Local influence in measurement error models with ridge estimate

Rasekh, Abdolrahman

doi:10.1016/j.csda.2005.04.022

Cited by 24 publications

(8 citation statements)

References 15 publications

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“…We first discuss the data raised from a study of pottery production and distribution in an Egyptian city. The detailed description can be found in [19,[33][34][35]. The data contain several mineral elements measured from samples of pottery made from different fabrics by two different techniques: neutron activation analysis (NAA) and inductively coupled plasma (ICP) spectrometry.…”

Section: Egyptian Pottery Datamentioning

confidence: 99%

Multivariate measurement error models for replicated data under heavy‐tailed distributions

Cao

Lin

Shi

et al. 2015

Journal of Chemometrics

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In this paper, we deal with multivariate measurement error models for replicated data under heavy-tailed distributions, providing appealing robust and adaptable alternatives to the usual Gaussian assumptions. The models contain both error-prone covariates and predictors measured without errors. The surrogates of the response and the multiple error-prone covariates are replicated and are allowed unpaired and/or unequal cases. Under the scale mixtures of normal distribution class, we provide an explicit iterative formula of the maximum likelihood estimation via an expectation-maximization-type algorithm. Closed forms of asymptotic variances of the estimators are also given. The effect and robustness performances are confirmed by the simulation studies. Two real data sets are analyzed by the proposed models.

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Section: Egyptian Pottery Datamentioning

confidence: 99%

Multivariate measurement error models for replicated data under heavy‐tailed distributions

Cao

Lin

Shi

et al. 2015

Journal of Chemometrics

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“…Billor et al (1999) studied the local influence of minor perturbations on the ridge estimate in the ordinary regression model using likelihood displacement. Rasekh (2006) assessed the local influence of observations on the ridge estimate in the measurement error models. Liu et al (2009) studied the local influence in the linear regression model with stochastic linear restriction.…”

Section: Introductionmentioning

confidence: 99%

Local Influence Analysis for The Ridge Regression Under Stochastic Linear Restrictions

Yang

2014

Communications in Statistics - Theory and Methods

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In this article, we assess the local influence for the ridge regression of linear models with stochastic linear restrictions in the spirit of Cook by using the log-likelihood of the stochastic restricted ridge regression estimator. The diagnostics under the perturbations of constant variance, responses and individual explanatory variables are derived. We also assess the local influence of the stochastic restricted ridge regression estimator under the approach suggested by Billor and Loynes. At the end, a numerical example on the Longley data is given to illustrate the theoretic results.

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“…By applying empirical influence function and Cook's statistic, they found that group number 5, 3, 13, and 19 were the most influence groups in model. Rasekh (2006) analysed the same data to detect influential observations on the ridge regression estimator using the local influence approach with minor perturbation on variance, six explanatory variables (Na, Al, K,V ,Cr and Mn). By the variance perturbation, He detected that groups 18, 23, 15 and 6 (imported vessels groups) are most influential groups in ridge measurement error regression.…”

Section: Egyptian Pottery Datamentioning

confidence: 99%

“…Rasekh and Feller (2003) derived influence function of ridge estimate in measurement error models using case deletion. Rasekh (2006) studied the local influence of minor perturbations on the ridge estimate in the ordinary regression model. He derived the diagnostics under the perturbation of variance and explanatory variables.…”

Section: Introductionmentioning

confidence: 99%

Influence Measures in Ridge Linear Measurement Error Models

Emami¹

2015

JSRI

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Abstract. Usually the existence of influential observations is complicated by the presence of collinearity in linear measurement error models. However no method of influence measure available for the possible effect's that collinearity can have on the influence of an observation in such models. In this paper, a new type of ridge estimator based corrected likelihood function (REC) for linear measurement error models is defined. We show when this type of ridge estimator is used to mitigate the effects of collinearity the influence of some observations can be drastically modified. We propose a case deletion formula to detect influential points in REC. As an illustrative example two real data set are analysed.

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Local influence in measurement error models with ridge estimate

Cited by 24 publications

References 15 publications

Multivariate measurement error models for replicated data under heavy‐tailed distributions

Multivariate measurement error models for replicated data under heavy‐tailed distributions

Local Influence Analysis for The Ridge Regression Under Stochastic Linear Restrictions

Influence Measures in Ridge Linear Measurement Error Models

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