampling methods in the context of SMSN-MEM.…”

Section: Final Conclusionmentioning

confidence: 99%

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On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions

2011

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In this paper, we discuss the extension of some diagnostic procedures to multivariate measurement error models with scale mixtures of skew-normal distributions (Lachos et al., Statistics 44:541-556, 2010c). This class provides a useful generalization of normal (and skew-normal) measurement error models since the random term distributions cover symmetric, asymmetric and heavy-tailed distributions, such as skew-t, skew-slash and skew-contaminated normal, among others. Inspired by the EM algorithm proposed by Lachos et al. (Statistics 44:541-556, 2010c), we develop a local influence analysis for measurement error models, following Zhu and Lee's (J R Stat Soc B 63:111-126, 2001) approach. This is because the observed data loglikelihood function associated with the proposed model is somewhat complex and Cook's well-known approach can be very difficult to apply to achieve local influence measures. Some useful perturbation schemes are also discussed. In addition, a score test for assessing the homogeneity of the skewness parameter vector is presented. Finally, the methodology is exemplified through a real data set, illustrating the usefulness of the proposed methodology.

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“…, which corresponds to considering that the distribution of Z i is heteroscedastic (Xie et al 2009). In this case, we have that…”

Section: Perturbation Of the Scale Matrixmentioning

confidence: 99%

“…However, the method proposed here can be used to test for homogeneity of any parameter involved in the variance, as discussed by Xie et al (2009).…”

Section: Perturbation Of the Scale Matrixmentioning

confidence: 99%

“…This section concentrates on this problem in SMSN-MEM. Following Xie et al (2009), we suppose that the skewness parameter can be modeled bȳ…”

Section: In the Smsn-mem The Variance Of The Ith Observation Ismentioning

confidence: 99%

Section: Final Conclusionmentioning

confidence: 99%

See 2 more Smart Citations

On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions

2011

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“…From Bayesian point of view, [13] considered the Bayesian estimation and the case influence diagnostics for nonlinear regression models with SMSN distributions. More related literature could be found in [14][15][16][17]. Generally speaking, for model fitting of the nonlinear regression with skewed distributions, a popular approach is to consider the hierarchical representation of variables with a specific distribution, in which the postulated distribution is expressed as several conditional distributions of simpler forms such as normal and Student's and Gamma.…”

Section: Introductionmentioning

confidence: 99%

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

Chen

Zeng

Song

2014

Abstract and Applied Analysis

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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.

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Heteroscedastic nonlinear regression models using asymmetric and heavy tailed two-piece distributions

2020

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Homogeneity diagnostics for skew-normal nonlinear regression models

Cited by 32 publications

References 17 publications

On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions

On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions

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

Heteroscedastic nonlinear regression models using asymmetric and heavy tailed two-piece distributions

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