the analysis of multitrait multimethod matrices via constrained components analysis multitrait multimethod mtmm matrices are often analyzed by means of confirmatory factor analysis cfa however fitting mtmm models often leads to improper solutions or non convergence in an attempt to overcome these problems various alternative cfa models have been proposed but with none of these the problem of finding improper solutions was solved completely in the present paper an approach is proposed where improper solutions are ruled out altogether and convergence is guaranteed the approach is based on constrained variants of components analysis ca besides the fact that these methods do not give improper solutions they have the advantage that they provide component scores which can later on be used to relate the components to external variables the new methods are illustrated by means of simulated data as well as empirical data sets

a variable selection heuristic for k means clustering one of the most vexing problems in cluster analysis is the selection and or weighting of variables in order to include those that truly define cluster structure while eliminating those that might mask such structure this paper presents a variable selection heuristic for nonhierarchical k means cluster analysis based on the adjusted rand index for measuring cluster recovery the heuristic was subjected to monte carlo testing across more than 2200 datasets with known cluster structure the results indicate the heuristic is extremely effective at eliminating masking variables a cluster analysis of real world financial services data revealed that using the variable selection heuristic prior to the k means algorithm resulted in greater cluster stability

four simultaneous component models for the analysis of multivariate time series from more than one subject to model intraindividual and interindividual differences a class of four simultaneous component models for the exploratory analysis of multivariate time series collected from more than one subject simultaneously is discussed in each of the models the multivariate time series of each subject is decomposed into a few series of component scores and a loading matrix the component scores series reveal the latent data structure in the course of time the interpretation of the components is based on the loading matrix the simultaneous component models model not only intraindividual variability but interindividual variability as well the four models can be ordered hierarchically from weakly to severely constrained thus allowing for big to small interindividual differences in the model the use of the models is illustrated by an empirical example

dynamics of competition between collectivity and noise in the stock market abstract detailed study of the financial empirical correlation matrix of the 30 companies which deutsche aktienindex dax comprised during the period of the last 11 years using the time window of 30 trading days is presented this allows clear identification of a nontrivial time dependence of the resulting correlations in addition as a rule the drawdowns are always accompanied by a sizable separation of one strong collective eigenstate of the correlation matrix which at the same time reduces the variance of the noise states the opposite applies to drawups in this case the dynamics spreads more uniformly over the eigenstates which results in an increase of the total information entropy analogous study of the market corresponding to daw jones industrial average djia leads to similar conclusions in the latter case however the correlations are weaker on average one possible reason for this effect is that the market represented by djia is less susceptible to various external factors than the one represented by dax

exploratory longitudinal factor analysis in multiple populations for multiple populatios a longtidinal factor analytic model which is entirely exploratory that is no explicit identification constraints is proposed factorial collapse and period practice effects are allowed an invariant and or stationary factor pattern is permitted this model is formulated stochastically to implement this model a stagewise em algorithm is developed finally a numerical illustration utilizing nesselroade and baltes data is presented

component analysis in cross sectional and longitudinal data an extension of component analysis to longitudinal or cross sectional data is presented in this method components are derived under the restriction of invariant and or stationary compositing weights optimal compositing weights are found numerically the method can be generalized to allow differential weighting of the observed variables in deriving the component solution some choices of weightings are discussed an illustration of the method using real data is presented

quantifying and interpreting collective behavior in financial markets firms having similar business activities are correlated we analyze two different cross correlation matrices c constructed from i 30 min price fluctuations of 1000 us stocks for the two year period 1994 95 and ii one day price fluctuations of 422 us stocks for the 35 year period 1962 96 we find that the eigenvectors of c corresponding to the largest eigenvalues allow us to partition the set of all stocks into distinct subsets these subsets are similar to business sectors and are stable for extended periods of time we find that price fluctuations of these subsets are characterized by power law decaying time correlations reminiscent of strongly interacting systems the internal structure of a complex system manifests itself in correlations among its constituents in complex physical systems interactions between constituents cause collective modes having special statistical properties which reflect the underlying dynamics can we quantify collective movement of stock prices in analogous terms to address this question we analyze the equal time correlation matrix c constructed from the price fluctuations of a large number of stocks first we find that the collective modes for the stock market problem partition the set of all stocks studied into distinct subsets typically these subsets are formed by combinations of related industries and in some cases they go beyond grouping by industry due to company diversification the traditional partitioning of firms into subsets by products and services is difficult and sometimes arbitrary and thus our results could be viewed as a statistical alternative to traditional industry classification 1 furthermore we find that the price fluctuations of the collective modes display long range power law time correla

some existence and nonexistence theorems for solutions of degenerate parabolic equations abstract the initial and boundary value problem for the degenerate parabolic equation v t v f v in the cylinder 0 r n bounded for a certain class of point functions satisfying v 0 e g v v m sign v is considered in the case that f v sign v c 1 v the equation has a global time solution the same is true for 1 provided the measure of is sufficiently small in the case that f v v is nondecreasing a condition is given on the initial state v x 0 which implies that the solution must blow up in finite time the existence of such initial states is discussed

generalized structured component analysis we propose an alternative method to partial least squares for path analysis with components called generalized structured component analysis the proposed method replaces factors by exact linear combinations of observed variables it employs a well defined least squares criterion to estimate model parameters as a result the proposed method avoids the principal limitation of partial least squares i e the lack of a global optimization procedure while fully retaining all the advantages of partial least squares e g less restricted distributional assumptions and no improper solutions the method is also versatile enough to capture complex relationships among variables including higher order components and multi group comparisons a straightforward estimation algorithm is developed to minimize the criterion

hierarchical classes models for three way three mode binary data interrelations and model selection several hierarchical classes models can be considered for the modeling of three way three mode binary data including the indclas model leenen van mechelen de boeck and rosenberg 1999 the tucker3 hiclas model ceulemans van mechelen and leenen 2003 the tucker2 hiclas model ceulemans and van mechelen 2004 and the tucker1 hiclas model that is introduced in this paper two questions then may be raised 1 how are these models interrelated and 2 given a specific data set which of these models should be selected and in which rank in the present paper we deal with these questions by 1 showing that the distinct hierarchical classes models for three way three mode binary data can be organized into a partially ordered hierarchy and 2 by presenting model selection strategies based on extensions of the well known scree test and on the akaike information criterion the latter strategies are evaluated by means of an extensive simulation study and are illustrated with an application to interpersonal emotion data finally the presented hierarchy and model selection strategies are related to corresponding work by kiers 1991 for principal component models for three way three mode real valued data

component analysis with different sets of constraints on different dimensions many of the classical multivariate data analysis and multidimensional scaling techniques call for approximations by lower dimensional configurations a model is proposed in which different sets of linear constraints are imposed on different dimensions in component analysis and classical multidimensional scaling frameworks a simple efficient and monotonically convergent algorithm is presented for fitting the model to the data by least squares the basic algorithm is extended to cover across dimension constraints imposed in addition to the dimensionwise constraints and to the case of a symmetric data matrix examples are given to demonstrate the use of the method

blowing up of solution for a nonlocal reaction diffusion problem in combustion theory abstract in a nonlocal reaction diffusion model in combustion theory the reaction function involves a physical parameter which is a measure of the strength of the reaction mechanism the purpose of this paper is to show the existence of a critical value such that for a unique global time dependent solution exists and converges to a steady state solution as t and for the solution blows up in finite time a characterization as well as upper and lower bounds of are given

blow up for a degenerate parabolic equation with a nonlocal source abstract in this paper existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution that exists globally or blows up in finite time are obtained for the degenerate parabolic problem x q u t u xx 0 a u m x t d x ku n x t in 0 a 0 t where 0 t a 0 m n 1 k 0 are constants

the blow up rate for a degenerate parabolic equation with a non local source abstract in this paper we establish the local existence of the solution and the finite time blow up result for the equation v v m xx a l l v q dx x l l 0 moreover it is proved that the solution has global blow up and there exist constants c 1 c 2 such that c 1 t 1 1 q 1 max x l l v x c 2 t 1 1 q 1 where t 1 is the blow up time

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

complete blow up for degenerate semilinear parabolic equations abstract let t a q and x0 be constants with a 0 q 0 and 0 x q u t u xx f u x 0 t 0 0 u x 0 u 0 x 0 0 x a u 0 t u a t 0 0 where f and u0 are given functions we show that under certain conditions u blows up in a finite time and the set of blow up points is the entire interval 0 a

interpreting canonical correlation analysis through biplots of structure correlations and weights this paper extends the biplot technique to canonical correlation analysis and redundancy analysis the plot of structure correlations is shown to the optimal for displaying the pairwise correlations between the variables of the one set and those of the second the link between multivariate regression and canonical correlation analysis redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients this plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables an example is used to show how the proposed biplots may be interpreted

alternating least squares algorithms for simultaneous components analysis with equal component weight matrices in two or more populations millsap and meredith 1988 have developed a generalization of principal components analysis for the simultaneous analysis of a number of variables observed in several populations or on several occasions the algorithm they provide has some disadvantages the present paper offers two alternating least squares algorithms for their method suitable for small and large data sets respectively lower and upper bounds are given for the loss function to be minimized in the millsap and meredith method these can serve to indicate whether or not a global optimum for the simultaneous components analysis problem has been attained

random matrix approach to cross correlations in financial data we analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory rmt using two large databases we calculate cross correlation matrices c of returns constructed from i 30 min returns of 1000 us stocks for the 2 yr period 1994 1995 ii 30 min returns of 881 us stocks for the 2 yr period 1996 1997 and iii 1 day returns of 422 us stocks for the 35 yr period 1962 1996 we test the statistics of the eigenvalues lambda i of c against a null hypothesis a random correlation matrix constructed from mutually uncorrelated time series we find that a majority of the eigenvalues of c fall within the rmt bounds lambda lambda for the eigenvalues of random correlation matrices we test the eigenvalues of c within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross correlation coefficients further we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction in addition we find that these deviating eigenvectors are stable in time we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks our analysis of the remaining deviating eigenvectors shows distinct groups whose identities correspond to conventionally identified business sectors finally we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return less

weak and strong convergence theorems for a finite family of i asymptotically nonexpansive mappings in this paper a new two step iterative scheme for a finite family of i i asymptotically nonexpansive nonself mappings t i i 1 r is constructed in a uniformly convex banach space weak and strong convergence theorems of this iterative scheme to a common fixed point of t i i 1 r and i i i 1 r are proved in a uniformly convex banach space the results of this paper improve and extend the corresponding results of temir 2

one factor model for the cross correlation matrix in the vietnamese stock market abstract random matrix theory rmt has been applied to the analysis of the cross correlation matrix of a financial time series the most important findings of previous studies using this method are that the eigenvalue spectrum largely follows that of random matrices but the largest eigenvalue is at least one order of magnitude higher than the maximum eigenvalue predicted by rmt in this work we investigate the cross correlation matrix in the vietnamese stock market using rmt and find similar results to those of studies realized in developed markets us europe japan 9 18 as well as in other emerging markets 20 21 19 22 importantly we found that the largest eigenvalue could be approximated by the product of the average cross correlation coefficient and the number of stocks studied we demonstrate this dependence using a simple one factor model the model could be extended to describe other characteristics of the realistic data

maximization of sums of quotients of quadratic forms and some generalizations monotonically convergent algorithms are described for maximizing six constrained functions of vectors x or matrices x with columns x 1 x r these functions are h 1 x sigma k x a k x x c k x 1 h 1 x sigma k tr x a k x x c k x 1 h over tilde 1 x sigma k sigma l x l a k x l x l c k x l 1 with x constrained to be columnwise orthonormal h 2 x sigma k x a k x 2 x c k x 1 subject to x x 1 h 2 x sigma k tr x a k x x a k x x c k x 1 subject to x x i and h over tilde 2 x sigma k sigma l x l a k x l 2 x l c k x l 1 subject to x x i in these functions the matrices c k are assumed to be positive definite the matrices a k can be arbitrary square matrices the general formulation of the functions and the algorithms allows for application of the algorithms in various problems that arise in multivariate analysis several applications of the general algorithms are given specifically algorithms are given for reciprocal principal components analysis binormamin rotation generalized discriminant analysis variants of generalized principal components analysis simple structure rotation for one of the latter variants and set component analysis for most of these methods the algorithms appear to be new for the others the existing algorithms turn out to be special cases of the newly derived general algorithms

finite mixtures in confirmatory factor analysis models in this paper various types of finite mixtures of confirmatory factor analysis models are proposed for handling data heterogeneity under the proposed mixture approach observations are assumed to be drawn from mixtures of distinct confirmatory factor analysis models but each observation does not need to be identified to a particular model prior to model fitting several classes of mixture models are proposed these models differ by their unique representations of data heterogeneity three different sampling schemes for these mixture models are distinguished a mixed type of the these three sampling schemes is considered throughout this article the proposed mixture approach reduces to regular multiple group confirmatory factor analysis under a restrictive sampling scheme in which the structural equation model for each observation is assumed to be known by assuming a mixture of multivariate normals for the data maximum likelihood estimation using the em expectation maximization algorithm and the as approximate scoring method are developed respectively some mixture models were fitted to a real data set for illustrating the application of the theory although the em algorithm and the as method gave similar sets of parameter estimates the as method was found computationally more efficient than the em algorithm some comments on applying the mixture approach to structural equation modeling are made

an efficient algorithm for tuckals3 on data with large numbers of observation units a modification of the tuckals3 algorithm is proposed that handles three way arrays of order i j k for any i when i is much larger than jk the modified algorithm needs less work space to store the data during the iterative part of the algorithm than does the original algorithm because of this and the additional feature that execution speed is higher the modified algorithm is highly suitable for use on personal computers

on the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings abstract the purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in banach spaces the results presented in this paper extend and improve the corresponding results of h bauschke the approximation of fixed points of compositions of nonexpansive mappings in hilbert space j math anal appl 202 1996 150 159 b halpern fixed points of nonexpansive maps bull amer math soc 73 1967 957 961 p l lions approximation de points fixes de contractions c r acad sci paris ser a 284 1977 1357 1359 s reich strong convergence theorems for resolvents of accretive operators in banach spaces j math anal appl 75 1980 287 292 z h sun strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings j math anal appl 286 2003 351 358 r wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 h k xu m g ori an implicit iterative process for nonexpansive mappings numer funct anal optimiz 22 2001 767 773 y y zhou s s chang convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in banach spaces numer funct anal optimiz 23 2002 911 921

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings in the present paper we prove that the modified implicit iteration sequence for a finite family of asymptotically quasi nonexpansive mappings converges strongly to a common fixed point of the family in a uniformly convex banach space requiring one member t in the family to be semi compact our results extend and improve some recent results

principal component analysis with external information on both subjects and variables a method for structural analysis of multivariate data is proposed that combines features of regression analysis and principal component analysis in this method the original data are first decomposed into several components according to external information the components are then subjected to principal component analysis to explore structures within the components it is shown that this requires the generalized singular value decomposition of a matrix with certain metric matrices the numerical method based on the qr decomposition is described which simplifies the computation considerably the proposed method includes a number of interesting special cases whose relations to existing methods are discussed examples are given to demonstrate practical uses of the method

some convergence theorems of non implicit iteration process with errors for a finite families of i asymptotically nonexpansive mappings the purpose of this paper is to study the weak and strong convergence of non implicit iteration process with errors to a common fixed point for a finite family of i asymptotically quasi nonexpansive mappings in banach spaces the results presented in this paper extend and improve the corresponding results of several authors 1 2 7 14 17 19 22 29

uniform blow up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source in this paper we introduce a new method for investigating the rate and profile of blow up of solutions of diffusion equations with nonlocal nonlinear reaction terms for large classes of equations we prove that the solutions have global blow up and that the rate of blow up is uniform in all compact subsets of the domain this results in a flat blow up profile except for a boundary layer whose thickness vanishes astapproaches the blow up timet in each case the blow up rate of u t is precisely determined furthermore in many cases we derive sharp estimates on the size of the boundary layer and on the asymptotic behavior of the solution in the boundary layer the size of the boundary layer then decays liket t and the solutionu t x behaves like u t d x t tin the boundary layer wheredis the distance to the boundary some fujita type critical exponents results are also given for the cauchy problem

composition of the first principal component of a stock index a comparison between sp500 and vnindex abstract we analyzed the components of the eigenvector corresponding to the largest eigenvalue of a cross correlation matrix of stock price change the 1 st eigenvector using the principle components pcs analysis method we found that the components of the 1 st eigenvector are not uniformly distributed in fact they are proportional to the correlations of individual stocks and the 1st pc and could be negative if the corresponding stock is in average negatively correlated to other stocks by analyzing data from the world stock index in a developed country sp500 and an emerging one such as vietnam vnindex from 2013 to 2017 we found negative components in the 1 st eigenvector in the vnindex and their distribution is also broader than that of sp500 furthermore we found that the largest components correspond to stocks of financial services brokerage or investment advisory firms firms in both indices those stocks are found to be center hubs in a minimum spanning tree mst analysis and play an important role whenever a systemic breakdown happens finally we found a phenomenological linear dependence between the components of the 1 st eigenvector and the average stock correlation in both indices and derived an approximation of this dependency using empirical stylized facts of the data this result provides an estimation of how the pc1 is composed

blow up at the boundary for degenerate semilinear parabolic equations this paper treats a superlinear parabolic equation degenerate in the time derivative it is shown that the solution may blow up in finite time moreover it is proved that for a large class of initial data blow up occurs at the boundary of the domain when the nonlinearity is no worse than quadratic various estimates are obtained which determine the asymptotic behaviour near the blow up the mathematical analysis is then extended to equations with other degeneracies

a multivariate reduced rank growth curve model with unbalanced data a multivariate reduced rank growth curve model is proposed that extends the univariate reducedrank growth curve model to the multivariate case in which several response variables are measured over multiple time points the proposed model allows us to investigate the relationships among a number of response variables in a more parsimonious way than the traditional growth curve model in addition the method is more flexible than the traditional growth curve model for example response variables do not have to be measured at the same time points nor the same number of time points it is also possible to apply various kinds of basis function matrices with different ranks across response variables it is not necessary to specify an entire set of basis functions in advance examples are given for illustration

canonical analysis of contingency tables with linear constraints a generalized least squares approach is presented for incorporating linear constraints on the standardized row and column scores obtained from a canonical analysis of a contingency table the method is easy to implement and may simplify considerably the interpretation of a data matrix the approach is compared to a restricted maximum likelihood procedure

blow up for a degenerate parabolic equation with a nonlocal source abstract in this paper we investigate the blowup properties of the positive solutions to the following nonlocal degenerate parabolic equation v x v m xx 0 l v p 1 dx kv q 1 with homogeneous dirichlet boundary conditions in the interval 0 l where 0 m 1 we first establish the local existence and uniqueness of its classical solutions then we show that the positive solution blows up in finite time if the initial datum is sufficient large finally we prove that the blow up set is the whole interval and we also obtain the estimates of the blow up rate

the effect of cluster size dimensionality and the number of clusters on recovery of true cluster structure an evaluation of four clustering methods and four external criterion measures was conducted with respect to the effect of the number of clusters dimensionality and relative cluster sizes on the recovery of true cluster structure the four methods were the single link complete link group average upgma and ward s minimum variance algorithms the results indicated that the four criterion measures were generally consistent with each other of which two highly similar pairs were identified the tirst pair consisted of the rand and corrected rand statistics and the second pair was the jaccard and the fowlkes and mallows indexes with respect to the methods recovery was found to improve as the number of clusters increased and as the number of dimensions increased the relative cluster size factor produced differential performance effects with ward s procedure providing the best recovery when the clusters were of equal size the group average method gave equivalent or better recovery when the clusters were of unequal size

convergence theorem for i asymptotically quasi nonexpansive mapping in hilbert space abstract let h be a hilbert space with inner product and norm and let k be weakly compact a subset of h let t k k be nonlinear mapping and i k k be a nonlinear bounded mapping in this paper we define the i asymptotically quasi nonexpansive mapping in hilbert space if t is an i asymptotically quasi nonexpansive mapping then we prove that 1 n i 0 n 1 t i u for u k as n is weakly almost convergent to its asymptotic center

the harris kaiser independent cluster rotation as a method for rotation to simple component weights procedures for oblique rotation of factors or principal components typically focus on rotating the pattern matrix such that it becomes optimally simple an important oblique rotation method that does so is harris and kaiser s 1964 independent cluster hkic rotation in principal components analysis a case can be made for interpreting the components on the basis of the component weights rather than on the basis of the pattern so it seems desirable to rotate the components such that the weights rather than the pattern become optimally simple in the present paper it is shown that hkic rotates the components such that both the pattern and the weights matrix become optimally simple in addition it is shown that the pattern resulting from hkic rotation is columnwise proportional to the associated weights matrix which implies that the interpretation of the components does not depend on whether it is based on the pattern or on the component weights matrix it is also shown that the latter result only holds for hkic rotation and slight modifications of it

some clarifications of the candecomp algorithm applied to indscal carroll and chang have claimed that candecomp applied to symmetric matrices yields equivalent coordinate matrices as needed for indscal although this claim has appeared to be valid for all practical purposes it has gone without a rigorous mathematical footing the purpose of the present paper is to clarify candecomp in this respect it is shown that equivalent coordinate matrices are not granted at global minima when the symmetric matrices are not gramian or when these matrices are gramian but the solution not globally optimal

an efficient algorithm for parafac of three way data with large numbers of observation units the candecomp algorithm for the parafac analysis ofn m p three way arrays is adapted to handle arrays in whichn mp more efficiently for such arrays the adapted algorithm needs less memory space to store the data during the iterations and uses less computation time than the original candecomp algorithm the size of the arrays that can be handled by the new algorithm is in no way limited by the number of observation units n in the data

strong convergence of an implicit iteration process for a finite family of nonexpansive mappings abstract the purpose of this paper is to prove the strong convergence of an implicit iteration process to a common fixed point for a finite family of nonexpansive mappings our theorems give an affirmative response to a question raised by xu and ori numer funct anal optim 22 2001 767 773

relationships among several methods of linearly constrained correspondence analysis this paper shows essential equivalences among several methods of linearly constrained correspondence analysis they include fisher s method of additive scoring hayashi s second type of quantification method ter braak s canonical correspondence analysis nishisato s type of quantification method ter braak s canonical correspondence analysis nishisato s anova of categorical data correspondence analysis of manipulated contingency tables bockenholt and bockenholt s least squares canonical analysis with linear constraints and van der heijden and meijerink s zero average restrictions these methods fall into one of two classes of methods corresponding to two alternative ways of imposing linear constraints the reparametrization method and the null space method a connection between the two is established through khatri s lemma

homogeneity analysis with k sets of variables an alternating least squares method with optimal scaling features homogeneity analysis or multiple correspondence analysis is usually applied tok separate variables in this paper we apply it to sets of variables by using sums within sets the resulting technique is called overals it uses the notion of optimal scaling with transformations that can be multiple or single the single transformations consist of three types nominal ordinal and numerical the corresponding overals computer program minimizes a least squares loss function by using an alternating least squares algorithm many existing linear and nonlinear multivariate analysis techniques are shown to be special cases of overals an application to data from an epidemiological survey is presented

on component analyses principal components analysis can be redefined in terms of the regression of observed variables upon component variables two criteria for the adequacy of a component representation in this context are developed and are shown to lead to different component solutions both criteria are generalized to allow weighting the choice of weights determining the scale invariance properties of the resulting solution a theorem is presented giving necessary and sufficient conditions for equivalent component solutions under different choices of weighting applications of the theorem are discussed that involve the components analysis of linearly derived variables and of external variables

random matrix theory analysis of cross correlations in financial markets we confirm universal behaviors such as eigenvalue distribution and spacings predicted by random matrix theory rmt for the cross correlation matrix of the daily stock prices of tokyo stock exchange from 1993 to 2001 which have been reported for new york stock exchange in previous studies it is shown that the random part of the eigenvalue distribution of the cross correlation matrix is stable even when deterministic correlations are present some deviations in the small eigenvalue statistics outside the bounds of the universality class of rmt are not completely explained with the deterministic correlations as proposed in previous studies we study the effect of randomness on deterministic correlations and find that randomness causes a repulsion between deterministic eigenvalues and the random eigenvalues this is interpreted as a reminiscent of level repulsion in rmt and explains some deviations from the previous studies observed in the market data we also study correlated groups of issues in these markets and propose a refined method to identify correlated groups based on rmt some characteristic differences between properties of tokyo stock exchange and new york stock exchange are found

dynamics of market correlations taxonomy and portfolio analysis the time dependence of the recently introduced minimum spanning tree description of correlations between stocks called the asset tree has been studied in order to reflect the financial market taxonomy the nodes of the tree are identified with stocks and the distance between them is a unique function of the corresponding element of the correlation matrix by using the concept of a central vertex chosen as the most strongly connected node of the tree an important characteristic is defined by the mean occupation layer during crashes due to the strong global correlation in the market the tree shrinks topologically and this is shown by a low value of the mean occupation layer the tree seems to have a scale free structure where the scaling exponent of the degree distribution is different for business as usual and crash periods the basic structure of the tree topology is very robust with respect to time we also point out that the diversification aspect of portfolio optimization results in the fact that the assets of the classic markowitz portfolio are always located on the outer leaves of the tree technical aspects such as the window size dependence of the investigated quantities are also discussed

multidimensional successive categories scaling a maximum likelihood method a single step maximum likelihood estimation procedure is developed for multidimensional scaling of dissimilarity data measured on rating scales the procedure can fit the euclidian distance model to the data under various assumptions about category widths and under two distributional assumptions the scoring algorithm for parameter estimation has been developed and implemented in the form of a computer program practical uses of the method are demonstrated with an emphasis on various advantages of the method as a statistical procedure

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

on the convergence theorems of implicit iteration process for a finite family of i asymptotically nonexpansive mappings in this paper we consider the weak and strong convergence of implicit iteration process to a common fixed point of i asymptotically nonexpansive mappings the main results extend to a finite family of i asymptotically nonexpansive mappings in a banach space

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

existence of classical solutions for degenerate semilinear parabolic problems let q be a nonnegative real number and t be a positive real number existence of a unique classical solution is established for the following degenerate semilinear parabolic initial boundary value problem x qu t u x x f u 0

modeling differences in the dimensionality of multiblock data by means of clusterwise simultaneous component analysis given multivariate multiblock data e g subjects nested in groups are measured on multiple variables one may be interested in the nature and number of dimensions that underlie the variables and in differences in dimensional structure across data blocks to this end clusterwise simultaneous component analysis sca was proposed which simultaneously clusters blocks with a similar structure and performs an sca per cluster however the number of components was restricted to be the same across clusters which is often unrealistic in this paper this restriction is removed the resulting challenges with respect to model estimation and selection are resolved