Multivariate Elliptically Contoured Distributions for Repeated Measurements

Lindsey, J. K.

doi:10.1111/j.0006-341x.1999.01277.x

Cited by 56 publications

(31 citation statements)

References 9 publications

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“…We used the Akaike (1974) Information Criterion (AIC) which was used by Lindsey (1999) and among others to compare the classical multivariate normal model and the multivariate power exponential model. In version 8 of SAS/STAT software AIC is defined as 'smaller-is-better'.…”

Section: Resultsmentioning

confidence: 99%

Random Regression Models Based On The Elliptically Contoured Distribution Assumptions With Applications To Longitudinal Data

Zheng

Rao

Bartolucci

et al. 2003

J. Mod. App. Stat. Meth.

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We generalize Lyles et al.'s (2000) random regression models for longitudinal data, accounting for both undetectable values and informative drop-outs in the distribution assumptions. Our models are constructed on the generalized multivariate theory which is based on the Elliptically Contoured Distribution (ECD). The estimation of the fixed parameters in the random regression models are invariant under the normal or the ECD assumptions. For the Human Immunodeficiency Virus Epidemiology Research Study data, ECD models fit the data better than classical normal models according to the Akaike (1974) Information Criterion. We also note that both univariate distributions of the random intercept and random slope and their joint distribution are non-normal short-tailed ECDs, and that the error term is distributed as a non-normal long-tailed ECD if we don't use the low undetectable limit or half of it to replace the undetectable values. Instead, we use the ECD cumulative distribution function to calculate the contribution to the likelihood due to the undetectable values.

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Section: Resultsmentioning

confidence: 99%

Random Regression Models Based On The Elliptically Contoured Distribution Assumptions With Applications To Longitudinal Data

Zheng

Rao

Bartolucci

et al. 2003

J. Mod. App. Stat. Meth.

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“…The class of ecpe distributions is used in a crossover trial on insulin applied to rabbits in [23], in image denoising in [24] and in colour texture retrieval in [25]. Applications of multivariate g-and-h distributions to jointly modeling body mass index and lean body mass are demonstrated in [26] and accompanied by star-shaped contoured density illustrations.…”

Section: Applicationsmentioning

confidence: 99%

Estimation of Star-Shaped Distributions

Liebscher

Richter

2016

Risks

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Scatter plots of multivariate data sets motivate modeling of star-shaped distributions beyond elliptically contoured ones. We study properties of estimators for the density generator function, the star-generalized radius distribution and the density in a star-shaped distribution model. For the generator function and the star-generalized radius density, we consider a non-parametric kernel-type estimator. This estimator is combined with a parametric estimator for the contours which are assumed to follow a parametric model. Therefore, the semiparametric procedure features the flexibility of nonparametric estimators and the simple estimation and interpretation of parametric estimators. Alternatively, we consider pure parametric estimators for the density. For the semiparametric density estimator, we prove rates of uniform, almost sure convergence which coincide with the corresponding rates of one-dimensional kernel density estimators when excluding the center of the distribution. We show that the standardized density estimator is asymptotically normally distributed. Moreover, the almost sure convergence rate of the estimated distribution function of the star-generalized radius is derived. A particular new two-dimensional distribution class is adapted here to agricultural and financial data sets.

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“…It has been used by J. K. Lindsey to obtain robust models for nonlinear repeated measurements (Lindsey [15]), to modeling dependencies among responses, as an alternative to models based upon the multivariate t distribution, and also to obtain robust models for the physiology of breathing. Basu et al [2] use the multivariate exponential power distribution, as a heavy tailed distribution, in the field of speech recognition.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Exponential Power Distributions as Mixtures of Normal Distributions with Bayesian Applications

Gómez-Sánchez-Manzano

Gómez–Villegas

Marín

2008

Communications in Statistics - Theory and Methods

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It is shown that a multivariate exponential power distribution is a scale mixture of normal distributions, with respect to a probability distribution function, when its kurtosis parameter belongs to the interval (0,1]. The corresponding mixing probability distribution function is presented. This result is used to design a Bayesian hierarchical model and an algorithm to generate samples of the posterior distribution; these are applied to a problem of Quantitative Genetics.

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Multivariate Elliptically Contoured Distributions for Repeated Measurements

Cited by 56 publications

References 9 publications

Random Regression Models Based On The Elliptically Contoured Distribution Assumptions With Applications To Longitudinal Data

Random Regression Models Based On The Elliptically Contoured Distribution Assumptions With Applications To Longitudinal Data

Estimation of Star-Shaped Distributions

Multivariate Exponential Power Distributions as Mixtures of Normal Distributions with Bayesian Applications

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