Multivariate Linear Regression Model with Elliptically Contoured Distributed Errors and Monotone Missing Dependent Variables

Batsidis, Apostolos; Zografos, K.

doi:10.1080/03610920701653102

Cited by 5 publications

(3 citation statements)

References 40 publications

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“…As pointed out by two reviewers, this paper is based on multivariate normal population. Like what did in Batsidis [11][12][13] for monotone missing data, an extension of the results given in this paper for hierarchical missing data from elliptic distribution is an interesting open problem. Moreover, the proposed study can be extended for the neutrosophic statistics as future research.…”

Section: Discussionmentioning

confidence: 52%

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Hierarchical Missing Data and Multivariate Behrens–Fisher Problem

2021

Journal of Mathematics

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This article firstly defines hierarchical data missing pattern, which is a generalization of monotone data missing pattern. Then multivariate Behrens–Fisher problem with hierarchical missing data is considered to illustrate that how ideas in dealing with monotone missing data can be extended to deal with hierarchical missing pattern. A pivotal quantity similar to the Hotelling T 2 is presented, and the moment matching method is used to derive its approximate distribution which is for testing and interval estimation. The precision of the approximation is illustrated through Monte Carlo data simulation. The results indicate that the approximate method is very satisfactory even for moderately small samples.

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Section: Discussionmentioning

confidence: 52%

“…Besides, Batsidis [11][12][13] extends the inferences on monotone missing data to the assumption of elliptically contoured distributions of which the multivariate normal is a special case. For theory and methods of multivariate analysis based on the elliptically contoured distributions, we refer to Fang and Zhang [14].…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Missing Data and Multivariate Behrens–Fisher Problem

2021

Journal of Mathematics

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“…Statistical inference with monotone incomplete multivariate normal samples has been widely studied; see [9][10][11][12][13][14][15][16][17][18][19][20][21] and the many references provided in those publications.…”

Section: Introductionmentioning

confidence: 99%

The Stein phenomenon for monotone incomplete multivariate normal data

Richards¹,

Yamada²

2010

Journal of Multivariate Analysis

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a b s t r a c tWe establish the Stein phenomenon in the context of two-step, monotone incomplete data drawn from N p+q (µ, Σ), a (p + q)-dimensional multivariate normal population with mean µ and covariance matrix Σ. On the basis of data consisting of n observations on all p + q characteristics and an additional N − n observations on the last q characteristics, where all observations are mutually independent, denote by µ the maximum likelihood estimator of µ. We establish criteria which imply that shrinkage estimators of James-Stein type have lower risk than µ under Euclidean quadratic loss. Further, we show that the corresponding positive-part estimators have lower risk than their unrestricted counterparts, thereby rendering the latter estimators inadmissible. We derive results for the case in which Σ is block-diagonal, the loss function is quadratic and non-spherical, and the shrinkage estimator is constructed by means of a nondecreasing, differentiable function of a quadratic form in µ. For the problem of shrinking µ to a vector whose components have a common value constructed from the data, we derive improved shrinkage estimators and again determine conditions under which the positive-part analogs have lower risk than their unrestricted counterparts.

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Multivariate linear regression with non-normal errors: a solution based on mixture models

Soffritti

Galimberti

2010

Stat Comput

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In some situations, the distribution of the error terms of a multivariate linear regression model may depart from normality. This problem has been addressed, for example, by specifying a different parametric distribution family for the error terms, such as multivariate skewed and/or heavy-tailed distributions. A new solution is proposed, which is obtained by modelling the error term distribution through a finite mixture of multi-dimensional Gaussian components. The multivariate linear regression model is studied under this assumption. Identifiability conditions are proved and maximum likelihood estimation of the model parameters is performed using the EM algorithm. The number of mixture components is chosen through model selection criteria; when this number is equal to one, the proposal results in the classical approach. The performances of the proposed approach are evaluated through Monte Carlo experiments and compared to the ones of other approaches. In conclusion, the results obtained from the analysis of a real dataset are presented.Keywords EM algorithm · Mixture model · Model selection criterion · Multivariate regression · Non-normal error distribution Electronic supplementary material The online version of this article (

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Multivariate Linear Regression Model with Elliptically Contoured Distributed Errors and Monotone Missing Dependent Variables

Cited by 5 publications

References 40 publications

Hierarchical Missing Data and Multivariate Behrens–Fisher Problem

Hierarchical Missing Data and Multivariate Behrens–Fisher Problem

The Stein phenomenon for monotone incomplete multivariate normal data

Multivariate linear regression with non-normal errors: a solution based on mixture models

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