a test for a specific principal component of a correlation matrix abstract in the application of principal components analysis it is common to replace an observed sample principal component vector by another vector closely resembling the sample vector but which is easier to use or interpret a useful test of hypothesis in this case is one that specifies the true ith principal component in this article we obtain an asymptotically chi squared procedure suitable for testing such a hypothesis when the principal components analysis is performed on a correlation matrix the procedure easily extends to a principal components analysis based on m estimates of scatter

covariance reducing models an alternative to spectral modelling of covariance matrices we introduce covariance reducing models for studying the sample covariance matrices of a random vector observed in different populations the models are based on reducing the sample covariance matrices to an informational core that is sufficient to characterize the variance heterogeneity among the populations they possess useful equivariance properties and provide a clear alternative to spectral models for covariance matrices

bayesian estimation in the presence of deterministic nuisance parameters part ii estimation methods one of the fundamental issues of estimation theory is the presence of deterministic nuisance parameters while in the bayesian paradigm the model parameters are random introduction of deterministic nuisance parameters into the model exceeds the bayesian framework to the hybrid framework in this type of scenarios the conventional bayesian estimators are not valid as they assume knowledge of the deterministic nuisance parameters this paper is the second of a two part study of bayesian parameter estimation in the presence of deterministic nuisance parameters in part i a new cramer rao cr type bound on the mean square error mse for bayesian estimation in the presence of deterministic nuisance parameters was established based on the concept of risk unbiasedness the proposed bound was named risk unbiased bound rub this paper presents properties of asymptotic uniform mean and risk unbiasedness of some bayesian estimators 1 the minimum mse mmse or maximum a posteriori probability map estimators with maximum likelihood ml estimates substituting the deterministic parameters named ms ml and map ml respectively and 2 joint map and ml estimator named jmap ml furthermore an asymptotic performance analysis of the ms ml and map ml estimators is presented these estimators are shown to asymptotically achieve the rub while the existing cr type bounds can be achieved only in distinct cases simulations verify these results for the problem of blind separation of nonstationary sources it is shown that unlike existing cr type bounds the rub is asymptotically tight

influence in principal components analysis summary in linear regression the theoretical influence function and the various sample versions of it have an established place as diagnostic tools these same functions are developed here to provide methods for the detection of influential observations in principal components analysis the perturbation theory of real symmetric matrices unifies this development some interesting points of contrast with the regression case are noted and explained theoretically

diagonality measures of hermitian positive definite matrices with application to the approximate joint diagonalization problem in this paper we introduce properly invariant diagonality measures of hermitian positive definite matrices these diagonality measures are defined as distances or divergences between a given positive definite matrix and its diagonal part we then give closed form expressions of these diagonality measures and discuss their invariance properties the diagonality measure based on the log determinant divergence is general enough as it includes a diagonality criterion used by the signal processing community as a special case these diagonality measures are then used to formulate minimization problems for finding the approximate joint diagonalizer of a given set of hermitian positive definite matrices numerical computations based on a modified newton method are presented and commented

the concurrent complementary operators method applied to two dimensional time harmonic radiation and scattering problems the concurrent complementary operators method c com has recently been applied to time harmonic solution of maxwell equations in two dimensional space in this paper we present the application of the c com to the problem of electromagnetic scattering by conducting cylindrical objects in two dimensional spaces we show that the c com can effectively annihilate surface waves that impinge on the boundary at or near grazing incidence the effectiveness of the c com is due to the fact that its wave absorption mechanism is independent of the wave number to demonstrate the effectiveness and robustness of the c com in time harmonic simulation we present several numerical experiments a strong agreement is obtained between the c com solution and the reference solutions even when the computational boundary is positioned only a fraction of a wavelength from the scatterer s body furthermore we present a numerical experiment that shows the behavior of c com when waves impinge on the outer boundary at oblique incidence

analyse harmonique sur les espaces symetriques nilpotents resume soit g un groupe de lie nilpotent connexe et simplement connexe h l ensemble des points fixes d une involution de g nous donnons la formule de plancherel de la representation ind h g 1 et en deduisons que tout operateur differentiel g invariant sur g h non nul admet une solution elementaire temperee h invariante

local influence in principal components analysis summary based on the definition of generalised influence function and generalised cook statistic local influence of small perturbations on the eigenvalues and eigenvectors of a covariance matrix are studied for population and sample versions the results based on the correlation matrix are also derived and some related topics are discussed finally an example is used for illustration bations although this method has been applied to many models beckman nachtsheim cook 1987 lawrance 1988 thomas cook 1990 assessing the local influence for multivariate data is still an unexplored area in this paper a method based on a generalised influence function and generalised cook statistic is introduced to assess the local influence of small perturbations on a statistic of interest and we prove that this method is equivalent to cook s work based on normal curvature in the likelihood framework since local influence on some statistics in multivariate analysis is not easy to study using the likelihood displacement of cook 1986 this method is expected to have wider applications in this paper we employ the generalised cook statistic to assess local influence in principal components analysis in 2 we introduce the definition of the generalised influ ence function and generalised cook statistic in 3 the perturbation theory of eigenvalues and eigenvectors of a real symmetric matrix is studied in 4 the local influence of small perturbations of observations on eigenvalues and the eigenvectors of sample covariance

fonctions orbitales surgc gr formule d inversion des integrales orbitales et formule de plancherel resume soitgun groupe de lie semi simple complexe connexe et simplement connexe d algebre de lie g soithune forme reelle degd algebre de lie h apres une etude generale des fonctions orbitales surg h nous construisons des series de fonctions orbitales propres sous l action de l algebre des operateurs differentielsg invariant surg h en utilisant les resultats de p harinck base de la serie la plus continue de fonctions generalisees spheriques surg c g r prepublication concernant les fonctions generalisees spheriques surg h nous demontrons la formule d inversion des integrales orbitales d une fonction de classec a support compact surg h nous en deduisons la formule de plancherel pour l espace symetriqueg h letgbe a complex connected and simply connected semisimple lie group with lie algebra g lethbe a real form ofgwith lie algebra h after a general study of orbital functions ong h we construct series of orbital functions which are eigen for the action ofg invariant differential operators ong h using the results harinck base de la serie la plus continue de fonctions generalisees spheriques surg c g r prepublication about spherical generalized functions ong h we prove the inversion formula for orbital integrals of ac function with compact support ong h we deduce the plancherel formula for the symmetric spaceg h

two generalizations of the common principal component model summary under the common principal component model the covariance matrices ti of k populations are assumed to have identical eigenvectors that is the same orthogonal matrix diagonalizes all ti simultaneously this paper modifies the common principal component model by assuming that only q out of p eigenvectors are common to all ti while the remaining p q eigenvectors are specific in each group this is called a partial common principal component model a related modification assumes that q eigenvectors of each matrix span the same subspace a problem that was first considered by krzanowski 1979 for both modifications this paper derives the normal theory maximum likelihood estimators it is shown that approximate maximum likelihood estimates can easily be computed if estimates of the ordinary common principal component model are available the methods are illustrated by numerical examples

efficient r estimation of principal and common principal components we propose rank based estimators of principal components both in the one sample and under the assumption of common principal components in the m sample cases those estimators are obtained via a rank based version of le cam s one step method combined with an estimation of cross information quantities under arbitrary elliptical distributions with in the m sample case possibly heterogeneous radial densities those r estimators remain root n consistent and asymptotically normal while achieving asymptotic efficiency under correctly specified radial densities contrary to their traditional counterparts computed from empirical covariances they do not require any moment conditions when based on gaussian score functions in the one sample case they uniformly dominate their classical competitors in the pitman sense their ares with respect to other robust procedures are quite high up to 30 in the gaussian case with respect to minimum covariance determinant estimators their finite sample performances

an efficient k nearest neighbor search for multivariate time series multivariate time series mts datasets are common in various multimedia medical and financial applications in order to efficiently perform k nearest neighbor searches for mts datasets we present a similarity measure eros extended frobenius norm an index structure muse multilevel distance based index structure for eros and a feature subset selection technique ropes recursive feature elimination on common principal components for eros eros is based on principal component analysis and computes the similarity between two mts items by measuring how close the corresponding principal components are using the eigenvalues as weights muse constructs each level as a distance based index structure without using the weights up to z levels which are combined at the query time with the weights ropes utilizes both the common principal components and the weights recursively in order to select a subset of features for eros the experimental results show the superiority of our techniques as compared to earlier approaches

optimal bayes classifiers for functional data and density ratios bayes classifiers for functional data pose a challenge this is because probability density functions do not exist for functional data as a consequence the classical bayes classifier using density quotients needs to be modified we propose to use density ratios of projections on a sequence of eigenfunctions that are common to the groups to be classified the density ratios can then be factored into density ratios of individual functional principal components whence the classification problem is reduced to a sequence of nonparametric one dimensional density estimates this is an extension to functional data of some of the very earliest nonparametric bayes classifiers that were based on simple density ratios in the one dimensional case by means of the factorization of the density quotients the curse of dimensionality that would otherwise severely affect bayes classifiers for functional data can be avoided we demonstrate that in the case of gaussian functional data the proposed functional bayes classifier reduces to a functional version of the classical quadratic discriminant a study of the asymptotic behavior of the proposed classifiers in the large sample limit shows that under certain conditions the misclassification rate converges to zero a phenomenon that has been referred to as perfect classification the proposed classifiers also perform favorably in finite sample applications as we demonstrate in comparisons with other functional classifiers in simulations and various data applications including wine spectral data functional magnetic resonance imaging fmri data for attention deficit hyperactivity disorder adhd patients and yeast gene expression data

spectral models for covariance matrices summary a new model for the simultaneous eigenstructure of multiple covariance matrices is proposed the model is much more flexible than existing models and subsumes most of them as special cases a fisher scoring algorithm for computing maximum likelihood estimates of the parameters under normality is given asymptotic distributions of the estimators are derived under normality as well as under arbitrary distributions having finite fourth order cumulants special attention is given to elliptically contoured distributions likelihood ratio tests are described and sufficient conditions are given under which the test statistics are asymptotically distributed as chi squared random variables procedures are derived for evaluating bartlett corrections under normality some conjectures made by flury 1988 are verified others are refuted a small simulation study of the adequacy of the bartlett correction is described and the new procedures are illustrated on two datasets

base de la serie la plus continue de fonctions generalisees spheriques surgc gr resume soit g un groupe de lie semi simple complexe connexe et simplement connexe d algebre de lie g soit h une forme reelle de g d algebre de lie h on suppose que h admet une sous algebre de cartan de type compact t pour un element regulier du dual de t on construit une base de l espace des fonctions generalisees spheriques sur g h propres sous l action de l algebre des operateurs differentiels g invariants sur g h pour le caractere defini par on etudie ensuite le prolongement meromorphe en et la croissance des elements de cette base ces fonctions generalisees sont ensuite exprimees en terme de coefficients de representations de g ces resultats sont generalises a d autres series de fonctions generalisees spheriques let g be a complex connected and simply connected semisimple lie group with lie algebra g let h be a real form of g with lie algebra h we suppose that h admits a cartan subalgebra t of compact type for a regular element of the dual of h we construct a basis of the space of spherical generalized functions f such that for all g invariant differential operator d on g h we have d f d f where is the character defined by then we study the meromorphic continuation and the growth of the element of this basis we give these functions in terms of coefficients of representations of g these results are generalized to other series of spherical generalized functions

nonorthogonal joint diagonalization free of degenerate solution the problem of approximate joint diagonalization of a set of matrices is instrumental in numerous statistical signal processing applications for nonorthogonal joint diagonalization based on the weighted least squares wls criterion the trivial zero solution can simply be avoided by adopting some constraint on the diagonalizing matrix or penalty terms however the resultant algorithms may converge to some undesired degenerate solutions nonzero but singular or ill conditioned solutions this paper discusses and analyzes the problem of degenerate solutions in detail to solve this problem a novel nonleast squares criterion for approximate nonorthogonal joint diagonalization is proposed and an efficient algorithm called fast approximate joint diagonalization fajd is developed as compared with the existing nonorthogonal diagonalization algorithms the new algorithm can not only avoid the trivial solution but also any degenerate solutions theoretical analysis shows that the fajd algorithm has some advantages over the existing nonorthogonal diagonalization algorithms simulation results are presented to demonstrate the efficiency of this paper s algorithm

regularized gaussian discriminant analysis through eigenvalue decomposition abstract friedman proposed a regularization technique rda of discriminant analysis in the gaussian framework rda uses two regularization parameters to design an intermediate classifier between the linear the quadratic the nearest means classifiers in this article we propose an alternative approach called edda that is based on the reparameterization of the covariance matrix k of a group gk in terms of its eigenvalue decomposition k k d k a k d k where k specifies the volume of density contours of gk the diagonal matrix of eigenvalues specifies its shape the eigenvectors specify its orientation variations on constraints concerning volumes shapes orientations k a k and d k lead to 14 discrimination models of interest for each model we derived the normal theory maximum likelihood parameter estimates our approach consists of selecting a model by minimizing the sample based estimate of future misclassification risk by cross validation numerical experiments on simulated and rea

a hierarchical eigenmodel for pooled covariance estimation summary although the covariance matrices corresponding to different populations are unlikely to be exactly equal they can still exhibit a high degree of similarity for example some pairs of variables may be positively correlated across most groups whereas the correlation between other pairs may be consistently negative in such cases much of the similarity across covariance matrices can be described by similarities in their principal axes which are the axes that are defined by the eigenvectors of the covariance matrices estimating the degree of across population eigenvector heterogeneity can be helpful for a variety of estimation tasks for example eigenvector matrices can be pooled to form a central set of principal axes and to the extent that the axes are similar covariance estimates for populations having small sample sizes can be stabilized by shrinking their principal axes towards the across population centre to this end the paper develops a hierarchical model and estimation procedure for pooling principal axes across several populations the model for the across group heterogeneity is based on a matrix valued antipodally symmetric bingham distribution that can flexibly describe notions of centre and spread for a population of orthogonal matrices

complementary operators a method to annihilate artificial reflections arising from the truncation of the computational domain in the solution of partial differential equations the ease and simplicity with which the finite difference time domain fdtd or the finite elements fe techniques can handle complex radiation or scattering problems have lead to a remarkable surge in the use of these methods while execution time is becoming less of an impediment when solving large problems the biggest constraint remains the memory needed to run the fdtd or the fe methods it is precisely this limitation that the article addresses a boundary operation is developed to minimize the artificial reflections that arise when truncating the computational domain of an open region scattering or radiation problem the method is based on the use of two boundary operators that are complementary in their action by solving the problem with each of the two operators and then averaging the two solutions the first order reflections that arise from the artificial boundary can be completely eliminated numerical results are presented to show that this new technique gives significant reduction in the error when compared to other widely used boundary conditions

a new discriminant subspace analysis approach for multi class problems fukunaga koontz transform fkt is a famous feature extraction method in statistical pattern recognition which aims to find a set of vectors that have the best representative power for one class while the poorest representative power for the other class li and savvides 1 propose a one against all strategy to deal with multi class problems in which the two class fkt method can be directly applied to find the presentative vectors of each class motivated by the fkt method in this paper we propose a new discriminant subspace analysis dsa method for the multi class feature extraction problems to solve dsa we propose an iterative algorithm for the joint diagonalization jd problem finally we generalize the linear dsa method to handle nonlinear feature extraction problems via the kernel trick to demonstrate the effectiveness of the proposed method for pattern recognition problems we conduct extensive experiments on real data sets and show that the proposed method outperforms most commonly used feature extraction methods

influence functions and outlier detection under the common principal components model a robust approach summary the common principal components model for several groups of multivariate observations assumes equal principal axes but different variances along these axes among the groups influence functions for plug in and projection pursuit estimates under a common principal component model are obtained asymptotic variances are derived from them outlier detection is possible using partial influence functions

unifying amplitude and phase analysis a compositional data approach to functional multivariate mixed effects modeling of mandarin chinese mandarin chinese is characterized by being a tonal language the pitch or f0 of its utterances carries considerable linguistic information however speech samples from different individuals are subject to changes in amplitude and phase which must be accounted for in any analysis that attempts to provide a linguistically meaningful description of the language a joint model for amplitude phase and duration is presented which combines elements from functional data analysis compositional data analysis and linear mixed effects models by decomposing functions via a functional principal component analysis and connecting registration functions to compositional data analysis a joint multivariate mixed effect model can be formulated which gives insights into the relationship between the different modes of variation as well as their dependence on linguistic and nonlinguistic covariates the model is applied to the cospro 1 dataset a comprehensive database of spoken taiwanese mandarin containing appro

frequency domain complementary operators for finite elements simulation a new mesh truncation technique is introduced for the frequency domain time harmonic solution of open region radiation problems the technique is based on the complementary operators method com where two independent solutions are averaged to eliminate first order boundary reflections the dual complementariness in the frequency domain is achieved by introducing a discrete domain operator that achieves the objective of spl part sub t in the original time domain development of com

robpca a new approach to robust principal component analysis we introduce a new method for robust principal component analysis pca classical pca is based on the empirical covariance matrix of the data and hence is highly sensitive to outlying observations two robust approaches have been developed to date the first approach is based on the eigenvectors of a robust scatter matrix such as the minimum covariance determinant or an s estimator and is limited to relatively low dimensional data the second approach is based on projection pursuit and can handle high dimensional data here we propose the robpca approach which combines projection pursuit ideas with robust scatter matrix estimation robpca yields more accurate estimates at noncontaminated datasets and more robust estimates at contaminated data robpca can be computed rapidly and is able to detect exact fit situations as a by product robpca produces a diagnostic plot that displays and classifies the outliers we apply the algorithm to several datasets from chemometrics and engineering

asymptotic theory for common principal component analysis on donne la distribution asymptotique des estimations du maximum de vraisemblance et on utilise les resultats pour obtenir des tests d egalite des vecteurs propres et de redondance de p q composantes principales

principal component analysis based on robust estimators of the covariance or correlation matrix influence functions and efficiencies a robust principal component analysis can be easily performed by computing the eigenvalues and eigenvectors of a robust estimator of the covariance or correlation matrix in this paper we derive the influence functions and the corresponding asymptotic variances for these robust estimators of eigenvalues and eigenvectors the behaviour of several of these estimators is investigated by a simulation study it turns out that the theoretical results and simulations favour the use of s estimators since they combine a high efficiency with appealing robustness properties 2000 biometrika trust

common principal components in k groups abstract this article generalizes the method of principal components to so called common principal components as follows consider the hypothesis that the covariance matrices i for k populations are simultaneously diagonalizable that is there is an orthogonal matrix such that i is diagonal for i 1 k i derive the normal theory maximum likelihood estimates of the common component i matrices and the log likelihood ratio statistics for testing this hypothesis the solution has some favorable properties that do not depend on normality assumptions numerical examples illustrate the method applications to data reduction multiple regression and nonlinear discriminant analysis are sketched

the concurrent complementary operators method for fdtd mesh truncation the complementary operators were developed for the purpose of truncating the computational domain of finite difference time domain fdtd open region simulations in the original implementation of the complementary operators method two independent simulations were performed the solutions from these two simulations were then averaged to obtain a solution devoid of first order reflections the complementary operators are implemented in a concurrent fashion this new implementation referred to as the concurrent complementary operators method c com requires only one simulation thus reducing the operation count by approximately one half the implementation for two dimensional 2 d space is outlined first with emphasis on reducing reflections from corner regions then the extension to three dimensions is developed numerical results are provided in addition to an analysis of the source of error that arises from this new implementation

semiparametric partial common principal component analysis for covariance matrices we consider the problem of jointly modeling multiple covariance matrices by partial common principal component analysis pcpca which assumes a proportion of eigenvectors to be shared across covariance matrices and the rest to be individual specific this paper proposes consistent estimators of the shared eigenvectors in the pcpca as the number of matrices or the number of samples to estimate each matrix goes to infinity we prove such asymptotic results without making any assumptions on the ranks of eigenvalues that are associated with the shared eigenvectors when the number of samples goes to infinity our results do not require the data to be gaussian distributed furthermore this paper introduces a sequential testing procedure to identify the number of shared eigenvectors in the pcpca in simulation studies our method shows higher accuracy in estimating the shared eigenvectors than competing methods applied to a motor task functional magnetic resonance imaging data set our estimator identifies meaningful brain networks that are consistent with current scientific understandings of motor networks during a motor paradigm

unmasking multivariate outliers and leverage points abstract detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers that is how the outliers get masked to avoid the masking effect we propose to compute distances based on very robust estimates of location and covariance these robust distances are better suited to expose the outliers in the case of regression data the classical least squares approach masks outliers in a similar way also here the outliers may be unmasked by using a highly robust regression method finally a new display is proposed in which the robust regression residuals are plotted versus the robust distances this plot classifies the data into regular observations vertical outliers good leverage points and bad leverage points several examples are discussed

principal component models for correlation matrices summary distributional theory regarding principal components is less well developed for correlation matrices than it is for covariance matrices the intent of this paper is to reduce this disparity methods are proposed that enable investigators to fit and to make inferences about flexible principal components models for correlation matrices the models allow arbitrary eigenvalue multiplicities and allow the distinct eigenvalues to be modelled parametrically or nonparametrically local parameterisations and implicit functions are used to construct full rank unconstrained parameterisations first order asymptotic distributions are obtained directly from the theory of estimating functions second order accurate distributions for making inferences under normality are obtained directly from likelihood theory simulation studies show that the bartlett correction is effective in controlling the size of the tests and that first order approximations to nonnull distributions are reasonably accurate the methods are illustrated on a dataset

modelling covariance structure in bivariate marginal models for longitudinal data summary it can be more challenging to efficiently model the covariance matrices for multivariate longitudinal data than for the univariate case due to the correlations arising between multiple responses the positive definiteness constraint and the high dimensionality are further obstacles in covariance modelling in this paper we develop a data based method by which the parametersinthecovariancematricesarereplacedbyunconstrainedandinterpretableparameterswith reduced dimensions the maximum likelihood estimators for the mean and covariance parameters are shown to be consistent and asymptotically normally distributed simulations and real data analysis show that the new approach performs very well even when modelling bivariate nonstationary dependence structures

fonctions generalisees spheriques induites sur gc gr et applications resume soit g un groupe de lie semi simple complexe d algebre de lie g soit h une forme reelle de g et soit h le sous groupe analytique de g d algebre de lie h par un procede d induction on construit une fonction generalisee spherique p indgl a partir d une fonction generalisee spherique definie sur un espace symetrique plus petit l l h lorsque est le coefficient d une representation on montre que p indgl est un coefficient de representation paraboliquement induite en appliquant ceci a l espace gl n c gl n r on obtient la formule de plancherel sur cet espace a partir de la formule d inversion demontree par s sano

absorbing boundary conditions for acoustic and elastic waves in stratified media abstract absorbing boundary conditions are needed for computing numerical models of wave motions in unbounded spatial domains prior progress on this problem for acoustic and elastic waves has generally been concerned with waves propagating through uniform media the present paper is concerned with waves in stratified media which are of interest for example in geophysical problems suppose that the medium consists of homogeneous layers separated by parallel horizontal interfaces and suppose that absorbing boundary conditions are needed along a vertical computational boundary the boundary conditions that are described in this paper are based on a quantity known as the ray parameter according to snell s law this parameter remains the same when a plane wave propagates through a stratified medium and undergoes reflection refraction and in the case of elastic waves conversion once can therefore use the same absorbing boundary conditions in all layers for acoustic waves the absorption properties are the same in all layers for elastic waves the absorption properties vary somewhat from one layer to another however one still obtains good absorption in all layers even in the presence of strong contrasts between layers the boundary conditions are also effective in absorbing rayleigh waves which propagate along free surfaces of elastic media the boundary formulas developed here can be applied without modification to problems in both two and three dimensions

gaussian parsimonious clustering models gaussian clustering models are useful both for understanding and suggesting powerful criteria banfield and raftery 1993 have considered a parametrization of the variance matrix ek of a cluster pk in terms of its eigenvalue decomposition ek lkdkakd k lk where lk defines the volume of pk dk is an orthogonal matrix which defines its orientation and ak is a diagonal matrix with determinant 1 which defines its shape this parametrization allows us to propose many general clustering criteria from the simplest one spherical cluster with equal volumes which leads to the classical k means criterion to the most complex one unknown and different volumes orientations and shapes for all clusters methods of optimization to derive the maximum likelihood estimates as well as the practical usefulness of these models are discussed we especially analyze the influence of the volumes of clusters we report monte carlo simulations and an application on stellar data which dramatically illustrated the relevance of allowing clusters to have different volumes

method of moments estimation of go garch models we propose a new estimation method for the factor loading matrix in generalized orthogonal garch go garch models the method is based on the eigenvectors of a suitably defined sample autocorrelation matrix of squares and cross products of the process the method can therefore be easily applied to high dimensional systems where likelihood based estimation will run into computational problems we provide conditions for consistency of the estimator and study its efficiency relative to maximum likelihood estimation using monte carlo simulations the method is applied to european sector returns and to the correlation between oil and kerosene returns and airline stock returns

analysis of linear combinations with extreme ratios of variance abstract if the covariance matrices 1 and 2 of two multivariate populations are not identical insight into the differences between 1 and 2 can often be gained by analyzing the linear combinations with extreme ratios of variances that is those defined by the eigenvectors associated with the extreme roots of 1 1 2 this article gives a descriptive method similar to variable selection procedures in regression for screening and simplifying these linear combinations a hypothesis of redundancy of variables is defined and a statistic for testing this hypothesis is derived the method is illustrated by an example

consistent noisy independent component analysis we study linear factor models under the assumptions that factors are mutually independent and independent of errors and errors can be correlated to some extent under the factor non gaussianity second to fourth order moments are shown to yield full identification of the matrix of factor loadings we develop a simple algorithm to estimate the matrix of factor loadings from these moments we run monte carlo simulations and apply our methodology to data on cognitive test scores and financial data on stock returns

raw data maximum likelihood estimation for common principal component models a state space approach the specifications of state space model for some principal component related models are described including the independent group common principal component cpc model the dependent group cpc model and principal component based multivariate analysis of variance some derivations are provided to show the equivalence of the state space approach and the existing wishart likelihood approach for each model a numeric example is used to illustrate the state space approach in addition a simulation study is conducted to evaluate the standard error estimates under the normality and nonnormality conditions in order to cope with the nonnormality conditions the robust standard errors are also computed finally other possible applications of the state space approach are discussed at the end

regularized generalized canonical correlation analysis for multiblock or multigroup data analysis this paper presents an overview of methods for the analysis of data structured in blocks of variables or in groups of individuals more specifically regularized generalized canonical correlation analysis rgcca which is a unifying approach for multiblock data analysis is extended to be also a unifying tool for multigroup data analysis the versatility and usefulness of our approach is illustrated on two real datasets

group comparison of eigenvalues and eigenvectors of diffusion tensors diffusion tensor imaging dti data differ from most medical images in that values at each voxel are not scalars but 3 3 symmetric positive definite matrices called diffusion tensors dts the anatomic characteristics of the tissue at each voxel are reflected by the dt eigenvalues and eigenvectors in this article we consider the problem of testing whether the means of two groups of dt images are equal at each voxel in terms of the dt s eigenvalues eigenvectors or both because eigendecompositions are highly nonlinear existing likelihood ratio statistics lrts for testing differences in eigenvalues or eigenvectors of means of gaussian symmetric matrices assume an orthogonally invariant covariance structure between the matrix entries while retaining the form of the lrts we derive new approximations to their true distributions when the covariance between the dt entries is arbitrary and possibly different between the two groups the approximate distributions are those of similar lrt statistics comput