Assessment of diagnostic procedures in symmetrical nonlinear regression models

Vanegas, Luis Hernando; Cysneiros, Francisco José A.

doi:10.1016/j.csda.2009.10.013

Cited by 30 publications

(11 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In conclusion, heavy-tailed in a asymmetric context, are less sensitive in the presence of outliers. These results agree with similar considerations presented in Vanegas and Cysneiros (2010) in a symmetric context (λ = 0).…”

Section: Simulation Studysupporting

confidence: 94%

“…We performed a Monte Carlo simulation study with the following nonlinear growthcurve model: For errors, we generated 2000 samples of SN(− √ 2/π ∆, σ 2 , λ). Following Vanegas and Cysneiros (2010), to guarantee the presence of one outlier we constructed Y * i = Y i −ϑ, where i is a central value of samples and ϑ = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. In each replication, we obtained the parameters estimates with and without outliers denoted byθ andθ ( all the models, the influence of the outliers in the estimative increases as ϑ also increases. In the ST models the influence increases when ν also increases.…”

Section: Simulation Studymentioning

confidence: 99%

“…For instance, Cysneiros and Vanegas (2008) studied the symmetrical nonlinear regression model and performed an analytical and empirical study to describe the behavior of the standardized residuals. Vanegas and Cysneiros (2010) propose diagnostic procedures based on case-deletion model for symmetrical nonlinear regression models. Cancho, Lachos, and Ortega (2009) introduce the skew-normal nonlinear regression models (SN-NLM) and they present a complete likelihood based analysis, including an efficient EM algorithm to maximum likelihood estimation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear regression models based on scale mixtures of skew-normal distributions

Garay

Lachos

Abanto-Valle

2011

Journal of the Korean Statistical Society

View full text Add to dashboard Cite

a b s t r a c tAn extension of some standard likelihood based procedures to nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. This novel class of models provides a useful generalization of the symmetrical nonlinear regression models since the random terms distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented and the observed information matrix is derived analytically. In order to examine the robust aspect of this flexible class against outlying and influential observations, some simulation studies have also been presented. Finally, an illustration of the methodology is given considering a data set previously analyzed under normal and skew-normal nonlinear regression models.

show abstract

Section: Simulation Studysupporting

confidence: 94%

Section: Simulation Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear regression models based on scale mixtures of skew-normal distributions

Garay

Lachos

Abanto-Valle

2011

Journal of the Korean Statistical Society

View full text Add to dashboard Cite

show abstract

“…Following Vanegas and Cysneiros (2010), to guarantee the presence of one outlier, we constructed Y * i = Y i − v, where i is the corresponding central value of the sample and v = 1, 2, 3,4,5,6,7,8,9. In each replication, we obtained the parameter estimates with and without outliers denoted byθ andθ (i) , respectively, under the skew normal (SN-NLM), the slash skew normal (SLSN-NLM) and the slash skew-T (SLST-NLM).…”

Section: Simulation 1: Robustness Of Estimatesmentioning

confidence: 99%

Nonlinear Regression Models Based on Slash Skew-elliptical‎ ‎Errors

Nahooji

Farnoosh

Nematollahi

2018

JIRSS

View full text Add to dashboard Cite

Abstract. In this paper, the nonlinear regression models when the model errors follow a slash skew-elliptical distribution, are considered. In the special case of nonlinear regression models under slash skew-t distribution, we present some distributional properties, and to estimate their parameters, we use an EM-type algorithm. Also, to find the estimation errors, we derive the observed information matrix analytically. To describe the influence of the observations on the ML estimates, we use a sensitivity analysis. Finally, we conduct some simulation studies and a real data analysis to show the performance of the proposed model.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Assessment of diagnostic procedures in symmetrical nonlinear regression models

Cited by 30 publications

References 17 publications

Nonlinear regression models based on scale mixtures of skew-normal distributions

Nonlinear regression models based on scale mixtures of skew-normal distributions

Nonlinear Regression Models Based on Slash Skew-elliptical‎ ‎Errors

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

Contact Info

Product

Resources

About