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138
Semiparametrically efficient rankbased inference for shape I: Optimal rankbased tests for sphericity
 Ann. Statist
, 2006
"... A class of Restimators based on the concepts of multivariate signed ranks and the optimal rankbased tests developed in Hallin and Paindaveine [Ann. Statist. 34 (2006)] is proposed for the estimation of the shape matrix of an elliptical distribution. These Restimators are rootn consistent under a ..."
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Cited by 48 (32 self)
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A class of Restimators based on the concepts of multivariate signed ranks and the optimal rankbased tests developed in Hallin and Paindaveine [Ann. Statist. 34 (2006)] is proposed for the estimation of the shape matrix of an elliptical distribution. These Restimators are rootn consistent under any radial density g, without any moment assumptions, and semiparametrically efficient at some prespecified density f. When based on normal scores, they are uniformly more efficient than the traditional normaltheory estimator based on empirical covariance matrices (the asymptotic normality of which, moreover, requires finite moments of order four), irrespective of the actual underlying elliptical density. They rely on an original rankbased version of Le Cam’s onestep methodology which avoids the unpleasant nonparametric estimation of crossinformation quantities that is generally required in the context of Restimation. Although they are not strictly affineequivariant, they are shown to be equivariant in a weak asymptotic sense. Simulations confirm their feasibility and excellent finitesample performances. 1. Introduction. 1.1. Rankbased inference for elliptical families. An elliptical density over Rk is determined by a location center θ ∈ Rk, a scale parameter σ ∈ R + 0, a realvalued positive definite symmetric k × k matrix V = (Vij) with V11 = 1,
A Flexible Class of SkewSymmetric Distributions
 Scandinavian Journal of Statistics
, 2004
"... ABSTRACT. We propose a flexible class of skewsymmetric distributions for which the probability density function has the form of a product of a symmetric density and a skewing function. By constructing an enumerable dense subset of skewing functions on a compact set, we are able to consider a family ..."
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Cited by 21 (7 self)
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ABSTRACT. We propose a flexible class of skewsymmetric distributions for which the probability density function has the form of a product of a symmetric density and a skewing function. By constructing an enumerable dense subset of skewing functions on a compact set, we are able to consider a family of distributions, which can capture skewness, heavy tails and multimodality systematically. We present three illustrative examples for the fibreglass data, the simulated data from a mixture of two normal distributions and the Swiss bills data. Key words: dense subset, generalized skewelliptical, multimodality, skewness, skewnormal 1.
On fundamental skew distributions
, 2005
"... A new class of multivariate skewnormal distributions, fundamental skewnormal distributions and their canonical version, is developed. It contains the product of independent univariate skewnormal distributions as a special case. Stochastic representations and other main properties of the associate ..."
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Cited by 20 (10 self)
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A new class of multivariate skewnormal distributions, fundamental skewnormal distributions and their canonical version, is developed. It contains the product of independent univariate skewnormal distributions as a special case. Stochastic representations and other main properties of the associated distribution theory of linear and quadratic forms are considered. A unified procedure for extending this class to other families of skew distributions such as the fundamental skewsymmetric, fundamental skewelliptical, and fundamental skewspherical class of distributions is also discussed.
Estimating copula densities through wavelets
 Insurance Math. Econom
, 2009
"... Laboratoire de probabilités et modèles aléatoires ..."
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A Bayesian Approach to Bandwidth Selection for Multivariate Kernel Density Estimation
, 2004
"... Abstract: Kernel density estimation for multivariate data is an important technique that has a wide range of applications. However, it has received significantly less attention than its univariate counterpart. The lower level of interest in multivariate kernel density estimation is mainly due to the ..."
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Cited by 19 (8 self)
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Abstract: Kernel density estimation for multivariate data is an important technique that has a wide range of applications. However, it has received significantly less attention than its univariate counterpart. The lower level of interest in multivariate kernel density estimation is mainly due to the increased difficulty in deriving an optimal datadriven bandwidth as the dimension of the data increases. We provide Markov chain Monte Carlo (MCMC) algorithms for estimating optimal bandwidth matrices for multivariate kernel density estimation. Our approach is based on treating the elements of the bandwidth matrix as parameters whose posterior density can be obtained through the likelihood crossvalidation criterion. Numerical studies for bivariate data show that the MCMC algorithm generally performs better than the plugin algorithm under the KullbackLeibler information criterion, and is as good as the plugin algorithm under the mean integrated squared error (MISE) criterion. Numerical studies for five dimensional data show that our algorithm is superior to the normal reference rule. Our MCMC algorithm is the first datadriven bandwidth selector for multivariate kernel density estimation that is applicable to data of any dimension. Keywords: Crossvalidation; KullbackLeibler information; Mean integrated squared errors;
Powering up with spacetime wind forecasting
 Journal of the American Statistical Association
, 2009
"... The technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality. Highquality shortterm forecasts of wind speed are vital to making this a more reliable energy source. Gneiting et al. (2006) have introduced a model for the average wind spe ..."
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Cited by 19 (5 self)
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The technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality. Highquality shortterm forecasts of wind speed are vital to making this a more reliable energy source. Gneiting et al. (2006) have introduced a model for the average wind speed two hours ahead based on both spatial and temporal information. The forecasts produced by this model are accurate, and subject to accuracy, the predictive distribution is sharp, i.e., highly concentrated around its center. However, this model is split into nonunique regimes based on the wind direction at an offsite location. This paper both generalizes and improves upon this model by treating wind direction as a circular variable and including it in the model. It is robust in many experiments, such as predicting at new locations. We compare this with the more common approach of modeling wind speeds and directions in the Cartesian space and use a skewt distribution for the errors. The quality of the predictions from all of these models can be more realistically assessed with a loss measure that depends upon the power curve relating wind speed to power output. This proposed loss measure yields more insight into the true value of each model’s predictions. Some key words: Circular variable, power curve, skewt distribution, wind direction, wind speed.
MULTIVARIATE SYMMETRY AND ASYMMETRY
, 2003
"... Univariate symmetry has interesting and diverse forms of generalization to the multivariate case. Here several leading concepts of multivariate symmetry — spherical, elliptical, central and angular — are examined and various closely related notions discussed. Methods for testing the hypothesis of s ..."
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Cited by 12 (0 self)
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Univariate symmetry has interesting and diverse forms of generalization to the multivariate case. Here several leading concepts of multivariate symmetry — spherical, elliptical, central and angular — are examined and various closely related notions discussed. Methods for testing the hypothesis of symmetry, and approaches for measuring the direction and magnitude of skewness, are reviewed.
Finite mixture modelling using the skew normal distribution
 Statistica Sinica
"... Abstract: Normal mixture models provide the most popular framework for modelling heterogeneity in a population with continuous outcomes arising in a variety of subclasses. In the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theo ..."
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Cited by 11 (2 self)
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Abstract: Normal mixture models provide the most popular framework for modelling heterogeneity in a population with continuous outcomes arising in a variety of subclasses. In the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this article, we address the problem of analyzing a mixture of skew normal distributions from the likelihoodbased and Bayesian perspectives, respectively. Computational techniques using EMtype algorithms are employed for iteratively computing maximum likelihood estimates. Also, a fully Bayesian approach using the Markov chain Monte Carlo method is developed to carry out posterior analyses. Numerical results are illustrated through two examples. Key words and phrases: ECM algorithm, ECME algorithm, Fisher information, Markov chain Monte Carlo, maximum likelihood estimation, skew normal mixtures. 1.
The impact of rapid wind variability upon air–sea thermal coupling
 J. Climate
"... The basic effect of extratropical atmosphere–ocean thermal coupling is to enhance the variance of both anomalous sea surface temperatures (SSTs) and air temperatures (AIRT) due to a decreased energy flux between the atmosphere and ocean, called reduced thermal damping. In this paper it is shown that ..."
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Cited by 11 (3 self)
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The basic effect of extratropical atmosphere–ocean thermal coupling is to enhance the variance of both anomalous sea surface temperatures (SSTs) and air temperatures (AIRT) due to a decreased energy flux between the atmosphere and ocean, called reduced thermal damping. In this paper it is shown that rapidly varying surface winds, through their influence upon the turbulent surface heat fluxes that drive this coupling, act to effectively weaken the coupling and thus partially counteract the reduced thermal damping. In effect, rapid fluctuations in wind speed somewhat insulate the atmosphere and ocean from each other. The nonlinear relationship between the rapidly varying wind speed anomalies and SST and AIRT anomalies results in a rapidly varying component of the surface heat fluxes. The clear separation between the dynamical time scales of the ocean and atmosphere allows this rapidly varying flux to be simply approximated by a stochastic process in which rapidly varying wind speed is represented as Gaussian white noise whose amplitude is modulated by the more slowly evolving thermal anomalies. Such statedependent (multiplicative) noise can alter the dynamics of atmosphere–ocean coupling because it induces an additional heat flux term, the noiseinduced drift, that effectively acts to weaken both coupling and dissipation. Another key implication of the outlined theory is that air–sea coupling includes both deterministic and