Statistical Diagnostics for Skew-t-Normal Nonlinear Models

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

doi:10.1080/03610910903249502

Cited by 20 publications

(11 citation statements)

References 26 publications

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“…These data, analyzed previously by Lin et al (2009), Lachos et al (2011 and Labra et al (2012), consist of 214 observations generated in an ultrasonic calibration study, in which the response variable, T , is the ultrasonic response, and the explanatory variable, X , is the distance to the metal. In the boxplots of T versus X (omitted here) it may be observed that the ultrasonic response decreases with the distance from the metal, and the skewness of the response distribution depends (in an unknown form) on the distance to the metal.…”

Section: Ultrasonic Calibrationmentioning

confidence: 99%

“…To deal with this problem, some proposals have been made in the literature to replace the normality assumption by more flexible classes of distributions. For example, in the context of asymmetric and heavy-tailed responses, Lin et al (2009) derived diagnostic methods in non-linear skew-t-normal regression models; Cancho et al (2010) studied non-linear skew-normal regression models using classical and Bayesian approaches; Lachos et al (2011) introduced heteroscedastic non-linear regression models based on scale mixtures of skew-normal distributions; and Labra et al (2012) derived diagnostic methods for the class of regression models introduced previously by Lachos et al (2011). Although the models studied in these papers are attractive, they have some limitations.…”

Section: Introductionmentioning

confidence: 99%

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A semiparametric approach for joint modeling of median and skewness

Vanegas

Paula

2014

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We motivate this paper by showing through Monte Carlo simulation that ignoring the skewness of the response variable distribution in non-linear regression models may introduce biases on the parameter estimates and/or on the estimation of the associated variability measures. Then, we propose a semiparametric regression model suitable for data set analysis in which the distribution of the response is strictly positive and asymmetric. In this setup, both median and skewness of the response variable distribution are explicitly modeled, the median using a parametric non-linear function and the skewness using a semiparametric function. The proposed model allows for the description of the response using the log-symmetric distribution, which is a generalization of the log-normal distribution and is flexible enough to consider bimodal distributions in special cases as well as distributions having heavier or lighter tails than those of the log-normal one. An iterative estimation process as well as some diagnostic methods are derived. Two data sets previously analyzed under parametric models are reanalyzed using the proposed methodology.

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Section: Ultrasonic Calibrationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A semiparametric approach for joint modeling of median and skewness

Vanegas

Paula

2014

TEST

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“…Cook (1977), Bolfarine et al (2007) and Lin et al (2009) have used the above method. we use the case-deletion approach to detect the influence of removing the ith case from the analysis by evaluating the matrix such as Cooks distance (see Cook, 1977).…”

Section: Diagnostic Analysismentioning

confidence: 99%

The Location-Scale Mixture of Generalized Gamma Distribution: Estimation and Case Influence Diagnostics

Rahnamaei¹

2016

JSRI

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Abstract. One of the most interesting problems in distribution theory is constructing the distributions, which are appropriate for fitting skewed and heavy-tailed data sets. In this paper, we introduce a skew-slash distribution by using the scale mixture of the generalized gamma distribution. Some properties of this distribution are obtained. An EM-type algorithm is presented to estimate the parameters. Finally, we provide a simulation study and an application to real data to illustrate the modeling strength of the proposed distribution.

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“…We use the ultrasonic calibration data described in Lin et al (2009) and Lachos et al (2011) to investigate our method. These data are generated from the National institutes of Standards and Technology (NIST) study by Dan Chwirut involving ultrasonic calibration (Chwirut, 1979), where the response variable and the predictor variable is metal distance.…”

Section: Real Datamentioning

confidence: 99%

“…This method has been used in some papers, such as Cook (1977), Lin et al (2009) and Rahnamaei et al (2012). We use the case-deletion approach to detect the influence of removing the case from the analysis by evaluating the metrics such as the likelihood distance and Cook's distance (see, Cook, 1977).…”

Section: Sensitivity Analysismentioning

confidence: 99%

Nonlinear Regression Models Based on Slash Skew-elliptical‎ ‎Errors

Nahooji

Farnoosh

Nematollahi

2018

JIRSS

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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.

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Statistical Diagnostics for Skew-t-Normal Nonlinear Models

Cited by 20 publications

References 26 publications

A semiparametric approach for joint modeling of median and skewness

A semiparametric approach for joint modeling of median and skewness

The Location-Scale Mixture of Generalized Gamma Distribution: Estimation and Case Influence Diagnostics

Nonlinear Regression Models Based on Slash Skew-elliptical‎ ‎Errors

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