Improved estimation in a general multivariate elliptical model

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

doi:10.1214/16-bjps331

Cited by 6 publications

(5 citation statements)

References 39 publications

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“…Additionally, for the qvariate power exponential, P E q (µ i , Σ, λ), with shape parameter λ > 0, we have g(u) = λΓ(q/2)2 −q/(2λ) π −q/2 e −u λ /2 / Γ(q/(2λ)). For this general model, Lemonte and Patriota (2011) proposed diagnostic tools and Melo et al (2015) obtained the second-order bias of the maximum likelihood estimator and conducted some simulation studies, which indicate that the proposed bias correction is effective.…”

Section: The Modelmentioning

confidence: 99%

“…The errors are assumed to follow a Student t distribution with ν = 4 degrees of freedom. This model provides a suitable fit for the data (Melo et al, 2015). The maximum likelihood estimates of the parameters (standard errors are given in parentheses) are β 0 = 33.519 (5.082), β 1 = 9.592 (4.417), β 2 = −63.501 (9.789), β 3 = 29.777 (4.710), and σ 2 = 0.006 (0.003).…”

Section: Simulation Studymentioning

confidence: 99%

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Improved hypothesis testing in a general multivariate elliptical model

Melo

Ferrari

Patriota

2016

Journal of Statistical Computation and Simulation

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Abstract:This paper investigates improved testing inferences under a general multivariate elliptical regression model. The model is very flexible in terms of the specification of the mean vector and the dispersion matrix, and of the choice of the error distribution. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal and Student-t distributions as special cases. We obtain Skovgaard's adjusted likelihood ratio statistics and Barndorff-Nielsen's adjusted signed likelihood ratio statistics and we conduct a simulation study. The simulations suggest that the proposed tests display superior finite sample behavior as compared to the standard tests. Two applications are presented in order to illustrate the methods.

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Section: The Modelmentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

Improved hypothesis testing in a general multivariate elliptical model

Melo

Ferrari

Patriota

2016

Journal of Statistical Computation and Simulation

Self Cite

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show abstract

“…Then they unify several elliptical models, such as nonlinear regressions, mixed-effects model with nonlinear fixed effects, errors-in-variables models, etc. Bias correction for the maximum likelihood estimator and adjustments of the likelihood-ratio statistics are also derived for this general model (see [38], [37]). The elliptical distributions can also be used as the basis to consider robustness in multivariate linear regression, as in [14], [21], [29], [36], [42], [50] and many others.…”

Section: Introductionmentioning

confidence: 99%

Envelopes for elliptical multivariate linear regression

Forzani¹,

Su²

2021

STAT SINICA

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We incorporate the idea of reduced rank envelope [7] to elliptical multivariate linear regression to improve the efficiency of estimation. The reduced rank envelope model takes advantage of both reduced rank regression and envelope model, and is an efficient estimation technique in multivariate linear regression. However, it uses the normal log-likelihood as its objective function, and is most effective when the normality assumption holds. The proposed methodology considers elliptically contoured distributions and it incorporates this distribution structure into the modeling. Consequently, it is more flexible and its estimator outperforms the estimator derived for the normal case. When the specific distribution is unknown, we present an estimator that performs well as long as the elliptically contoured assumption holds.

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“…This result has become widely used in the literature to obtain general expressions for the O(n −1 ) bias and to propose bias-corrected estimators in various parametric models. For instance, Lemonte et al (2007), Cysneiros et al (2010), Simas et al (2011), Barreto-Souza andVasconcellos (2011) and Melo et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Improved estimators in beta prime regression models

Medeiros¹,

Araújo²,

Bourguignon³

2020

Preprint

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In this paper, we consider the beta prime regression model recently proposed by Bourguignon et al. (2018), which is tailored to situations where the response is continuous and restricted to the positive real line with skewed and long tails and the regression structure involves regressors and unknown parameters. We consider two different strategies of bias correction of the maximum-likelihood estimators for the parameters that index the model. In particular, we discuss bias-corrected estimators for the mean and the dispersion parameters of the model. Furthermore, as an alternative to the two analytically bias-corrected estimators discussed, we consider a bias correction mechanism based on the parametric bootstrap. The numerical results show that the bias correction scheme yields nearly unbiased estimates. An example with real data is presented and discussed.

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Improved estimation in a general multivariate elliptical model

Cited by 6 publications

References 39 publications

Improved hypothesis testing in a general multivariate elliptical model

Improved hypothesis testing in a general multivariate elliptical model

Envelopes for elliptical multivariate linear regression

Improved estimators in beta prime regression models

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