on the general linear group and hochschild homology our main result here is a rational computation of the homology of the adjoint action of the infinite general linear group of an arbitrary ring before stating the result we establish some notation and conventions rings are associative and with unit if a is a ring then gl a uk 0glk a is its infinite general linear group an a bimodule is an abelian group b which is both a left a module and a right a module and satisfies alb a2 al ba2 for ai ea be b for example b a if b is an a bimodule then m b uk omk b is the infinite additive group of matrices with entries in b conjugation defines an action the adjoint action of gl a on m b note that an a q bimodule is just an a bimodule which is also a rational vector space if b is an a q bimodule then hj a c q b denotes the hochschild homology of a q with coefficients in b our main result it appears in slightly more detailed form as theorem v 3 is

the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

estimating the proportion of true null hypotheses with application to dna microarray data summary we consider the problem of estimating the proportion of true null hypotheses 0 i n a multiple hypothesis set up the tests are based on observed p values we first review published estimators based on the estimator that was suggested by schweder and spjotvoll then we derive new estimators based on nonparametric maximum likelihood estimation of the p value density restricting to decreasing and convex decreasing densities the estimators of 0 are all derived under the assumption of independent test statistics their performance under dependence is investigated in a simulation study we find that the estimators are relatively robust with respect to the assumption of independence and work well also for test statistics with moderate dependence

system reliability and component importance under dependence a copula approach abstractsystem reliability and component importance are of great interest in reliability modeling especially when the components within the system are dependent we characterize the influence of dependence structures on system reliability and component importance in coherent systems with discrete marginal distributions the effects of dependence are captured through copula theory we extend our framework to coherent multi state system applications of the derived results are demonstrated using a gaussian copula which yields simple interpretations simulations and two examples are presented to demonstrate the importance of modeling dependence when estimating system reliability and ranking of component importance proofs algorithms code and data are provided in supplementary materials available online

on the structure and estimation of hierarchical archimedean copulas in this paper we provide a method for estimating multivariate distributions defined through hierarchical archimedean copulas in general the true structure of the hierarchy is unknown but we develop a computationally efficient technique to determine it from the data for this purpose we introduce a hierarchical estimation procedure for the parameters and provide an asymptotic analysis we consider both parametric and nonparametric estimation of the marginal distributions a simulation study and an empirical application show the effectiveness of the grouping procedure in the sense of structure selection

copula based daily rainfall disaggregation model 1 a daily rainfall disaggregation model which uses a copula to model the dependence structure between total depth total duration of wet periods and the maximum proportional depth of a wet period is presented the wet 1 dry 0 binary sequence is modeled by the nonrandomized bartlett lewis model with diurnal effect incorporated before superimposing the ar 1 depth process submodel unlike previous studies the model is structured such that all wet day data available are considered in the analysis without the need to discard any good quality daily data embedded in a month having some missing data this increased the data size thus improving the modeling process further the daily data are classified according to the total duration of wet periods duration within the day in this way a large proportion of the model parameters become seasonal invariant the overriding factor being the total duration of wet periods the potential of the developed model has been demonstrated by disaggregating both the data set used in developing the model parameters and also a 12 year continuous rainfall data set not used in the model parameterization gross rainfall statistics of several aggregation levels down to 6 min have been very well reproduced by the disaggregation model the copula dependence structure and the variation of the depth process submodel parameters with the total duration of wet periods are also very well captured by the presented model

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

factor copula models for item response data factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item responses the factor copula models have interpretations of latent maxima minima in comparison with latent means and can lead to more probability in the joint upper or lower tail compared with factor models based on the discretized multivariate normal distribution or multidimensional normal ogive model details on maximum likelihood estimation of parameters for the factor copula model are given as well as analysis of the behavior of the log likelihood our general methodology is illustrated with several item response data sets and it is shown that there is a substantial improvement on existing models both conceptually and in fit to data

a copula transformation in multivariate mixed discrete continuous models abstract copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions especially if the density function can be represented as the product of the marginal density functions and the copula density function this leads to both an intuitive interpretation of the conditional distribution and convenient estimation procedures however this is no longer the case for copula models with mixed discrete and continuous marginal distributions because the corresponding density function cannot be decomposed so nicely in this paper we introduce a copula transformation method that allows to represent the density function of a distribution with mixed discrete and continuous marginals as the product of the marginal probability mass density functions and the copula density function with the proposed method conditional distributions can be described analytically and the computational complexity in the estimation procedure can be reduced depending on the type of copula used

cylindrical korteweg de vries equation and painleve property the authors demonstrate that the lax representation for the cylindrical korteweg de vries equation can be obtained with the help of the painleve property of this equation

pair copula based mixture models and their application in clustering finite mixtures are often used to perform model based clustering of multivariate data sets in real life applications such data may exhibit complex nonlinear form of dependence among the variables also the individual variables margins may follow different families of distributions most of the existing mixture models are unable to accommodate these two aspects of the data this paper presents a finite mixture model that involves a pair copula based construction of a multivariate distribution such a model de couples the margins and the dependence structures hence the margins can be modeled using different families again many possible dependence structures can also be studied using different copulas the resulting mixture model called dvmm is then capable of capturing a broad family of distributions including non gaussian models here we study dvmm in the context of clustering of multivariate data we design an expectation maximization procedure for estimating the mixture parameters we perform extensive experiments on the basis of a number of well known data sets a detailed evaluation of the clustering quality obtained by dvmm in comparison to other mixture models is presented the experimental results show that the performance of dvmm is quite satisfactory

on a kdv equation with higher order nonlinearity traveling wave solutions abstract in this work the improved tanh coth method is used to obtain wave solutions to a korteweg de vries kdv equation with higher order nonlinearity from which the standard kdv and the modified korteweg de vries mkdv equations with variable coefficients can be derived as particular cases however the model studied here include other important equations with applications in several fields of physical and nonlinear sciences periodic and soliton solutions are formally derived

accounting for parameter uncertainty in large scale stochastic simulations with correlated inputs this paper considers large scale stochastic simulations with correlated inputs having normal to anything norta distributions with arbitrary continuous marginal distributions examples of correlated inputs include processing times of workpieces across several workcenters in manufacturing facilities and product demands and exchange rates in global supply chains our goal is to obtain mean performance measures and confidence intervals for simulations with such correlated inputs by accounting for the uncertainty around the norta distribution parameters estimated from finite historical input data this type of uncertainty is known as the parameter uncertainty in the discrete event stochastic simulation literature we demonstrate how to capture parameter uncertainty with a bayesian model that uses sklar s marginal copula representation and cooke s copula vine specification for sampling the parameters of the norta distribution the development of such a bayesian model well suited for handling many correlated inputs is the primary contribution of this paper we incorporate the bayesian model into the simulation replication algorithm for the joint representation of stochastic uncertainty and parameter uncertainty in the mean performance estimate and the confidence interval we show that our model improves both the consistency of the mean line item fill rate estimates and the coverage of the confidence intervals in multiproduct inventory simulations with correlated demands

generalized measures of correlation for asymmetry nonlinearity and beyond some antecedents on causality this note comments on the generalized measure of correlation gmc that was suggested by zheng shi and zhang the gmc concept was partly anticipated in some publications over 100 years earlier by

quantile association for bivariate survival data bivariate survival data arise frequently in familial association studies of chronic disease onset as well as in clinical trials and observational studies with multiple time to event endpoints the association between two event times is often scientifically important in this article we examine the association via a novel quantile association measure which describes the dynamic association as a function of the quantile levels the quantile association measure is free of marginal distributions allowing direct evaluation of the underlying association pattern at different locations of the event times we propose a nonparametric estimator for quantile association as well as a semiparametric estimator that is superior in smoothness and efficiency the proposed methods possess desirable asymptotic properties including uniform consistency and root n convergence they demonstrate satisfactory numerical performances under a range of dependence structures an application of our methods suggests interesting association patterns between time to myocardial infarction and time to stroke in an atherosclerosis study

covariance model simulation using regular vines we propose a new and flexible simulation method for non normal data with user specified marginal distributions covariance matrix and certain bivariate dependencies the vita vine to anything method is based on regular vines and generalizes the norta normal to anything method fundamental theoretical properties of the vita method are deduced two illustrations demonstrate the flexibility and usefulness of vita in the context of structural equation models r code for the implementation is provided

exact solutions to kdv equations with variable coefficients and or nonuniformities abstract a class of kdv equations with variable coefficients and or nonuniformities is discussed we derive easily the constraint conditions which must apply to this class in order to obtain exact solutions by a direct method we obtain solutions in a number of generic as well as specific cases

a variable coefficient korteweg de vries equation similarity analysis and exact solution ii a korteweg de vries kdv equation with time dependent coefficients is studied in this paper the similarity transformation for this system is investigated and an exact solution in a particular case is obtained the ablowitz ramani segur ars conjecture is used to identify the integrability of the system it is found that in some special cases the system may be integrable

general linear and functor cohomology over finite fields in recent years there has been considerable success in computing extgroups of modular representations associated to the general linear group by relating this problem to one of computing ext groups in functor categories f l s f s in this paper we extend our ability to make such ext group calculations by establishing several fundamental results throughout this paper we work over fields of positive characteristic p the reader familiar with the representation theory of algebraic objects will recognize the importance of an understanding of ext groups for example the existence of nonzero ext groups of positive degree is equivalent to the existence of objects which are not direct sums of simple objects indeed a knowledge of ext groups provides considerable knowledge of compound objects in the study of modular representation theory of finite chevalley groups such as gln fq ext groups play an even more central role it has been shown in cps that a knowledge of certain ext groups is sufficient to prove lusztig s conjecture concerning the dimension and characters of irreducible representations we consider two different categories of functors the category f fq of all functors from finite dimensional fq vector spaces to fq vector spaces where fq is the finite field of cardinality q and the category p fq of strict polynomial functors of finite degree as defined in f s the category p fq presents several advantages over the category f fq from the point of view of computing extgroups these are the accessibility of injectives and projectives the existence of a base change and an even easier access to ext groups of tensor products this explains the usefulness of our comparison in theorem 3 10 of ext groups in the category p fq with ext groups in the category f fq weaker forms of this theorem have been known to us since 1995 and to s betley independently

new exact explicit solutions of the generalized kdv equations abstract as kdv equations are characterized by the painleve equations we show here that generalized kdv equations are characterized by euler painleve equations a plethora of exact explicit similarity solutions are found which include inverse of hypergeometric function

a note on composite likelihood inference and model selection a composite likelihood consists of a combination of valid likelihood objects usually related to small subsets of data the merit of composite likelihood is to reduce the computational complexity so that it is possible to deal with large datasets and very complex models even when the use of standard likelihood or bayesian methods is not feasible in this paper we aim to suggest an integrated general approach to inference and model selection using composite likelihood methods in particular we introduce an information criterion for model selection based on composite likelihood we also describe applications to the modelling of time series of counts through dynamic generalised linear models and to the analysis of the well known old faithful geyser dataset

multivariate logit copula model with an application to dental data applications of copulas for multivariate continuous data abound but there are only a few that treat multivariate binary data in the present paper we model multivariate binary data based on copulas using mixtures of max infinitely divisible copulas introduced by joe and hu j multivar anal 1996 57 2 240 265 when applying copulas to binary data the marginal distributions also contribute to the dependence measures we propose the use of covariate information in the copula parameters to obtain a direct effect of a covariate on dependence to deal with model uncertainty due to selecting among several candidate models we use a model averaging technique we apply the model to data from the signal tandmobiel dental study and in particular to four binary responses that refer to caries experience in the mandibular and maxillary left and right molars we aim to model kendall s tau associations between them and examine how covariate information affects these associations we found that there are systematically larger associations between the two mandibular and the two maxillary molars using covariates to model these associations more closely we found that the systematic fluoride and age of the children affect the associations note that such relationships could not have been revealed by methods that focus on the marginal models copyright 2008 john wiley sons ltd

new exact solutions for a generalized variable coefficient kdv equation new exact solutions for a generalized variable coefficient kdv equation were obtained using the generalized expansion method r sabry m a zahran e g fan phys lett a 326 2004 93 the obtained solutions include solitary wave solutions besides jacobi and weierstrass doubly periodic wave solutions

generalized linear models with varying dispersion summary generalized linear models are further generalized to include a linear predictor for the dispersion as well as for the mean it is shown how the convenient structure of generalized linear models can be carried over to this more general setting by considering the mean and dispersion structure separately mean and dispersion submodels are formulated for this the dependent variable for the dispersion submodel being the deviance components of the mean submodel the fact that both submodels are essentially generalized linear models themselves is used to derive simple expressions for the likelihood equations and for asymptotic tests estimation algorithms are proposed which have good convergence properties the results apply mainly to the normal inverse gaussian and gamma distributions but can be extended to discrete distributions by using quasi likelihoods the methods developed are applied to a well known data set

copula index for detecting dependence and monotonicity between stochastic signals abstract this paper introduces a nonparametric copula based index for detecting the strength and monotonicity structure of linear and nonlinear statistical dependence between pairs of random variables or stochastic signals our index termed copula index for detecting dependence and monotonicity cim satisfies several desirable properties of measures of association including most of renyi s properties the data processing inequality dpi and consequently self equitability synthetic data simulations reveal that the statistical power of cim compares favorably to other state of the art measures of association that are proven to satisfy the dpi simulation results with real world data reveal cim s unique ability to detect the monotonicity structure among stochastic signals to find interesting dependencies in large datasets additionally simulations show that cim compares favorably to estimators of mutual information when discovering markov network structure

copula based multivariate input models for stochastic simulation as large scale discrete event stochastic simulation becomes a tool that is used routinely for the design and analysis of stochastic systems the need for input modeling support with the ability to represent complex interactions and interdependencies among the components of multivariate time series input processes is more critical than ever motivated by the failure of independent and identically distributed random variables to represent such input processes a comprehensive framework called vector autoregressive to anything varta has been introduced for multivariate time series input modeling despite its flexibility in capturing a wide variety of distributional shapes we show that varta falls short in representing dependence structures that arise in situations where extreme component realizations occur together we demonstrate that it is possible to extend varta to work for such dependence structures via the use of the copula theory which has been used primarily for random vectors in the simulation input modeling literature for multivariate time series input modeling we show that our copula based multivariate time series input model which includes varta as a special case allows the development of statistically valid fitting and fast sampling algorithms well suited for driving large scale stochastic simulations

d dimensional dependence functions and archimax copulas we introduce a new class of dependence functions and method for constructing tail and pickands dependence functions finally we conjecture the structure of d dimensional archimax copulas and discuss some classes of d dimensional archimax copulas

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

auto backlund transformation lax pairs and painleve property of a variable coefficient korteweg de vries equation i using the painleve property of partial differential equations the auto backlund transformation and lax pairs for a korteweg de vries kdv equation with time dependent coefficients are obtained the lax pair criterion also makes it possible for some new models of the variable coefficient kdv equation to be found that can represent nonsoliton dynamical systems this can explain the wave breaking phenomenon in variable depth shallow water

on the evaluation of finite time ruin probabilities in a dependent risk model this paper establishes some enlightening connections between the explicit formulas of the finite time ruin probability obtained by ignatovand kaishev 2000 2004 and ignatov et al 2001 for a risk model allowing dependence the numerical properties of these formulas are investigated and efficient algorithms for computing ruin probability with prescribed accuracy are presented extensive numerical comparisons and examples are provided

regression models for a bivariate discrete and continuous outcome with clustering abstract developmental toxicity studies of laboratory animals play a crucial role in the testing and regulation of chemicals and pharmaceutical compounds exposure to developmental toxicants typically causes a variety of adverse effects such as fetal malformations and reduced fetal weight at term in this article we discuss regression methods for jointly analyzing bivariate discrete and continuous outcomes that are motivated by the statistical problems that arise in analyzing data from developmental toxicity studies we focus on marginal regression models that is models in which the marginal expectation of the bivariate response vector is related to a set of covariates by some known link functions in these models the regression parameters for the marginal expectation are of primary scientific interest whereas the association between the binary and continuous response is considered to be a nuisance characteristic of the data we describe a likelihood based approach based on the general location mode

integrable nonlinear evolution equations with time dependent coefficients a simple and straightforward method for generating completely integrable nonlinear evolution equations with time dependent coefficients is presented herein for the equations under consideration the solutions to those given by vector fields which are independent of time are given thus explicit links between equations are obtained as an application of the proposed method it is shown that the linear superposition with arbitrary time dependent coefficients of different members of an integrable hierarchy is again integrable furthermore it turns out that for some integrable equations like the korteweg de vries kdv the benjamin ono bo or the kadomtsev petviashvili kp the resolvent operator of lower order flows can be explicitly obtained from that of any higher order flow those flows demonstrated for the kdv which can be generated by lie homomorphisms coming from first order problems are completely classified many well known equations which can be found in the literature are of that type as an application of such a first order link a direct link is given from kdv to the cylindrical kdv and from there to the kp with nontrivial dependence on the second spatial variable

pair copula constructions for multivariate discrete data multivariate discrete response data can be found in diverse fields including econometrics finance biometrics and psychometrics our contribution through this study is to introduce a new class of models for multivariate discrete data based on pair copula constructions pccs that has two major advantages first by deriving the conditions under which any multivariate discrete distribution can be decomposed as a pcc we show that discrete pccs attain highly flexible dependence structures second the computational burden of evaluating the likelihood for an m dimensional discrete pcc only grows quadratically with m this compares favorably to existing models for which computing the likelihood either requires the evaluation of 2 m terms or slow numerical integration methods we demonstrate the high quality of inference function for margins and maximum likelihood estimates both under a simulated setting and for an application to a longitudinal discrete dataset on headache severity this article has onli

skew normal antedependence models for skewed longitudinal data antedependence models also known as transition models have proven to be useful for longitudinal data exhibiting serial correlation especially when the variances and or same lag correlations are time varying statistical inference procedures associated with normal antedependence models are well developed and have many nice properties but they are not appropriate for longitudinal data that exhibit considerable skewness we propose two direct extensions of normal antedependence models to skew normal antedependence models the first is obtained by imposing antedependence on a multivariate skew normal distribution and the second is a sequential autoregressive model with skew normal innovations for both models necessary and sufficient conditions for formula see text th order antedependence are established and likelihood based estimation and testing procedures for models satisfying those conditions are developed the procedures are applied to simulated data and to real data from a study of cattle growth

robust optimization of mixed cvar starr ratio using copulas abstract we introduce the robust optimization models for two variants of stable tail adjusted return ratio starr one with mixed conditional value at risk mcvar and the other with deviation mcvar dmcvar under joint ambiguity in the distribution modeled using copulas the two models are shown to be computationally tractable linear programs we apply a two step procedure to capture the joint dependence structure among the assets we first extract the filtered residuals from the return series of each asset using autoregressive moving average glosten jagannathan runkle generalized autoregressive conditional heteroscedastic arma gjr garch model subsequently we exploit the regular vine copulas to model the joint dependence among the transformed residuals the tree structure in the regular vines is accomplished using kendall s tau we compare the performance of the proposed two robust models with their conventional counterparts when the joint distribution in the latter is described using gaussian copula only we also examine the performance of the obtained portfolios against those from the markowitz model and multivariate garch models using the rolling window analysis we illustrate the superior performance of the proposed robust models than their conventional counterpart models on excess mean returns sortino ratio rachev ratio var ratio and treynor ratio on three data sets comprising of indices across the globe

joint regression analysis for discrete longitudinal data we introduce an approximation to the gaussian copula likelihood of song li and yuan 2009 biometrics 65 60 68 used to estimate regression parameters from correlated discrete or mixed bivariate or trivariate outcomes our approximation allows estimation of parameters from response vectors of length much larger than three and is asymptotically equivalent to the gaussian copula likelihood we estimate regression parameters from the toenail infection data of de backer et al 1996 british journal of dermatology 134 16 17 which consist of binary response vectors of length seven or less from 294 subjects although maximizing the gaussian copula likelihood yields estimators that are asymptotically more efficient than generalized estimating equation gee estimators our simulation study illustrates that for finite samples gee estimators can actually be as much as 20 more efficient

joint regression analysis of correlated data using gaussian copulas this article concerns a new joint modeling approach for correlated data analysis utilizing gaussian copulas we present a unified and flexible machinery to integrate separate one dimensional generalized linear models glms into a joint regression analysis of continuous discrete and mixed correlated outcomes this essentially leads to a multivariate analogue of the univariate glm theory and hence an efficiency gain in the estimation of regression coefficients the availability of joint probability models enables us to develop a full maximum likelihood inference numerical illustrations are focused on regression models for discrete correlated data including multidimensional logistic regression models and a joint model for mixed normal and binary outcomes in the simulation studies the proposed copula based joint model is compared to the popular generalized estimating equations which is a moment based estimating equation method to join univariate glms two real world data examples are used in the illustration

goodness of fit test for specification of semiparametric copula dependence models this paper concerns goodness of fit tests for semiparametric copula models our contribution is two fold we first propose a new test constructed via the comparison between in sample and out of sample pseudo likelihoods under the null hypothesis that the copula model is correctly specified we show that the proposed test statistic converges in probability to a constant equal to the dimension of the parameter space we establish the asymptotic normality and investigate the local power of the test we also extend the proposed test to the specification test of a class of multivariate time series models and propose a new bootstrap procedure to establish the finite sample null distribution which is shown to have better control of type i error than the commonly used bootstrap secondly we introduce a bonferroni based hybrid mechanism to combine several test statistics which yields a useful test this hybrid method is particularly appealing when there exists no single dominant optimal test we conduct comprehensive simulation experiments to compare the proposed new test and hybrid approach with two of the best blanket tests in the literature for illustration we apply the proposed tests to analyze two real datasets

painleve property auto backlund transformation lax pairs and reduction to the standard form for the korteweg de vries equation with nonuniformities it is demonstrated that the kdv equation with nonuniformities ut a t u b x t u x c t uux d t uxxx e x t 0 has the painleve property if the compatibility condition among the coefficients of it holds bt a lc b bbx dbxxx 2ah hl d c2 dh dt ce x 2a2 al d3 c4 da dt l d c l d c2 d dt l d c where l d dt lg and h t is an arbitrary function of t the auto backlund transformation and lax pairs for this equation are obtained by truncating the laurent expansion furthermore assuming the compatibility condition then the kdv equation with nonuniformities is transformable via suitable variable transformations to the standard kdv

limited information goodness of fit testing in multidimensional contingency tables we introduce a family of goodness of fit statistics for testing composite null hypotheses in multidimensional contingency tables these statistics are quadratic forms in marginal residuals up to order r they are asymptotically chi square under the null hypothesis when parameters are estimated using any asymptotically normal consistent estimator for a widely used item response model when r is small and multidimensional tables are sparse the proposed statistics have accurate empirical type i errors unlike pearson s x2 for this model in nonsparse situations the proposed statistics are also more powerful than x2 in addition the proposed statistics are asymptotically chi square when applied to subtables and can be used for a piecewise goodness of fit assessment to determine the source of misfit in poorly fitting models

complete integrability and analytic solutions of a kdv type equation the complete integrability of the variable coefficient version of a kdv equation via the painleve approach is analyzed through the painleve backlund equations its auto backlund transformation lax pairs symmetry strong symmetry bilinear form and analytic solutions are obtained

vines a new graphical model for dependent random variables a new graphical model called a vine for dependent random variables is introduced vines generalize the markov trees often used in modelling high dimensional distributions they differ from markov trees and bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence

copula functions for residual dependency most item response theory models are not robust to violations of conditional independence however several modeling approaches e g conditioning on other responses additional random effects exist that try to incorporate local item dependencies but they have some drawbacks such as the nonreproducibility of marginal probabilities and resulting interpretation problems in this paper a new class of models making use of copulas to deal with local item dependencies is introduced these models belong to the bigger class of marginal models in which margins and association structure are modeled separately it is shown how this approach overcomes some of the problems associated with other local item dependency models

generalized causal mediation analysis the goal of mediation analysis is to assess direct and indirect effects of a treatment or exposure on an outcome more generally we may be interested in the context of a causal model as characterized by a directed acyclic graph dag where mediation via a specific path from exposure to outcome may involve an arbitrary number of links or stages methods for estimating mediation or pathway effects are available for a continuous outcome and a continuous mediator related via a linear model while for a categorical outcome or categorical mediator methods are usually limited to two stage mediation we present a method applicable to multiple stages of mediation and mixed variable types using generalized linear models we define pathway effects using a potential outcomes framework and present a general formula that provides the effect of exposure through any specified pathway some pathway effects are nonidentifiable and their estimation requires an assumption regarding the correlation between counterfactuals we provide a sensitivity analysis to assess the impact of this assumption confidence intervals for pathway effect estimates are obtained via a bootstrap method the method is applied to a cohort study of dental caries in very low birth weight adolescents a simulation study demonstrates low bias of pathway effect estimators and close to nominal coverage rates of confidence intervals we also find low sensitivity to the counterfactual correlation in most scenarios

semiparametric gaussian copula models geometry and efficient rank based estimation we propose for multivariate gaussian copula models with unknown margins and structured correlation matrices a rank based semiparametrically efficient estimator for the euclidean copula parameter this estimator is defined as a one step update of a rank based pilot estimator in the direction of the efficient influence function which is calculated explicitly moreover finite dimensional algebraic conditions are given that completely characterize efficiency of the pseudo likelihood estimator and adaptivity of the model with respect to the unknown marginal distributions for correlation matrices structured according to a factor model the pseudo likelihood estimator turns out to be semiparametrically efficient on the other hand for toeplitz correlation matrices the asymptotic relative efficiency of the pseudo likelihood estimator can be as low as 20 these findings are confirmed by monte carlo simulations we indicate how our results can be extended to joint regression models

estimation of copula models with discrete margins via bayesian data augmentation estimation of copula models with discrete margins can be difficult beyond the bivariate case we show how this can be achieved by augmenting the likelihood with continuous latent variables and computing inference using the resulting augmented posterior to evaluate this we propose two efficient markov chain monte carlo sampling schemes one generates the latent variables as a block using a metropolis hastings step with a proposal that is close to its target distribution the other generates them one at a time our method applies to all parametric copulas where the conditional copula functions can be evaluated not just elliptical copulas as in much previous work moreover the copula parameters can be estimated joint with any marginal parameters and bayesian selection ideas can be employed we establish the effectiveness of the estimation method by modeling consumer behavior in online retail using archimedean and gaussian copulas the example shows that elliptical copulas can be poor at modeling depend

joint analysis of spikes and local field potentials using copula recent technological advances which allow for simultaneous recording of spikes and local field potentials lfps at multiple sites in a given cortical area or across different areas have greatly increased our understanding of signal processing in brain circuits joint analysis of simultaneously collected spike and lfp signals is an important step to explicate how the brain orchestrates information processing in this contribution we present a novel statistical framework based on gaussian copula to jointly model spikes and lfp in our approach we use copula to link separate marginal regression models to construct a joint regression model in which the binary valued spike train data are modeled using generalized linear model glm and the continuous valued lfp data are modeled using linear regression model parameters can be efficiently estimated via maximum likelihood in particular we show that our model offers a means to statistically detect directional influence between spikes and lfp akin to granger causality measure and that we are able to assess its statistical significance by conducting a wald test through extensive simulations we also show that our method is able to reliably recover the true model used to generate the data to demonstrate the effectiveness of our approach in real setting we further apply the method to a mixed neural dataset consisting of spikes and lfp simultaneously recorded from the visual cortex of a monkey performing a contour detection task

copula based regression models for a bivariate mixed discrete and continuous outcome this paper is concerned with regression models for correlated mixed discrete and continuous outcomes constructed using copulas our approach entails specifying marginal regression models for the outcomes and combining them via a copula to form a joint model specifically we propose marginal regression models e g generalized linear models to link the outcomes marginal means to covariates to account for associations between outcomes we adopt the gaussian copula to indirectly specify their joint distributions our approach has two advantages over current methods one regression parameters in models for both outcomes are marginally meaningful and two the association is margin free in the sense that it is characterized by the copula alone by assuming a latent variable framework to describe discrete outcomes the copula used still uniquely determines the joint distribution in addition association measures between outcomes can be interpreted in the usual way we report results of simulations concerning the bias and efficiency of two likelihood based estimation methods for the model finally we illustrate the model using data on burn injuries

a boundary mixture approach to violations of conditional independence conditional independence is a fundamental principle in latent variable modeling and item response theory violations of this principle commonly known as local item dependencies are put in a test information perspective and sharp bounds on these violations are defined a modeling approach is proposed that makes use of a mixture representation of these boundaries to account for the local dependence problem by finding a balance between independence on the one side and absolute dependence on the other side in contrast to alternative approaches the nature of the proposed boundary mixture model does not necessitate a change in formulation of the typical item characteristic curves used in item response theory this has attractive interpretational advantages and may be useful for general test construction purposes

a parameterization of positive definite matrices in terms of partial correlation vines abstract we present a parameterization of the class pd n of positive definite n n matrices using regular vines and partial correlations using a bijection from 1 1 n 2 c n c n is the class of n n correlation matrices with a clear probabilistic interpretation ann statist 30 4 2002 1031 we suggest a new approach to various problems involving positive definiteness

limited information estimation and testing of discretized multivariate normal structural models discretized multivariate normal structural models are often estimated using multistage estimation procedures the asymptotic properties of parameter estimates standard errors and tests of structural restrictions on thresholds and polychoric correlations are well known it was not clear how to assess the overall discrepancy between the contingency table and the model for these estimators it is shown that the overall discrepancy can be decomposed into a distributional discrepancy and a structural discrepancy a test of the overall model specification is proposed as well as a test of the distributional specification i e discretized multivariate normality also the small sample performance of overall distributional and structural tests as well as of parameter estimates and standard errors is investigated under conditions of correct model specification and also under mild structural and or distributional misspecification it is found that relatively small samples are needed for parameter estimates standard errors and structural tests larger samples are needed for the distributional and overall tests furthermore parameter estimates standard errors and structural tests are surprisingly robust to distributional misspecification

full information item bi factor analysis a plausibles factor solution for many types of psychological and educational tests is one that exhibits a general factor ands 1 group or method related factors the bi factor solution results from the constraint that each item has a nonzero loading on the primary dimension and at most one of thes 1 group factors this paper derives a bi factor item response model for binary response data in marginal maximum likelihood estimation of item parameters the bi factor restriction leads to a major simplification of likelihood equations and a permits analysis of models with large numbers of group factors b permits conditional dependence within identified subsets of items and c provides more parsimonious factor solutions than an unrestricted full information item factor analysis in some cases

on the kdv type equation with variable coefficients in this paper the kdv type equations with variable coefficients appearing a lot in the literature are discussed generally the explicit transformations which transform various kdv mkdv and kp type nonlinear evolution equations into their canonical forms with constant coefficients are given the results presented here tie up many of the investigations scattered in the literature

estimation of mediation effects for zero inflated regression models the goal of mediation analysis is to identify and explicate the mechanism that underlies a relationship between a risk factor and an outcome via an intermediate variable mediator in this paper we consider the estimation of mediation effects in zero inflated zi models intended to accommodate extra zeros in count data focusing on the zi negative binomial zinb models we provide a mediation formula approach to estimate the overall mediation effect in the standard two stage mediation framework under a key sequential ignorability assumption we also consider a novel decomposition of the overall mediation effect for the zi context using a three stage mediation model estimation of the components of the overall mediation effect requires an assumption involving the joint distribution of two counterfactuals simulation study results demonstrate low bias of mediation effect estimators and close to nominal coverage probability cp of confidence intervals we also modify the mediation formula method by replacing exact integration with a monte carlo integration method the method is applied to a cohort study of dental caries in very low birth weight adolescents for overall mediation effect estimation sensitivity analysis was conducted to quantify the degree to which key assumption must be violated to reverse the original conclusion

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

meta analysis of diagnostic tests accounting for disease prevalence a new model using trivariate copulas in real life and somewhat contrary to biostatistical textbook knowledge sensitivity and specificity and not only predictive values of diagnostic tests can vary with the underlying prevalence of disease in meta analysis of diagnostic studies accounting for this fact naturally leads to a trivariate expansion of the traditional bivariate logistic regression model with random study effects in this paper a new model is proposed using trivariate copulas and beta binomial marginal distributions for sensitivity specificity and prevalence as an expansion of the bivariate model two different copulas are used the trivariate gaussian copula and a trivariate vine copula based on the bivariate plackett copula this model has a closed form likelihood so standard software e g sas proc nlmixed can be used the results of a simulation study have shown that the copula models perform at least as good but frequently better than the standard model the methods are illustrated by two examples