On estimation of a heteroscedastic measurement error model under heavy-tailed distributions

Cao, Chunzheng; Lin, Jin-Guan; Zhu, Xiaoyan

doi:10.1016/j.csda.2011.08.011

Cited by 13 publications

(11 citation statements)

References 23 publications

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“…The approach used in the present paper is different from the latter, since here we consider an elliptical joint distribution for the vector of the random errors. Although the class of scale-mixture of normal distributions is a special case of the the elliptical distributions, our proposal does not extend to the class proposed by Cao et al [5]. This is because they assumed that the errors' distributions are independent, while we assume that they are uncorrelated but not independent.…”

Section: Applicationmentioning

confidence: 90%

“…In this paper, we consider a data set from the WHO MONICA Project that was considered in Kulathinal et al [15], Patriota et al [20], and Cao et al [5]. This data set was first analyzed under normal distributions for the marginals of the random errors ( [15], [20]), and thereafter under scale-mixture of normal distributions for the marginals of the random errors (Cao et al [5]). The approach used in the present paper is different from the latter, since here we consider an elliptical joint distribution for the vector of the random errors.…”

Section: Applicationmentioning

confidence: 99%

“…Kulathinal et al [15] and Patriota et al [20] study a univariate heteroskedastic errors-in-variables model with equation error and normal distribution. An extension to the scalemixture of normal distributions is presented by Cao et al [5]. The results in these three latter papers were applied to an epidemiological dataset of the WHO MONICA (World Health Organization Multinational MONItoring of trends and determinants in CArdiovascular disease) Project.…”

Section: Introductionmentioning

confidence: 99%

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Modified likelihood ratio tests in heteroskedastic multivariate regression models with measurement error

Melo

Ferrari

Patriota

2013

Journal of Statistical Computation and Simulation

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In this paper, we develop modified versions of the likelihood ratio test for multivariate heteroskedastic errors-in-variables regression models. The error terms are allowed to follow a multivariate distribution in the elliptical class of distributions, which has the normal distribution as a special case. We derive the Skovgaard adjusted likelihood ratio statistics, which follow a chisquared distribution with a high degree of accuracy. We conduct a simulation study and show that the proposed tests display superior finite sample behavior as compared to the standard likelihood ratio test. We illustrate the usefulness of our results in applied settings using a data set from the WHO MONICA Project on cardiovascular disease.

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Section: Applicationmentioning

confidence: 90%

Section: Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modified likelihood ratio tests in heteroskedastic multivariate regression models with measurement error

Melo

Ferrari

Patriota

2013

Journal of Statistical Computation and Simulation

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“…This dataset was first analyzed under normal distributions for the marginals of the random errors (Kulathinal et al 2002;Patriota et al 2009a). Thereafter, it was studied under a scale mixture of normal distributions for the marginals of the random errors (Cao et al, 2012). The approach used in the present paper is different from the others because here we consider a joint elliptical distribution for the vector of random errors.…”

Section: Who Monica Datamentioning

confidence: 99%

Improved estimation in a general multivariate elliptical model

Melo¹,

Ferrari²,

Patriota³

2018

Braz. J. Probab. Stat.

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The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in common. Many frequently used models are special cases of this general formulation, namely: errors-in-variables models, nonlinear mixed-effects models, heteroscedastic nonlinear models, among others. In any of these models, the vector of the errors may have any multivariate elliptical distribution. We obtain the second-order bias of the maximum likelihood estimator, a bias-corrected estimator, and a bias-reduced estimator. Simulation results indicate the effectiveness of the bias correction and bias reduction schemes.

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“…This provides appealing robust and adaptable models, for example, the ME models under Student's t-distribution [21,22]. Furthermore, the scale mixtures of normal (SMN) distributions have also been applied into some non-replicated ME models seen in [23][24][25], among others. As one of the most important subclasses of the elliptical symmetric distributions [26], the SMN distribution class contains many heavier-than-normal tailed members, such as Student's t, slash, power exponential, and contaminated normal.…”

Section: Introductionmentioning

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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On estimation of a heteroscedastic measurement error model under heavy-tailed distributions

Cited by 13 publications

References 23 publications

Modified likelihood ratio tests in heteroskedastic multivariate regression models with measurement error

Modified likelihood ratio tests in heteroskedastic multivariate regression models with measurement error

Improved estimation in a general multivariate elliptical model

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

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