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

Melo, Tatiane F. N.; Ferrari, Silvia L. P.; Patriota, Alexandre G.

doi:10.1080/00949655.2013.787691

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…General results for structural heteroskedastic models are presented by Patriota et al (2009), Patriota et al (2011), and Melo et al (2013, among others. Instead, in our work, as in Vilca-Labra et al (2011), we take the calibration model on its own grounds and explore specific inferential problems.…”

Section: Introductionmentioning

confidence: 99%

Inference in a structural heteroskedastic calibration model

Castro

Galea

2014

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The main goal of this paper is to study inference in an heteroskedastic calibration model. We embrace a multivariate structural model with known diagonal covariance error matrices, which is a common setup when different measurement methods are compared. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators and a graphical device for model checking are also discussed. Test statistics are proposed for testing hypotheses of interest with the asymptotic chisquare distribution which guarantees correct asymptotic significance levels. Results of simulations comprising point estimation, interval estimation, and hypothesis testing are reported. An application to a real data set is given. Up to best of our knowledge, topics such as model checking and hypotheses testing have received only scarce attention in the literature on calibration models.

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Section: Introductionmentioning

confidence: 99%

Inference in a structural heteroskedastic calibration model

Castro

Galea

2014

Stat Papers

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“…For instance, it is often doubtful and suffers from a lack of robustness against influential observations on the parameter estimates. For this reason, several works have considered relaxations of the normality assumption, such as considering asymmetric distributions, see , Kheradmandi and Rasekh (2015) and models based on distributions with tails heavier than the ones of a normal distribution, see Cao, Lin and Zhu (2012), Melo, Ferrari and Patriota (2014).…”

Section: Introductionmentioning

confidence: 99%

Some extensions in measurement error models

Tomaya¹,

Yanet²

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In this dissertation, we approach three different contributions in measurement error model (MEM). Initially, we carry out maximum penalized likelihood inference in MEM's under the normality assumption. The methodology is based on the method proposed by Firth (1993), which can be used to improve some asymptotic properties of the maximum likelihood estimators. In the second contribution, we develop two new estimation methods based on generalized fiducial inference for the precision parameters and the variability product under the Grubbs model considering the two-instrument case. One method is based on a fiducial generalized pivotal quantity and the other one is built on the method of the generalized fiducial distribution. Comparisons with two existing approaches are reported. Finally, we propose to study inference in a heteroscedastic MEM with known error variances. Instead of the normal distribution for the random components, we develop a model that assumes a skew-t distribution for the true covariate and a centered Student's t distribution for the error terms. The proposed model enables to accommodate skewness and heavy-tailedness in the data, while the degrees of freedom of the distributions can be different. We use the maximum likelihood method to estimate the model parameters and compute them via an EM-type algorithm. All proposed methodologies are assessed numerically through simulation studies and illustrated with real datasets extracted from the literature.

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