analysis of proportional mean residual life model with latent variables end stage renal disease esrd is one of the most serious diabetes complications numerous studies have been devoted to revealing the risk factors of the onset time of esrd in this article we propose a proportional mean residual life mrl model with latent variables to assess the effects of observed and latent risk factors on the mrl function of esrd in a cohort of chinese type 2 diabetic patients the proposed model generalizes the conventional proportional mrl model to accommodate the latent risk factor that cannot be measured by a single observed variable we employ a factor analysis model to characterize the latent risk factors via multiple observed variables we develop a borrow strength estimation procedure which incorporates the expectation maximization algorithm and an extended estimating equation approach the asymptotic properties of the proposed estimators are established simulation shows that the performance of the proposed methodology is satisfactory the application to the study of type 2 diabetes reveals insights into the prevention of esrd copyright 2016 john wiley sons ltd

classification of irreducible weight modules over w algebra w 2 2 in this paper we show that the support of an irreducible weight module over the w algebra w 2 2 which has an infinite dimensional weight space coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional as a corollary we obtain that every irreducible weight module over the w algebra w 2 2 having a nontrivial finite dimensional weight space is a harish chandra module and hence is either an irreducible highest or a lowest weight module or an irreducible module of the intermediate series

component models for fuzzy data the fuzzy perspective in statistical analysis is first illustrated with reference to the informational paradigm allowing us to deal with different types of uncertainties related to the various informational ingredients data model assumptions the fuzzy empirical data are then introduced referring to j lr fuzzy variables as observed on i observation units each observation is characterized by its center and its left and right spreads lr1 fuzzy number or by its left and right centers and its left and right spreads lr2 fuzzy number two types of component models for lr1 and lr2 fuzzy data are proposed the estimation of the parameters of these models is based on a least squares approach exploiting an appropriately introduced distance measure for fuzzy data a simulation study is carried out in order to assess the efficacy of the suggested models as compared with traditional principal component analysis on the centers and with existing methods for fuzzy and interval valued data an application to real fuzzy data is finally performed

a family of simple weight modules over the virasoro algebra abstract using simple modules over the derivation lie algebra c t d d t for the polynomial algebra c t we construct new weight modules over the witt algebra where all the weight spaces are infinite dimensional we determine the necessary and sufficient conditions for these new modules being simple as well as determining the necessary and sufficient conditions for two witt modules being isomorphic if a module is not simple we obtain all its submodules as a consequence we fully determine the simplicity and isomorphism classes for the witt modules defined by 3 which are a small proportion of the modules constructed in this study

a latent variable transformation model approach for exploring dysphagia multiple outcomes are often collected in applications where the quantity of interest cannot be measured directly or is difficult or expensive to measure in a head and neck cancer study conducted at dana farber cancer institute the investigators wanted to determine the effect of clinical and treatment factors on unobservable dysphagia through collected multiple outcomes of mixed types latent variable models are commonly adopted in this setting these models stipulate that multiple collected outcomes are conditionally independent given the latent factor mixed types of outcomes e g continuous vs ordinal and censored outcomes present statistical challenges however as a natural analog of the multivariate normal distribution does not exist for mixed data recently lin et al proposed a semiparametric latent variable transformation model for mixed outcome data however it may not readily accommodate event time outcomes where censoring is present in this paper we extend the work of lin et al by proposing both semiparametric and parametric latent variable models that allow for the estimation of the latent factor in the presence of measurable outcomes of mixed types including censored outcomes both approaches allow for a direct estimate of the treatment or other covariate effect on the unobserved latent variable greatly enhancing the interpretability of the models the semiparametric approach has the added advantage of allowing the relationship between the measurable outcomes and latent variables to be unspecified rendering more robust inference the parametric and semiparametric models can also be used together providing a comprehensive modeling strategy for complicated latent variable problems copyright 2014 john wiley sons ltd

simulation of fuzzy random variables this work deals with the simulation of fuzzy random variables which can be used to model various realistic situations where uncertainty is not only present in form of randomness but also in form of imprecision described by means of fuzzy sets utilizing the common arithmetics in the space of all fuzzy sets only induces a conical structure as a consequence it is difficult to directly apply the usual simulation techniques for functional data in order to overcome this difficulty two different approaches based on the concept of support functions are presented the first one makes use of techniques for simulating hilbert space valued random elements and afterwards projects on the cone of all fuzzy sets it is shown by empirical results that the practicability of this approach is limited the second approach imitates the representation of every element of a separable hilbert space in terms of an orthonormal basis directly on the space of fuzzy sets in this way a new approximation of fuzzy sets useful to approximate and simulate fuzzy random variables is developed this second approach is adequate to model various realistic situations

a mixed effects regression model for longitudinal multivariate ordinal data summary a mixed effects item response theory model that allows for three level multivariate ordinal outcomes and accommodates multiple random subject effects is proposed for analysis of multivariate ordinal outcomes in longitudinal studies this model allows for the estimation of different item factor loadings item discrimination parameters for the multiple outcomes the covariates in the model do not have to follow the proportional odds assumption and can be at any level assuming either a probit or logistic response function maximum marginal likelihood estimation is proposed utilizing multidimensional gauss hermite quadrature for integration of the random effects an iterative fisher scoring solution which provides standard errors for all model parameters is used an analysis of a longitudinal substance use data set where four items of substance use behavior cigarette use alcohol use marijuana use and getting drunk or high are repeatedly measured over time is used to illustrate application of the proposed model

regression analysis of additive hazards model with latent variables we propose an additive hazards model with latent variables to investigate the observed and latent risk factors of the failure time of interest each latent risk factor is characterized by correlated observed variables through a confirmatory factor analysis model we develop a hybrid procedure that combines the expectation maximization em algorithm and the borrow strength estimation approach to estimate the model parameters we establish the consistency and asymptotic normality of the parameter estimators various nice features including finite sample performance of the proposed methodology are demonstrated by simulation studies our model is applied to a study concerning the risk factors of chronic kidney disease for type 2 diabetic patients supplementary materials for this article are available online

simulation of random fuzzy variables an empirical approach to statistical probabilistic studies with fuzzy experimental data in this paper we simulate different types of random fuzzy variables to get some conclusions concerning fuzzy valued random variables this simulation was carried out to illustrate certain limit results formalizing the convergence of the arithmetic mean of sampled fuzzy data to the population mean or an expected value of the random fuzzy variable like the well known strong law of large numbers and the law of iterated logarithm since the theoretical results have recently been proved this simulation analysis represents a complementary study in which we can determine sample sizes providing us with suitable approximations finally future directions regarding statistical inference with fuzzy data and other applications are commented

a possibilistic approach to latent component analysis for symmetric fuzzy data in many situations the available amount of data is huge and can be intractable when the data set is single valued latent component models are recognized techniques which provide a useful compression of the information this is done by considering a regression model between observed and unobserved latent variables in this paper an extension of latent component analysis to deal with fuzzy data is proposed our extension follows the possibilistic approach widely used both in the cluster and regression frameworks in this case the possibilistic approach involves the formulation of a latent component analysis for fuzzy data by optimization specifically a non linear programming problem in which the fuzziness of the model is minimized is introduced in order to show how our model works the results of two applications are proposed

latent transition regression for mixed outcomes l etat sanitaire d un patient est une observation complexe souvent caracterisee par plusieurs mesures l etude des transitions entre etats sanitaires successifs necessite la prise en compte de multiples variables mesurees longitudinalement les difficultes d analyse de ces donnees longitudinales multivariees sont encore renforcees lorsque les resultats d interet combinent des variables continues categorielles et des effectifs pour resoudre ces difficultes nous proposons une approche entierement bayesienne de regression sur les transitions latentes qui permet l analyse conjointe d un melange de variables longitudinales quelle qu en soit la distribution l etat sanitaire est considere comme une variable categorielle latente et les autres variables de resultat sont traitees comme des mesures secondaires de l etat sanitaire latent avec des erreurs de mesure cette approche permet l estimation conjointe de la prevalence de chaque etat sanitaire et des probabilites de transition entre etats en fonction des covariables les resultats observes sont lies aux etats sanitaires sous jacents par des modeles de regression qui incluent des effets individuels pour tenir compte de la correlation residuelle entre mesures repetees au cours du temps et des covariables pour tenir compte des differentes mesures de l etat sanitaire latent nous illustrons la methode proposee avec des donnees provenant d une etude longitudinale sur le mal de dos

a parameterized l2 metric between fuzzy numbers and its parameter interpretation abstract when handling fuzzy number data it is a common practice to make use of a metric to quantify distances between fuzzy numbers several metrics have been suggested in the literature for this purpose when statistically analyzing fuzzy number valued data l 2 metrics become especially useful this paper introduces a new family of generalized l 2 metrics which take into account key features of the involved fuzzy numbers namely a measure of central location and two measures associated with the shape of the fuzzy numbers are used a crucial property related to these three measures is that necessary and sufficient conditions can be established for them to characterize fuzzy numbers furthermore the family of generalized l 2 metrics depends on one parameter a discussion is provided regarding the interpretation of this parameter which can guide selection of its value in practice

joint models for the association of longitudinal binary and continuous processes with application to a smoking cessation trial joint models for the association of a longitudinal binary and a longitudinal continuous process are proposed for situations in which their association is of direct interest the models are parameterized such that the dependence between the two processes is characterized by unconstrained regression coefficients bayesian variable selection techniques are used to parsimoniously model these coefficients a markov chain monte carlo mcmc sampling algorithm is developed for sampling from the posterior distribution using data augmentation steps to handle missing data several technical issues are addressed to implement the mcmc algorithm efficiently the models are motivated by and are used for the analysis of a smoking cessation clinical trial in which an important question of interest was the effect of the exercise treatment on the relationship between smoking cessation and weight gain

the alternating syzygy behavior of monomial algebras abstract in this paper we present a minimal projective resolution of a monomial algebra over its enveloping algebra the syzygies for this resolution exhibit an alternating behavior which is explained by the construction of a special sequence of paths from the quiver of

self organizing maps for imprecise data self organizing maps soms consist of a set of neurons arranged in such a way that there are neighbourhood relationships among neurons following an unsupervised learning procedure the input space is divided into regions with common nearest neuron vector quantization allowing clustering of the input vectors in this paper we propose an extension of the soms for data imprecisely observed self organizing maps for imprecise data soms id the learning algorithm is based on two distances for imprecise data in order to illustrate the main features and to compare the performances of the proposed method we provide a simulation study and different substantive applications

fraction representations and highest weight like representations of the virasoro algebra abstract in this paper two new classes of irreducible modules over the centerless virasoro algebra v are obtained these modules are generally not weight modules or whittaker modules we first construct a class of modules over v parameterized by any 2 n 2 complex numbers for any nonnegative integer n which we call fraction modules the necessary and sufficient conditions for fraction modules to be irreducible are determined also we determine the necessary and sufficient conditions for two irreducible fraction modules to be isomorphic then we define highest weight like verma modules over v these modules behave like highest weight verma modules it is proved that each highest weight like verma module has an irreducible quotient module which is isomorphic to a subquotient of some reducible fraction module

a random effects model for multiple characteristics with possibly missing data abstract the use of random effects models for the analysis of longitudinal data with missing responses has been discussed by several authors this article extends the random effects model for a single characteristic to the case of multiple characteristics allowing for arbitrary patterns of observed data two different structures for the covariance matrix of measurement error are considered uncorrelated error between responses and correlation of error terms at the same measurement times parameters for this model are estimated via the em algorithm the set of equations for this estimation procedure is derived these equations are appropriately modified to deal with missing data the methodology is illustrated with an example from clinical trials

homological invariants relating the super jordan plane to the virasoro algebra abstract nichols algebras are an important tool for the classification of hopf algebras within those with finite gk dimension we study homological invariants of the super jordan plane that is the nichols algebra a b v 1 2 these invariants are hochschild homology the hochschild cohomology algebra the lie structure of the first cohomology space which is a lie subalgebra of the virasoro algebra and its representations h n a a and also the yoneda algebra we prove that the algebra a is k 2 moreover we prove that the yoneda algebra of the bosonization a k z of a is also finitely generated but not k 2

efficiency and power of tests for multiple binary outcomes abstract global tests provide a useful tool for comparing two or more groups with respect to multiple correlated outcomes we adapt and compare the performance of tests that have been suggested for use with multiple continuous outcomes to the case of multiple binary outcomes comparisons and guidelines are based on asymptotic relative efficiencies are s and simulations these results are illustrated using an application from teratology we extend the work of lefkopoulou and ryan to include general m group comparisons alternatives where group effects may differ for each outcome a concise form for this general class of score tests is derived to compute the are s for this class of tests we devise a useful characterization of the alternative space based on multivariate polar coordinates our findings indicate that the common outcome effect tests are efficient for a remarkably large range of circumstances a simple formula applies to compute the maximum number of unaffected outcomes that can be included i

principal component analysis of fuzzy data using autoassociative neural networks this paper describes an extension of principal component analysis pca allowing the extraction of a limited number of relevant features from high dimensional fuzzy data our approach exploits the ability of linear autoassociative neural networks to perform information compression in just the same way as pca without explicit matrix diagonalization fuzzy input values are propagated through the network using fuzzy arithmetics and the weights are adjusted to minimize a suitable error criterion the inputs being taken as target outputs the concept of correlation coefficient is extended to fuzzy numbers allowing the interpretation of the new features in terms of the original variables experiments with artificial and real sensory evaluation data demonstrate the ability of our method to provide concise representations of complex fuzzy data

latent variable models for longitudinal data with multiple continuous outcomes summary multiple outcomes are often used to properly characterize an effect of interest this paper proposes a latent variable model for the situation where repeated measures over time are obtained on each outcome these outcomes are assumed to measure an underlying quantity of main interest from different perspectives we relate the observed outcomes using regression models to a latent variable which is then modeled as a function of covariates by a separate regression model random effects are used to model the correlation due to repeated measures of the observed outcomes and the latent variable an em algorithm is developed to obtain maximum likelihood estimates of model parameters unit specific predictions of the latent variables are also calculated this method is illustrated using data from a national panel study on changes in methadone treatment practices

a latent variable approach to study gene environment interactions in the presence of multiple correlated exposures many existing cohort studies initially designed to investigate disease risk as a function of environmental exposures have collected genomic data in recent years with the objective of testing for gene environment interaction g e effects in environmental epidemiology interest in g e arises primarily after a significant effect of the environmental exposure has been documented cohort studies often collect rich exposure data as a result assessing g e effects in the presence of multiple exposure markers further increases the burden of multiple testing an issue already present in both genetic and environment health studies latent variable lv models have been used in environmental epidemiology to reduce dimensionality of the exposure data gain power by reducing multiplicity issues via condensing exposure data and avoid collinearity problems due to presence of multiple correlated exposures we extend the lv framework to characterize gene environment interaction in presence of multiple correlated exposures and genotype categories further similar to what has been done in case control g e studies we use the assumption of gene environment g e independence to boost the power of tests for interaction the consequences of making this assumption or the issue of how to explicitly model g e association has not been previously investigated in lv models we postulate a hierarchy of assumptions about the lv model regarding the different forms of g e dependence and show that making such assumptions may influence inferential results on the g e and g e parameters we implement a class of shrinkage estimators to data adaptively trade off between the most restrictive to most flexible form of g e dependence assumption and note that such class of compromise estimators can serve as a benchmark of model adequacy in lv models we demonstrate the methods with an example from the early life exposures in mexico city to neuro toxicants element study of lead exposure iron metabolism genes and birth weight

change point analysis of imprecise time series abstract in this paper we describe how to conduct a change point analysis when dealing with time series imprecisely or vaguely observed i e time ordered observations whose values are not known exactly such as interval or ordinal time series imprecise time series in order to treat such time series we propose to employ a fuzzy approach i e data are parameterized in the form of fuzzy variables then to detect the number and location of change points we employ a deviation measure for fuzzy variables in the framework of atheoretical regression trees art we present simulation results pertaining to the behavior of the proposed approach as well as two empirical applications to real imprecise time series

analysis of data with multiple sources of correlation in the framework of generalized estimating equations this paper is motivated by a study of physical activity participation habits in african american women with three potential sources of correlation among study outcomes according to method of assessment timing of measurement and intensity of physical activity to adjust for the multiple sources of correlation in this study we implement an approach based on generalized estimating equations that models association via a patterned correlation matrix we present a general algorithm that is relatively straightforward to program an analysis of our physical activity study and some asymptotic relative efficiency comparisons between correctly specifying the correlation structure vs ignoring two sources of correlation in the analysis of data from this study the efficiency comparisons demonstrate that correctly modeling the correlation structure can prevent substantial losses in efficiency in estimation of the regression parameter

the analysis of multiple endpoints in clinical trials treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall type i error rate one option is to select a single primary endpoint for formal statistical inference but this is not always feasible another approach is to apply bonferroni correction i e multiply each p value by the total number of endpoints its conservatism for correlated endpoints is examined for multivariate normal data a third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics quantitative binary and survival endpoints are all considered within this general framework two examples are presented and the relative merits of the proposed strategies are discussed

irreducible virasoro modules from tensor products ii abstract in this paper we obtain a class of virasoro modules by taking tensor products of a finite number of irreducible virasoro modules of the form i a i defined in 19 with irreducible highest weight modules v h or with irreducible virasoro modules ind n defined in 24 i e the tensor product i 1 m i a i v where v is v h or ind n we obtain the necessary and sufficient conditions for such tensor product modules to be irreducible and determine the necessary and sufficient conditions for two of them to be isomorphic we compare the tensor products with other known irreducible non weight virasoro modules we also characterize these irreducible tensor products

residual based diagnostics for structural equation models classical diagnostics for structural equation models are based on aggregate forms of the data and are ill suited for checking distributional or linearity assumptions we extend recently developed goodness of fit tests for correlated data based on subject specific residuals to structural equation models with latent variables the proposed tests lend themselves to graphical displays and are designed to detect misspecified distributional or linearity assumptions to complement graphical displays test statistics are defined the null distributions of the test statistics are approximated using computationally efficient simulation techniques the properties of the proposed tests are examined via simulation studies we illustrate the methods using data from a study of in utero lead exposure

a class of simple weight virasoro modules abstract for a simple module m over the positive part of the virasoro algebra actually for any simple module over some finite dimensional solvable lie algebras a r and any c a class of weight modules n m over the virasoro algebra is constructed these weight modules have infinite dimensional weight spaces if dim m 1 the necessary and sufficient conditions for n m to be simple are obtained we also determine the necessary and sufficient conditions for two such irreducible virasoro modules to be isomorphic many examples for such irreducible virasoro modules with different features are provided in particular the irreducible weight virasoro modules 1 2 1 2 are defined on the polynomial algebra c x c t t 1 for any 1 2 1 2 c with 1 or 2 nonzero by twisting the weight modules n m we also obtain nonweight simple virasoro modules n m for any nonconstant c t t 1

modules induced from polynomial subalgebras of the virasoso algebra abstract the virasoro lie algebra is a one dimensional central extension of the witt algebra which can be realized as the lie algebra of derivations on the algebra c t of laurent polynomials using this fact we define a natural family of subalgebras of the virasoro algebra which we call polynomial subalgebras we describe the one dimensional modules for polynomial subalgebras and we use this description to study the corresponding induced modules for the virasoro algebra we show that these induced modules are frequently simple and generalize a family of recently discovered simple modules additionally we explore tensor products involving these induced modules this allows us to describe new simple modules and also recover results on recently discovered simple modules for the virasoro algebra

projective resolutions of associative algebras and ambiguities abstract the aim of this article is to give a method to construct bimodule resolutions of associative algebras generalizing bardzell s well known resolution of monomial algebras we stress that this method leads to concrete computations providing thus a useful tool for computing invariants associated to the considered algebras we illustrate how to use it by giving several examples in the last section of the article in particular we give necessary and sufficient conditions for noetherian down up algebras to be 3 calabi yau

two and three way component models for lr fuzzy data in a possibilistic framework abstract in this work we address the data reduction problem for fuzzy data in particular following a possibilistic approach several component models for handling two and three way fuzzy data sets are introduced the two way models are based on classical principal component analysis pca whereas the three way ones on three way generalizations of pca as tucker3 and candecomp parafac the here proposed models exploit the potentiality of the possibilistic regression in fact the component models for fuzzy data can be seen as particular regression analyses between a set of observed fuzzy variables response variables and a set of unobservable crisp variables explanatory variables in order to show how the models work the results of an application to a three way fuzzy data set are illustrated

classification of harish chandra modules over some lie algebras related to the virasoro algebra abstract in this paper we provide a uniform method to thoroughly classify all harish chandra modules over some lie algebras related to the virasoro algebras we first classify such modules over the lie algebra w s for s 0 1 2 with this result and method we can also do such works for some lie algebras related to the virasoro algebra including the several kinds of schrodinger virasoro lie algebras which are open up to now

simple weight modules for schrodinger algebra abstract let v be a simple weight module for the schrodinger algebra s 1 but not a simple sl 2 module let supp v if v is neither a highest weight module nor a lowest weight module for s 1 we prove that supp v z and all non trivial weight spaces of v have the same dimensions finally we construct an example of a simple s 1 module with infinite dimensional weight spaces

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

wn and wn module structures on u hn abstract let h n be the cartan subalgebra of the witt algebras w n der c t 1 t 2 t n and w n der c t 1 1 t 2 1 t n 1 where 1 n in this paper we classify the modules over w n and over w n which are free u h n modules of rank 1 these are the w n modules n a s for some n 1 n c n a c and s 1 2 n and w n modules n a for some n c n and some a c

latent variable models with fixed effects we discuss latent variable models that allow for fixed effect covariates as well as covariates affecting the latent variable directly restricted maximum likelihood and maximum likelihood are used to estimate model parameters a generalized likelihood ratio test can be used to test significance of the covariates effecting the latent outcomes special cases of the proposed model correspond to factor analysis mixed models random effects models and simultaneous equations the model is applied to birth defects data where continuous data on the size of infants who were exposed to anticonvulsant medications in utero are compared to controls

the cohomology ring of the 12 dimensional fomin kirillov algebra abstract the 12 dimensional fomin kirillov algebra fk 3 is defined as the quadratic algebra with generators a b and c which satisfy the relations a 2 b 2 c 2 0 and a b b c c a 0 b a c b a c by a result of a milinski and h j schneider this algebra is isomorphic to the nichols algebra associated to the yetter drinfeld module v over the symmetric group s 3 corresponding to the conjugacy class of all transpositions and the sign representation exploiting this identification we compute the cohomology ring ext fk 3 k k showing that it is a polynomial ring s x with coefficients in the symmetric braided algebra of v as an application we also compute the cohomology rings of the bosonization fk 3 k s 3 and of its dual which are 72 dimensional ordinary hopf algebras

on a class of fuzzy c numbers clustering procedures for fuzzy data this paper describes a class of fuzzy clustering procedures for fuzzy data most fuzzy clustering techniques are designed for handling crisp data with their class memberships using the idea of fuzzy set theory here we derive new types of fuzzy clustering procedures in dealing with fuzzy data these procedures are called fuzzy c numbers fcn clusterings specially we construct these fcns for u type triangular trapezoidal and normal fuzzy numbers k jwoy s cluster analysis fuzzy clustering fuzzy data analysis fuzzy numbers fuzzy intervals fuzzy c means clustering fuzzy c numbers clustering

joint modeling of performance and subjective reporting to assess sensitivity to drug induced sleepiness in an nasa ground study two forms of cognitive tests were evaluated in terms of their sensitivity to sleepiness induced by the drug promethazine pmz performance for the two test modes y 1 and y 2 pmz concentration and a self reported sleepiness using the karolinska sleepiness scale kss were monitored for 12 h post dose a problem arises when using kss to establish an association between true sleepiness and performance because kss scores are discrete and also because they tend to concentrate on certain values therefore we define a latent sleepiness measure x as an unobserved continuous random variable describing a subject s actual state of sleepiness under the assumption that drug concentration affects x which then affects y 1 y 2 and kss we use bayesian methods to estimate joint equations that permit unbiased comparison of the performance measures sensitivity to x the equations incorporate subject random effects and include a negativity constraint on subject specific slopes of performance with respect to sleepiness

procedures for comparing samples with multiple endpoints summary five procedures are considered for the comparison of two or more multivariate samples these procedures include a newly proposed nonparametric rank sum test and a generalized least squares test also considered are the following tests ordinary least squares hotelling s p and a bonferroni per experiment error rate approach applications are envisaged in which each variable represents a qualitatively different measure of response to treatment the null hypothesis of no treatment difference is tested with power directed towards alternatives in which at least one treatment is uniformly better than the others in all simulations the nonparametric procedure provided relatively good power and accurate control over the size of the test and is recommended for general use alternatively the generalized least squares procedure may also be useful with normally distributed data in moderate or large samples a convenient expression for this procedure is obtained and its asymptotic relative efficiency with respect to the ordinary least squares test is evaluated clinical trials are often conducted for the purpose of evaluating the relative efficacy of two or more modes of therapy when the therapies are administered to independent groups and efficacy is measured on the basis of a single response variable appropriate parametric and nonparametric one way analysis of variance anova procedures and their properties are well known often however efficacy is measured by more than one variable although univariate methods for assessing each characteristic individually are useful in this setting there is often the additional need for a single overall objective probability statement that addresses the question of whether or not the experimental therapy is efficacious this need is particularly acute when the medical question is controversial and the sample size is small although a large literature exists on the comparison of multivariate samples the procedures tend to be infrequently used in practice as pointed out by meier 1975 p 523 the standard analysis for the comparison of two multivariate samples which is based on hotelling s t2 statistic addresses somewhat the wrong question and consequently has very poor power for the alternatives of primary interest specifically the t2 procedure addresses the question are one or more of the treatments different making no distinction between variables that change favorably and variables that change unfavorably a second approach would be to assign per experiment error rates to each of the univariate tests by using bonferroni s inequality i e by multiplying each univariate p value by the number of variables studied the desired overall probability statement is then given by the minimum of the per experiment univariate p values although this approach may be useful in some settings it may lack power for alternatives in which most or all measures of efficacy are improved this will be of particular concern when the number k of endpoints studied is large relative to sample size in fact statistical significance will not be possible in some instances this problem will be exacerbated when the measures of efficacy are highly

bayesian latent variable models for median regression on multiple outcomes souvent il est impossible de mesurer une reponse d interet et on doit necessairement faire appel a des grandeurs accessoires multiples qu on suppose independantes conditionnellement aux valeurs de la variable latente et des covariables observees de facon typique les modeles en variable latente supposent que les residuees sont gaussions cet article propose une regression bayesienne modelisant la mediane et qui dispense d hypothese sur les distributions des residus en s appuyant sur une approximation basee sur les quartiles pour traiter de la dependance intra sujet les quartiles de la reponse des variables de remplacement sont liees a des distributions normales sous jacentes dependant d une variable latente normale la structure de covariance gaussienne qui en resulte simplifie l interpretatin et l ajustement sans limiter les distributions marginales des variables de remplacement pour les calculs des distributions a posteriori nous proposons un algorithme de chaine de markov monte carlo les methodes sont appliquees sont appliquees pour d une etude de toxicologie genetique aux dosages par electrophorese sur cellule unique essai cornet

generalizing the notion of koszul algebra we introduce a generalization of the notion of a koszul algebra which includes graded algebras with relations in different degrees and we establish some of the basic properties of these algebras this class is closed under twists twisted tensor products regular central extensions and ore extensions we explore the monomial algebras in this class and we include some well known examples of algebras that fall into this class

classification of simple weight virasoro modules with a finite dimensional weight space we show that the support of a simple weight module over the virasoro algebra which has an infinite dimensional weight space coincides with the weight lattice and that all non trivial weight spaces of such module are infinite dimensional as a corollary we obtain that every simple weight module over the virasoro algebra having a non trivial finite dimensional weight space is a harish chandra module and hence is either a simple highest or lowest weight module or a simple module from the intermediate series this implies positive answers to two conjectures about simple pointed and simple mixed modules over the virasoro algebra

weight modules with a finite dimensional weight space over truncated virasoro algebras truncated virasoro algebras can be viewed as quotient algebras of the loop virasoro algebra in this paper we prove that any weight module m with a finite dimensional weight space over any truncated virasoro algebra l f vir c t 1 fc t 1 has a harish chandra submodule where vir is the virasoro algebra and f is a nonzero and not invertible laurent polynomial in c t 1 more precisely if m has a nontrivial upper bounded vir submodule then it has a highest weight l f submodule if m has a nontrivial lower bounded vir submodule then it has a lowest weight l f submodule if m is nontrivial over l f and does not contain any nontrivial upper bounded nor any nontrivial lower bounded vir submodules then it has a nontrivial harish chandra l f submodule s such that dims 1 for all supp s 0 as a corollary any irreducible weight module with a finite dimensional weight space over l f is a harish chandra module

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

a class of representations over the virasoro algebra abstract in 3 and 4 the indecomposable and irreducible harish chandra modules over the virasoro algebra are studied and classified in this paper we construct a class of indecomposable modules with infinite dimensional weight spaces over the virasoro algebra in some cases the indecomposable modules are irreducible

classification of the indecomposable bounded admissible modules over the virasoro lie algebra with weightspaces of dimension not exceeding two in view of 1 2 any bounded admissible modulea over the virasoro lie algebra open image in new window is a finite length extension of irreducible modules with one dimensional weightspaces to each extension of finite lengthn are associatedn 1 invariants a1 1 n we prove that we have i j 0 1 6 n 1b for all i j with 1 i j n in the casen 2 this result allows us to construct all the indecomposable bounded admissible open image in new window modules where the dimensions of the weightspaces are less than or equal to two in particular we obtain all the extensions of two irreducible bounded open image in new window modules

fuzzy clustering of fuzzy data based on robust loss functions and ordered weighted averaging abstract in many real cases the data are not expressed in term of single values but are imprecise in all these cases standard clustering methods for single valued data are unable to properly take into account the imprecise nature of the data in this paper by considering the partitioning around medoids pam approach in a fuzzy framework we propose a fuzzy clustering method for imprecise data formalized in a fuzzy manner in particular in order to neutralize the negative effects of possible outlier fuzzy data in the clustering process we proposed a robust fuzzy c medoids clustering method for fuzzy data based on the combination of huber s m estimators and yager s owa ordered weighted averaging operators the proposed method is able to smooth the influence of anomalous data by means of a suitable parameter the so called typicality parameter capable to tune the influence of the outliers the performance of the proposed method has been shown by means of a simulation study composed of experiments on i simple two dimensional dataset ii benchmark datasets and iii the fuzzy art outliers dataset the comparison made with the robust clustering methods known from the literature indicates the competitiveness of the introduced method to others an application of the suggested method to a real dataset is also provided and the results of the method has been compared with other clustering methods suggested in the literature in the application the comparative assessment has shown the informational gain in term of additional information of the proposed method vs the other robust methods