Influence diagnostics in nonlinear reproductive dispersion models

Tang, Niansheng; Wei, Bo‐Cheng; Wang, Xueren

doi:10.1016/s0167-7152(99)00087-5

Cited by 24 publications

(26 citation statements)

References 9 publications

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“…Similar to [19], we assume that σ 2 is known and d(y; μ) satisfies E(ḋ 2 (y; μ)) = 0 and 0 < E(d 2 (y; μ)) < +∞, whereḋ 2 (y; μ) = ∂d(y; μ)/∂μ andd 2 (y; μ) = ∂ 2 d(y; μ)/∂μ 2 . Following [23], Model (1) is referred to as the reproductive dispersion family (RDF) distribution which is also called as the reproductive dispersion model by Jorgenson [10] , it includes normal distribution, extreme value distribution and exponential family distribution as its special cases.…”

Section: Model and Estimationmentioning

confidence: 99%

“…Following [23], Model (1) is referred to as the reproductive dispersion family (RDF) distribution which is also called as the reproductive dispersion model by Jorgenson [10] , it includes normal distribution, extreme value distribution and exponential family distribution as its special cases. Tang et al [19] proposed nonlinear reproductive dispersion models by using RDF to replace exponential family distribution in exponential family nonlinear models [25] . In this paper, we consider further extension of the nonlinear reproductive dispersion model to a more general model which is referred to as a semiparametric reproductive dispersion nonlinear model (SRDNM) and is defined in Equations (1) and (2).…”

Section: Model and Estimationmentioning

confidence: 99%

“…This method has been successfully extended to all models in the past few decades (see [1,2,4,7,11,16,18,19,21,25,26]). However, case-deletion method cannot be used to identify the impact of the model perturbation.…”

Section: Introductionmentioning

confidence: 99%

“…respectively, where G = diag{E(d 2 (y 1 ; μ 1 ))/2, · · · , E(d 2 (y n ; μ n ))/2}, (6) and (7) that the Fisher scoring algorithm for calculating the maximum penalized likelihood estimates β and g of β and g leads to iteratively solve the following equation [19] :…”

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confidence: 99%

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Local influence analysis for semiparametric reproductive dispersion nonlinear models

Chen

Tang

Wang

2011

Acta Math. Appl. Sin. Engl. Ser.

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The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM) which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models.Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented. Assessment of local influence for various perturbation schemes are investigated. Some local influence diagnostics are given. A simulation study and a real example are used to illustrate the proposed methodologies.

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Section: Model and Estimationmentioning

confidence: 99%

Section: Model and Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Local influence analysis for semiparametric reproductive dispersion nonlinear models

Chen

Tang

Wang

2011

Acta Math. Appl. Sin. Engl. Ser.

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“…For example, Tang et al [2] proposed a nonlinear reproductive dispersion model and studied its influence diagnostics; Chen et al [3] discussed influence diagnostics of semiparametric nonlinear reproductive dispersion models; Fu et al [4] investigated local influence analysis for nonlinear structural equation models with non-ignorable missing outcomes from a reproductive dispersion model.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Subset Selection for Reproductive Dispersion Linear Models

Zhao

Duan

et al. 2014

Journal of Systems Science and Information

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We propose a full Bayesian subset selection method for reproductive dispersion linear models, which bases on expanding the usual link function to a function that incorporates all possible subsets of predictors by adding indictors as parameters. The vector of indicator variables dictates which predictors to delete. An efficient MCMC procedure that combining Gibbs sampler and MetropolisHastings algorithm is presented to approximate the posterior distribution of the indicator variables. The promising subsets of predictors can be identified as those with higher posterior probability. Several numerical examples are used to illustrate the newly developed methodology.

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Variational Bayesian partially linear mean shift models for high‐dimensional Alzheimer's disease neuroimaging data

Tang

2021

Statistics in Medicine

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Alzheimer's disease can be diagnosed by analyzing brain images (eg, magnetic resonance imaging, MRI) and neuropsychological tests (eg, mini‐mental state examination, MMSE). A partially linear mean shift model (PLMSM) is here proposed to investigate the relationship between MMSE score and high‐dimensional regions of interest in MRI, and detect the outliers. In the presence of high‐dimensional data, existing Bayesian approaches (eg, Markov chain Monte Carlo) to analyze a PLMSM take intensive computational cost and require huge memory, and have low convergence rate. To address these issues, a variational Bayesian inference is developed to simultaneously estimate parameters and nonparametric functions and identify outliers in a PLMSM. A Bayesian P‐splines method is presented to approximate nonparametric functions, a Bayesian adaptive Lasso approach is employed to select predictors, and outliers are detected by the classification variable. Two simulation studies are conducted to assess the finite sample performance of the proposed method. An MRI dataset with elderly cognitive ability is provided to corroborate the proposed method.

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Influence diagnostics in nonlinear reproductive dispersion models

Cited by 24 publications

References 9 publications

Local influence analysis for semiparametric reproductive dispersion nonlinear models

Local influence analysis for semiparametric reproductive dispersion nonlinear models

Bayesian Subset Selection for Reproductive Dispersion Linear Models

Variational Bayesian partially linear mean shift models for high‐dimensional Alzheimer's disease neuroimaging data

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