stability analysis for stochastic differential equations with infinite markovian switchings abstract this paper is concerned with stability analysis of linear ito stochastic differential equations with countably infinite markovian switchings a spectral criterion is proposed for exponential stability of the considered models by means of the established spectral criterion the relationship between exponential stability and stochastic l 2 stability is clarified moreover under the disturbance of random signals with finite energy a sufficient condition is presented for l 2 input output stability of the perturbed stochastic differential equations

stability and stabilization of a class of stochastic switching systems with lower bound of sojourn time abstract this paper is concerned with the stability and stabilization issues for a family of discrete time stochastic switching systems with bounded sojourn time the stochastic switching systems are modeled by semi markov jump linear systems and the semi markov kernel approach is employed to handle the stability and stabilization problems the sojourn time of each system mode is considered to have both upper and lower bounds which is more general than the scenarios in previous literature that only consider the upper bound of sojourn time the concept of error mean square stability is put forward in a new form by taking into account the lower bounds of sojourn time for all system modes by virtue of a lyapunov function that not only depends on the current system mode but also on the elapsed time the system has been in the current mode together with certain techniques eliminating powers of matrices numerically testable stability and stabilization criteria in the sense of the proposed error mean square stability are obtained for the closed loop stochastic switching system finally a numerical example and a practical example of a dc motor are utilized to demonstrate the effectiveness of the proposed control strategy and the superiority of allowing for the lower bound of sojourn time

reductive pairs arising from representations let g be a reductive algebraic group and v a g module we consider the question of when gl v g is a reductive pair of algebraic groups where is the representation afforded by v we first make some observations about general g and v then specialise to the group sl2 k with k algebraically closed of positive characteristic p for this group we provide complete answers for the classes of simple and weyl modules the behaviour being determined by the base p expansion of the highest weight of the module we conclude by illustrating some of the results from the first section with examples for the group sl3 k

maximum likelihood estimation of multilevel structural equation models with random slopes for latent covariates a maximum likelihood estimation routine for two level structural equation models with random slopes for latent covariates is presented because the likelihood function does not typically have a closed form solution numerical integration over the random effects is required the routine relies upon a method proposed by du toit and cudeck psychometrika 74 1 65 82 2009 for reformulating the likelihood function so that an often large subset of the random effects can be integrated analytically reducing the computational burden of high dimensional numerical integration the method is demonstrated and assessed using a small scale simulation study and an empirical example

a unified approach for stochastic and mean square stability of continuous time linear systems with markovian jumping parameters and additive disturbances necessary and sufficient conditions for stochastic stability ss and mean square stability mss of continuous time linear systems subject to markovian jumps in the parameters and additive disturbances are established we consider two scenarios regarding the additive disturbances one in which the system is driven by a wiener process and one characterized by functions in l 2 m omega cal f mathbb p which is the usual scenario for the h infty approach the markov process is assumed to take values in an infinite countable set mathcal s it is shown that ss is equivalent to the spectrum of an augmented matrix lying in the open left half plane to the existence of a solution for a certain lyapunov equation and implies is equivalent for mathcal s finite asymptotic wide sense stationarity awss it is also shown that ss is equivalent to the state x t belonging to l 2 n omega cal f mathbb p whenever the disturbances are in l 2 m omega cal f mathbb p for the case in which mathcal s is finite ss and mss are equivalent and the lyapunov equation can be written down in two equivalent forms with each one providing an easier to check sufficient condition

some remarks on the ring of twisted tilting modules for algebraic groups abstract in a recent paper s doty a henke decomposition of tensor products of modular irreducibles for sl2 q j math 56 2005 189 207 doty and henke give a decomposition of the tensor product of two rational simple modules for the special linear group of degree 2 over an algebraically closed field of characteristic p 0 in performing this calculation it proved useful to know that the simple modules are twisted tensor products of tilting modules it seems natural therefore to consider the ring of twisted tilting modules for a semisimple group g a subring of the representation ring of g however we quickly specialize to the case in which g is the special linear group of degree 2 we show that in this case the ring is reduced and describe associated varieties we give formulas from which one may determine the multiplicities of the indecomposable module summands of the tensor product of twisted tilting modules

latent variables measurement error and methods for analysing longitudinal binary and ordinal data we explore structural equations with latent variables for modelling between individual variability and measurement error in the analysis of longitudinal binary and ordinal data the structural equation formulation provides insight into the assumptions and differences in interpretation of methods that are popular for longitudinal data analysis introducing the concept of continuous latent variables makes it clear that marginal and cluster specific models differ because their predicted variables are scaled to different standard deviations and that adjustment for measurement error in the outcome involves a change in scale as well we apply both structural equation modelling and common longitudinal modelling approaches to data from a study of sleep disorders in the process we compare results from marginal modelling using an sas gee routine karim and zeger 1988 qu s gauss program qu 1992 for generalized mixed models using gee the mixor package for cluster specific mixed effects models hedeker and gibbons 1994 and liscomp for structural models muthen 1988

optimal control for continuous time linear quadratic problems with infinite markov jump parameters the subject matter of this paper is the optimal control problem for continuous time linear systems subject to markovian jumps in the parameters and the usual infinite time horizon quadratic cost what essentially distinguishes our problem from previous ones inter alia is that the markov chain takes values on a countably infinite set to tackle our problem we make use of powerful tools from semigroup theory in banach space and a decomplexification technique the solution for the problem relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution of the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd these concepts are couched into the theory of operators in banach space and parallel to the classical linear quadratic lq case bound up with the spectrum of a certain infinite dimensional linear operator

joint maximum likelihood estimation for diagnostic classification models joint maximum likelihood estimation jmle is developed for diagnostic classification models dcms jmle has been barely used in psychometrics because jmle parameter estimators typically lack statistical consistency the jmle procedure presented here resolves the consistency issue by incorporating an external statistically consistent estimator of examinees proficiency class membership into the joint likelihood function which subsequently allows for the construction of item parameter estimators that also have the consistency property consistency of the jmle parameter estimators is established within the framework of general dcms the jmle parameter estimators are derived for the loglinear cognitive diagnosis model lcdm two consistency theorems are proven for the lcdm using the framework of general dcms makes the results and proofs also applicable to dcms that can be expressed as submodels of the lcdm simulation studies are reported for evaluating the performance of jmle when used with tests of varying length and different numbers of attributes as a practical application jmle is also used with real world educational data collected with a language proficiency test

bayesian non parametric models for spatially indexed data of mixed type we develop bayesian nonparametric models for spatially indexed data of mixed type our work is motivated by challenges that occur in environmental epidemiology where the usual presence of several confounding variables that exhibit complex interactions and high correlations makes it difficult to estimate and under stand the effects of risk factors on health outcomes of interest the modeling approach we adopt assumes that responses and confounding variables are manifestations of continuous latent variables and uses mul tivariate gaussians to jointly model these responses and confounding variables are not treated equally as relevant parameters of the distributions of the responses only are modeled in terms of explanatory variables or risk factors spatial dependence is introduced by allowing the weights of the nonparametric process priors to be location specific obtained as probit transformations of gaussian markov random fields con founding variables and spatial configuration have a similar role in the model in that they only in uence along with the responses the allocation probabilities of the areas into the mixture components thereby allowing for exible adjustment of the effects of observed confounders while allowing for the possibility of residual spatial structure possibly occurring due to unmeasured or undiscovered spatially varying factors aspects of the model are illustrated in simulation studies and an application to a real data set

lie algebraic stability criteria for switched systems it was recently shown that a family of exponentially stable linear systems whose matrices generate a solvable lie algebra possesses a quadratic common lyapunov function which implies that the corresponding switched linear system is exponentially stable for arbitrary switching in this paper we prove that the same properties hold under the weaker condition that the lie algebra generated by given matrices can be decomposed into a sum of a solvable ideal and a subalgebra with a compact lie group the corresponding local stability result for nonlinear switched systems is also established moreover we demonstrate that if a lie algebra fails to satisfy the above condition then it can be generated by a family of stable matrices such that the corresponding switched linear system is not stable relevant facts from the theory of lie algebras are collected at the end of the paper for easy reference

thurstonian modeling of ranking data via mean and covariance structure analysis although thurstonian models provide an attractive representation of choice behavior they have not been extensively used in ranking applications since only recently efficient estimation methods for these models have been developed these however require the use of special purpose estimation programs which limits their applicability here we introduce a formulation of thurstonian ranking models that turns an idiosyncratic estimation problem into an estimation problem involving mean and covariance structures with dichotomous indicators well known standard solutions for the latter can be readily applied to this specific problem and as a result any thurstonian model for ranking data can be fitted using existing general purpose software for mean and covariance structure analysis although the most popular programs for covariance structure analysis e g lisrel and eqs cannot be presently used to estimate thurstonian ranking models other programs such as mecosa already exist that can be straightforwardly used to estimate these models

stabilization of continuous time jump linear systems we investigate almost sure and moment stabilization of continuous time jump linear systems with a finite state markov jump form process we first clarify the concepts of spl delta moment stabilizability exponential spl delta moment stabilizability and stochastic spl delta moment stabilizability we then present results on the relationships among these concepts coupled riccati equations that provide necessary and sufficient conditions for mean square stabilization are given in detail and an algorithm for solving the coupled riccati equations is proposed moreover we show that individual mode controllability implies almost sure stabilizability which is not true for other types of stabilizability finally we present some testable sufficient conditions for spl delta moment stabilizability and almost sure stabilizability

fast moment estimation for generalized latent dirichlet models we develop a generalized method of moments gmm approach for fast parameter estimation in a new class of dirichlet latent variable models with mixed data types parameter estimation via gmm has co

building an identifiable latent class model with covariate effects on underlying and measured variables in recent years latent class models have proven useful for analyzing relationships between measured multiple indicators and covariates of interest such models summarize shared features of the multiple indicators as an underlying categorical variable and the indicators substantive associations with predictors are built directly and indirectly in unique model parameters in this paper we provide a detailed study on the theory and application of building models that allow mediated relationships between primary predictors and latent class membership but that also allow direct effects of secondary covariates on the indicators themselves theory for model identification is developed we detail an expectation maximization algorithm for parameter estimation standard error calculation and convergent properties comparison of the proposed model with models underlying existing latent class modeling software is provided a detailed analysis of how visual impairments affect older persons functioning requiring distance vision is used for illustration

latent variable modeling in heterogeneous populations common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values this article describes the problem and gives an overview of methodology that can address heterogeneity artificial examples of mixtures are given where if the mixture is not recognized strongly distorted results occur mimic structural modeling is shown to be a useful method for detecting and describing heterogeneity that cannot be handled in regular multiple group analysis other useful methods instead take a random effects approach describing heterogeneity in terms of random parameter variation across groups these random effects models connect with emerging methodology for multilevel structural equation modeling of hierarchical data examples are drawn from educational achievement testing psychopathology and sociology of education estimation is carried out by the liscomp program

brief paper on almost sure stability of continuous time markov jump linear systems in this paper we study the almost sure stability of continuous time jump linear systems with a finite state markov form process a sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches it is shown that if the system is exponentially almost sure stable there exists a finite m such that the criterion is satisfied in order to evaluate the expected value appearing in the condition an efficient monte carlo algorithm is worked out

robust h control of descriptor discrete time markovian jump systems this paper considers the stochastic stability and the robust control of descriptor discrete time systems with markovian jumping parameters in terms of linear matrix inequalities a necessary and sufficient condition is proposed which ensures a discrete time descriptor markovian jump system to be regular causal and stochastically stable a robust admissibility condition and a robust bounded real lemma are also developed based on these a sufficient condition on the existence of a state feedback controller which guarantees the robust admissibility and the performance is also given by employing the linear matrix inequality technique a robustly stabilizing state feedback controller can be constructed through the numerical solutions of linear matrix inequalities finally an example is provided to demonstrate the effectiveness of the proposed approach

stabilizability and insensitivity of switched linear systems this note identifies two types of stabilizability for switched systems the pointwise stabilizability and the consistent stabilizability necessary conditions and sufficient conditions for both types are presented for switched linear systems insensitivity issues are briefly addressed as well

a result on almost sure stability of linear continuous time markovian switching systems this work investigates the almost sure stability for linear markovian switching systems in continuous time by using lyapunov function method the distribution of switching points is combined into constructing the lyapunov function which gives rise to the fluctuation in bounding the transient phase over the time interval confined between two successive switching points due to the randomness of their locations showing that the influence of the accumulated fluctuations by averaging it out will be negligible is the key step in proving our stability result illustrative examples are included to show the effectiveness of the theoretical result

random perturbation of low rank matrices improving classical bounds abstract matrix perturbation inequalities such as weyl s theorem concerning the singular values and the davis kahan theorem concerning the singular vectors play essential roles in quantitative science in particular these bounds have found application in data analysis as well as related areas of engineering and computer science in many situations the perturbation is assumed to be random and the original matrix has certain structural properties such as having low rank we show that in this scenario classical perturbation results such as weyl and davis kahan can be improved significantly we believe many of our new bounds are close to optimal and also discuss some applications

tracking switched dynamic network topologies from information cascades contagions such as the spread of popular news stories or infectious diseases propagate in cascades over dynamic networks with unobservable topologies however social signals such as product purchase time or blog entry timestamps are measurable and implicitly depend on the underlying topology making it possible to track it over time interestingly network topologies often jump between discrete states that may account for sudden changes in the observed signals the present paper advocates a switched dynamic structural equation model to capture the topology dependent cascade evolution as well as the discrete states driving the underlying topologies conditions under which the proposed switched model is identifiable are established leveraging the edge sparsity inherent to social networks a recursive ell 1 norm regularized least squares estimator is put forth to jointly track the states and network topologies an efficient first order proximal gradient algorithm is developed to solve the resulting optimization problem numerical experiments on both synthetic data and real cascades measured over the span of one year are conducted and test results corroborate the efficacy of the advocated approach

latent variable models for mixed discrete and continuous outcomes we propose a latent variable model for mixed discrete and continuous outcomes the model accommodates any mixture of outcomes from an exponential family and allows for arbitrary covariate effects as well as direct modelling of covariates on the latent variable an em algorithm is proposed for parameter estimation and estimates of the latent variables are produced as a by product of the analysis a generalized likelihood ratio test can be used to test the significance of covariates affecting the latent outcomes this method is applied to birth defects data where the outcomes of interest are continuous measures of size and binary indicators of minor physical anomalies infants who were exposed in utero to anticonvulsant medications are compared with controls

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

generalized multilevel structural equation modeling a unifying framework for generalized multilevel structural equation modeling is introduced the models in the framework called generalized linear latent and mixed models gllamm combine features of generalized linear mixed models glmm and structural equation models sem and consist of a response model and a structural model for the latent variables the response model generalizes glmms to incorporate factor structures in addition to random intercepts and coefficients as in glmms the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower level units in the higher level units and missing data a wide range of response processes can be modeled including ordered and unordered categorical responses counts and responses of mixed types the structural model is similar to the structural part of a sem except that it may include latent and observed variables varying at different levels for example unit level latent variables factors or random coefficients can be regressed on cluster level latent variables special cases of this framework are explored and data from the british social attitudes survey are used for illustration maximum likelihood estimation and empirical bayes latent score prediction within the gllamm framework can be performed using adaptive quadrature in gllamm a freely available program running in stata

event triggered control for semi global stabilisation of systems with actuator saturation abstractthis paper investigates the problem of event triggered control for semi global stabilisation of null controllable systems subject to actuator saturation first for a continuous time system novel event triggered low gain control algorithms based on riccati equations are proposed to achieve semi global stabilisation the algebraic riccati equation with a low gain parameter is utilised to design both the event triggering condition and the linear controller a minimum inter event time based on the riccati ordinary differential equation is set a priori to exclude the zeno behaviour in addition the high low gain techniques are utilised to extend the semi global results to event based global stabilisation furthermore for a discrete time system novel low gain and high low gain control algorithms are proposed to achieve event triggered stabilisation numerical examples are provided to illustrate the theoretical results

dynamic latent trait models for multidimensional longitudinal data this article presents a new approach for analysis of multidimensional longitudinal data motivated by studies using an item response battery to measure traits of an individual repeatedly over time a general modeling framework is proposed that allows mixtures of count categorical and continuous response variables each response is related to age specific latent traits through a generalized linear model that accommodates item specific measurement errors a transition model allows the latent traits at a given age to depend on observed predictors and on previous latent traits for that individual following a bayesian approach to inference a markov chain monte carlo algorithm is proposed for posterior computation the methods are applied to data from a neurotoxicity study of the pesticide methoxychlor and evidence of a dose dependent increase in motor activity is presented

an instrumental variable estimator for mixed indicators analytic derivatives and alternative parameterizations methodological development of the model implied instrumental variable miiv estimation framework has proved fruitful over the last three decades major milestones include bollen s psychometrika 61 1 109 121 1996 original development of the miiv estimator and its robustness properties for continuous endogenous variable sems the extension of the miiv estimator to ordered categorical endogenous variables bollen and maydeu olivares in psychometrika 72 3 309 2007 and the introduction of a generalized method of moments estimator bollen et al in psychometrika 79 1 20 50 2014 this paper furthers these developments by making several unique contributions not present in the prior literature 1 we use matrix calculus to derive the analytic derivatives of the piv estimator 2 we extend the piv estimator to apply to any mixture of binary ordinal and continuous variables 3 we generalize the piv model to include intercepts and means 4 we devise a method to input known threshold values for ordinal observed variables and 5 we enable a general parameterization that permits the estimation of means variances and covariances of the underlying variables to use as input into a sem analysis with piv an empirical example illustrates a mixture of continuous variables and ordinal variables with fixed thresholds we also include a simulation study to compare the performance of this novel estimator to wlsmv

almost sure stabilization for feedback controls of regime switching linear systems with a hidden markov chain this work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown markov chain the control system displays continuous dynamics represented by differential equations and discrete events given by a hidden markov chain in the previous investigation on this class of problems averaging criteria were used which provides only the system behavior in some expectation sense a closer scrutiny of the system behavior necessarily requires the consideration of sample path properties different from previous work on stabilization of adaptive controlled systems with a hidden markov chain where average criteria were considered this work focuses on the almost sure stabilization or sample path stabilization of the underlying processes under simple conditions it is shown that as long as the feedback controls have linear growth in the continuous component the resulting process is regular moreover by appropriate choice of the lyapunov functions it is shown that the adaptive system is stabilizable almost surely as a by product it is also established that the controlled process is positive recurrent

almost sure stability of switching markov jump linear systems recently a special hybrid system called switching markov jump linear system smjls is studied a smjls is subject to a deterministic switching and a stochastic markovain switching to extend the results already obtained and to investigate some new aspects of such systems our main contributions in this paper are i transient analysis of markov process i e the expectations of the sojourn time the activation number of any mode and the number of switchings between any two modes and ii two sufficient conditions of the exponential almost sure stability for a general smjls different from previous work which is a special case of our study the transition rate matrix for the random markov process in our study is not fixed but varies when a deterministic switching takes place

on stability and h control of switched systems with random switching signals abstract in this paper the stability analysis and h control problems for a class of continuous time switched systems with a random switching signal are addressed the dwell time of the switched systems is characterized with a fixed part and a random part a new stability criterion which is equivalent to a necessary and sufficient condition developed previously is established first and then it is reformulated in terms of linear matrix inequalities based on the stability analysis result l 2 gain performance analysis and h control problems are studied several numerical examples are given to illustrate the effectiveness of our results

bivariate latent variable models for clustered discrete and continuous outcomes abstract we use the concept of a latent variable to derive the joint distribution of a continuous and a discrete outcome and then extend the model to allow for clustered data the model can be parameterized in a way that allows one to write the joint distribution as a product of a standard random effects model for the continuous variable and a correlated probit model for the discrete variable this factorization suggests a convenient approach to parameter estimation using quasi likelihood techniques our approach is motivated by the analysis of developmental toxicity experiments for which a number of discrete and continuous outcomes are measured on offspring clustered within litters fetal weight and malformation data illustrate the results

forecasting using principal components from a large number of predictors this article considers forecasting a single time series when there are many predictors n and time series observations t when the data follow an approximate factor model the predictors can be summarized by a small number of indexes which we estimate using principal components feasible forecasts are shown to be asymptotically efficient in the sense that the difference between the feasible forecasts and the infeasible forecasts constructed using the actual values of the factors converges in probability to 0 as both n and t grow large the estimated factors are shown to be consistent even in the presence of time variation in the factor model

multivariate thurstonian models the recent development of probabilistic thurstonian choice models for analyzing preference data has been motivated by the need to describe both inter and intra individual difference the multidimensional nature of choice objects and the effects of similarity and comparability among choice objects a common feature of these models is that they focus on asingle preference judgment it is customary however to ask subjects not only for an overall preference judgment but also for additional paired comparison responses regarding specific attributes this paper proposes a generalization of thurstonian probabilistic choice models for analyzing both multiple preference responses and their relationships the approach is illustrated by modeling data from two multivariate preference experiments

alpha dimension free and model based internal consistency reliability as pointed out by sijtsma in press coefficient alpha is inappropriate as a single summary of the internal consistency of a composite score better estimators of internal consistency are available in addition to those mentioned by sijtsma an old dimension free coefficient and structural equation model based coefficients are proposed to improve the routine reporting of psychometric internal consistency the various ways to measure internal consistency are also shown to be appropriate to binary and polytomous items

fixed order robust h sub spl infin filter design for markovian jump systems with uncertain switching probabilities this paper discusses the fixed order robust h sub spl infin filtering problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertainties under consideration are assumed to be norm bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix respectively first a criterion based on linear matrix inequalities is provided for testing the h sub spl infin filtering level of a filter over all the admissible uncertainties then a sufficient condition for the existence of the fixed order robust h sub spl infin filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints to determine the filter a globally convergent algorithm involving convex optimization is suggested finally a numerical example is used to illustrate that the developed theory is more effective than the existing results

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

a note on exploratory item factor analysis by singular value decomposition we revisit a singular value decomposition svd algorithm given in chen et al psychometrika 84 124 146 2019b for exploratory item factor analysis ifa this algorithm estimates a multidimensional ifa model by svd and was used to obtain a starting point for joint maximum likelihood estimation in chen et al 2019b thanks to the analytic and computational properties of svd this algorithm guarantees a unique solution and has computational advantage over other exploratory ifa methods its computational advantage becomes significant when the numbers of respondents items and factors are all large this algorithm can be viewed as a generalization of principal component analysis to binary data in this note we provide the statistical underpinning of the algorithm in particular we show its statistical consistency under the same double asymptotic setting as in chen et al 2019b we also demonstrate how this algorithm provides a scree plot for investigating the number of factors and provide its asymptotic theory further extensions of the algorithm are discussed finally simulation studies suggest that the algorithm has good finite sample performance

a general structural equation model with dichotomous ordered categorical and continuous latent variable indicators a structural equation model is proposed with a generalized measurement part allowing for dichotomous and ordered categorical variables indicators in addition to continuous ones a computationally feasible three stage estimator is proposed for any combination of observed variable types this approach provides large sample chi square tests of fit and standard errors of estimates for situations not previously covered two multiple indicator modeling examples are given one is a simultaneous analysis of two groups with a structural equation model underlying skewed likert variables the second is a longitudinal model with a structural model for multivariate probit regressions

structural equation models with continuous and polytomous variables a two stage procedure is developed for analyzing structural equation models with continuous and polytomous variables at the first stage the maximum likelihood estimates of the thresholds polychoric covariances and variances and polyserial covariances are simultaneously obtained with the help of an appropriate transformation that significantly simplifies the computation an asymptotic covariance matrix of the estiates is also computed at the second stage the parameters in the structural covariance model are obtained via the generalized least squares approach basic statistical properties of the estimates are derived and some illustrative examples and a small simulation study are reported

stability of nonlinear discrete repetitive processes with markovian switching repetitive processes are a class of 2d systems that operate over a subset of the upper right quadrant of the 2d plane applications include iterative learning control where experimental verification has been reported based on a linear time invariant model approximation of the dynamics this paper considers discrete nonlinear repetitive processes with markovian switching and applies as one application the resulting stability theory to iterative learning control for a class of networked systems where time varying dynamics arise

higher extensions between modules for abstract we calculate ext sl 2 k ext sl 2 k l ext sl 2 k l ext sl 2 k l l where is the weyl module of highest weight l is the simple sl 2 k module of highest weight and our field k is algebraically closed of positive characteristic we also get analogous results for the dipper donkin quantisation to do thus we construct the lyndon hochschild serre spectral sequence in a new way and find a new condition for the e 2 page of any spectral sequence to be the same as the e page

simultaneous factor analysis of dichotomous variables in several groups a new method is proposed for a simultaneous factor analysis of dichotomous responses from several groups of individuals the method makes it possible to compare factor loading pattern factor variances and covariances and factor means over groups the method uses information from first and second order proportions and estimates the model by generalized least squares hypotheses regarding different degrees of invariance over groups may be evaluated by a large sample chi square test

on stability of randomly switched nonlinear systems this note is concerned with stability analysis and stabilization of randomly switched systems these systems may be regarded as piecewise deterministic stochastic systems the discrete switches are triggered by a stochastic process which is independent of the state of the system and between two consecutive switching instants the dynamics are deterministic our results provide sufficient conditions for almost sure stability and stability in the mean using lyapunov based methods when individual subsystems are stable and a certain ldquoslow switchingrdquo condition holds this slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants this condition is shown to hold for switching signals coming from the states of finite dimensional continuous time markov chains our results therefore hold for markovian jump systems in particular for systems with control inputs we provide explicit control schemes for feedback stabilization using the universal formula for stabilization of nonlinear systems

kernel based structural equation models for topology identification of directed networks structural equation models sems have been widely adopted for inference of causal interactions in complex networks recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases or rumors propagate the appeal of sems in these settings stems from their simplicity and tractability since they typically assume linear dependencies among observable variables acknowledging the limitations inherent to adopting linear models the present paper put forth nonlinear sems which account for possible nonlinear dependencies among network nodes the advocated approach leverages kernels as a powerful encompassing framework for nonlinear modeling and an efficient estimator with affordable tradeoffs is put forth interestingly pursuit of the novel kernel based approach yields a convex regularized estimator that promotes edge sparsity a property exhibited by most real world networks and the resulting optimization problem is amenable to proximal splitting optimization methods to this end solvers with complementary merits are developed by leveraging the alternating direction method of multipliers and proximal gradient iterations experiments conducted on simulated data demonstrate that the novel approach outperforms linear sems with respect to edge detection errors furthermore tests on a real gene expression dataset unveil interesting new edges that were not revealed by linear sems which could shed more light on regulatory behavior of human genes

latent variable structural equation modeling with categorical data abstract structural equation modeling with latent variables is overviewed for situations involving a mixture of dichotomous ordered polytomous and continuous indicators of latent variables special emphasis is placed on categorical variables models in psychometrics econometrics and biometrics are interrelated via a general model due to muthen limited information least squares estimators and full information estimation are discussed an example is estimated with a model for a four wave longitudinal data set where dichotomous responses are related to each other and a set of independent variables via latent variables with a variance component structure

on certain tilting modules for sl2 abstract we give a complete picture of when the tensor product of an induced module and a weyl module is a tilting module for the algebraic group s l 2 over an algebraically closed field of characteristic p whilst the result is recursive by nature we give an explicit statement in terms of the p adic expansions of the highest weight of each module

strict stationarity of generalized autoregressive processes in this paper we consider the multivariate equation x n 1 a n 1 x n b n 1 with i i d coefficients which have only a logarithmic moment we give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future as an application we characterize the multivariate arma equations with general noise which have such a solution

lq control of discrete time jump systems with markov chain in a general borel space in this technical note it is studied the lq optimal control problem for discrete time markov jump linear systems considering the case in which the markov chain takes values in a general borel space cal m it is shown that the solution of the lq optimal control problem is obtained in terms of the positive semi definite solution s ell ell in cal m of cal m coupled algebraic riccati equations by cal m coupled we mean that the algebraic riccati equations are coupled via an integral over a transition probability kernel cal g cdot vert cdot having a density g cdot vert cdot with respect to a sigma finite measure mu on cal m it is obtained sufficient conditions based on the concept of stochastic stabilizability and stochastic detectability for the existence and uniqueness of this positive semi definite solution these results generalize previous ones in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

full informationh control for discrete time infinite markov jump parameter systems abstract in this paper we consider the full information discrete timeh control problem for the class of linear systems with markovian jumping parameters the state space of the markov chain is assumed to take values in a countably infinite set full information here means that the controller has access to both the state variables and jump variables a necessary and sufficient condition for the existence of a feedback controller that makes the l 2 induced norm of the system less than a prespecified bound is obtained this condition is written in terms of a set of infinite coupled algebraic riccati equations

fusion categories arising from semisimple lie algebras using tilting modules we equip certain semisimple categories with a reduced tensor product structure the fusion rules for this tensor product are determined via known character formulas for the involved modules

structural modeling and psychometrika an historical perspective on growth and achievements the field of linear structural equation modeling with continuous variables is reviewed trends in psychometric theory and data analysis across the five decades of publication ofpsychometrika are discussed especially the clarification of concepts of population and sample explication of the parametric structure of models delineation of concepts of exploratory and confirmatory data analysis expansion of statistical theory in psychometrics estimation via optimization of an explicit objective function and implementation of general function minimization methods developments in the ideas of factor analysis latent variables as well as structural and causal modeling are noted some major conceptual achievements involving general covariance structure representations multiple population models and moment structures are reviewed the major statistical achievements of normal theory generalized least squares estimation elliptical and distribution free estimation and higher moment estimation are discussed computer programs that implement some of the theoretical developments are described

maximal versus strong solution to algebraic riccati equations arising in infinite markov jump linear systems abstract we deal with a perturbed algebraic riccati equation in an infinite dimensional banach space which appears for instance in the optimal control problem for infinite markov jump linear systems from now on imjls infinite or finite here has to do with the state space of the markov chain being infinite countable or finite see e g m d fragoso j baczynski optimal control for continuous time lq problems with infinite markov jump parameters siam j control optim 40 1 2001 270 297 by using a certain concept of stochastic stability a sort of l 2 stability we have proved in j baczynski m d fragoso maximal solution to algebraic riccati equations linked to infinite markov jump linear systems internal report lncc no 6 2006 existence and uniqueness of maximal solution for this class of equations as it is noticed in this paper unlike the finite case including the linear case we cannot guarantee anymore that maximal solution is a strong solution in this setting via a discussion on the main mathematical hindrance behind this issue we devise some mild conditions for this implication to hold specifically our main result here is that under stochastic stability along with a condition related with convergence in the infinite dimensional scenario and another one related to spectrum weaker than spectral continuity we ensure the maximal solution to be also a strong solution these conditions hold trivially in the finite case allowing us to recover the result of strong solution of c e de souza m d fragoso on the existence of maximal solution for generalized algebraic riccati equations arising in stochastic control systems control lett 14 1990 233 239 set for mjls the issue of whether the convergence condition is restrictive or not is brought to light and together with some counterexamples unveil further differences between the finite and the infinite countable case

high dimensional maximum marginal likelihood item factor analysis by adaptive quadrature although the bock aitkin likelihood based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations a serious limitation of the method is its reliance on fixed point gauss hermite g h quadrature in the solution of the likelihood equations and likelihood ratio tests when the number of latent dimensions is large computational considerations require that the number of quadrature points per dimension be few but with large numbers of items the dispersion of the likelihood given the response pattern becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space in this paper we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data in particular we show that adaptive g h quadrature combined with mean and covariance adjustments at each iteration of an em algorithm produces an accurate fast converging solution with as few as two points per dimension evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions unlike an earlier application of adaptive gibbs sampling to this problem by meng and schilling the simulations also confirm the validity of the present method in calculating likelihood ratio chi square statistics for determining the number of factors required in the model finally we apply the method to a sample of real data from a test of teacher qualifications

almost sure and moments stability of jump linear systems abstract the stability of piecewise deterministic linear systems driven by an underlying finite markov chain is analyzed necessary and sufficient conditions for moment stability are obtained by means of an explicit formula for the corresponding liapunov exponent the relationship between almost sure and moment stability is elucidated revealing the possible occurrence of high order moment instability and large deviations from a stable sample path behavior

the polyserial correlation coefficient the polyserial and point polyserial correlations are discussed as generalizations of the biserial and point biserial correlations the relationship between the polyserial and point polyserial correlation is derived the maximum likelihood estimator of the polyserial correlation is compared with a two step estimator and with a computationally convenient ad hoc estimator all three estimators perform reasonably well in a monte carlo simulation some practical applications of the polyserial correlation are described

quadratic control with partial information for discrete time jump systems with the markov chain in a general borel space this paper deals with the finite horizon quadratic optimal control problem of discrete time markov jump linear systems mjls considering the case in which the markov chain takes values in a general borel space s it is assumed that the controller has access to an output variable as well as the jump parameter the goal is to design a dynamic markov jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time it is shown that an optimal controller can be obtained from two s coupled difference riccati equations one associated to a filtering problem and the other one associated to a control problem in which the state variable is fully available by s coupled it is meant that the difference riccati equations are coupled via an integral over s this result which can be seen as a separation principle for discrete time mjls generalizes previous ones that were restricted to the markov chain taking values in a finite set

feedback control of switched stochastic systems using randomly available active mode information almost sure asymptotic stabilization of a discrete time switched stochastic system is investigated information on the active operation mode of the switched system is assumed to be available for control purposes only at random time instants we propose a stabilizing feedback control framework that utilizes the information obtained through mode observations we first consider the case where stochastic properties of mode observation instants are fully known we obtain sufficient asymptotic stabilization conditions for the closed loop switched stochastic system under our proposed control law we then explore the case where exact knowledge of the stochastic properties of mode observation instants is not available we present a set of alternative stabilization conditions for this case the results for both cases are predicated on the analysis of a sequence valued process that encapsulates the stochastic nature of the evolution of active operation mode between mode observation instants finally we demonstrate the efficacy of our results with numerical examples

a clebsch gordan decomposition in positive characteristic abstract let k be an algebraically closed field and g sl 2 k let e be the natural module and s r e the rth symmetric power we consider here for r s 0 the tensor product of s r e and the dual of s s e in characteristic zero this tensor product decomposes according to the clebsch gordan formula we consider here the situation when k is a field of positive characteristic we show that each indecomposable component occurs with multiplicity one and identify which modules occur for given r and s

pairwise likelihood ratio tests and model selection criteria for structural equation models with ordinal variables correlated multivariate ordinal data can be analysed with structural equation models parameter estimation has been tackled in the literature using limited information methods including three stage least squares and pseudo likelihood estimation methods such as pairwise maximum likelihood estimation in this paper two likelihood ratio test statistics and their asymptotic distributions are derived for testing overall goodness of fit and nested models respectively under the estimation framework of pairwise maximum likelihood estimation simulation results show a satisfactory performance of type i error and power for the proposed test statistics and also suggest that the performance of the proposed test statistics is similar to that of the test statistics derived under the three stage diagonally weighted and unweighted least squares furthermore the corresponding under the pairwise framework model selection criteria aic and bic show satisfactory results in selecting the right model in our simulation examples the derivation of the likelihood ratio test statistics and model selection criteria under the pairwise framework together with pairwise estimation provide a flexible framework for fitting and testing structural equation models for ordinal as well as for other types of data the test statistics derived and the model selection criteria are used on data on trust in the police selected from the 2010 european social survey the proposed test statistics and the model selection criteria have been implemented in the r package lavaan

a problem with discretizing vale maurelli in simulation studies previous influential simulation studies investigate the effect of underlying non normality in ordinal data using the vale maurelli vm simulation method we show that discretized data stemming from the vm method with a prescribed target covariance matrix are usually numerically equal to data stemming from discretizing a multivariate normal vector this normal vector has however a different covariance matrix than the target it follows that these simulation studies have in fact studied data stemming from normal data with a possibly misspecified covariance structure this observation affects the interpretation of previous simulation studies

statistical assessment of mediational effects for logistic mediational models the concept of mediation has broad applications in medical health studies although the statistical assessment of a mediational effect under the normal assumption has been well established in linear structural equation models sem it has not been extended to the general case where normality is not a usual assumption in this paper we propose to extend the definition of mediational effects through causal inference the new definition is consistent with that in linear sem and does not rely on the assumption of normality here we focus our attention on the logistic mediation model where all variables involved are binary three approaches to the estimation of mediational effects delta method bootstrap and bayesian modelling via monte carlo simulation are investigated simulation studies are used to examine the behaviour of the three approaches measured by 95 per cent confidence interval ci coverage rate and root mean square error rmse criteria it was found that the bayesian method using a non informative prior outperformed both bootstrap and the delta methods particularly for small sample sizes case studies are presented to demonstrate the application of the proposed method to public health research using a nationally representative database extending the proposed method to other types of mediational model and to multiple mediators are also discussed

covariance structure models and influence diagrams statisticians use covariance structure modeling as a versatile tool for modeling and testing theory the models that result provide explicit and detailed descriptions of stochastic systems we show how covariance structure models are related mathematically conceptually philosophically and practically to gaussian influence diagrams as described by shachter and kenley 1989 this relationship suggests ways in which covariance structure modeling can be used to advantage in the prescriptive domain of decision analysis the paper includes an example concerning the management of hazardous materials in which a covariance structure model is converted to an influence diagram for use in a prescriptive analysis

a short note on the estimation of the asymptotic covariance matrix for polychoric correlations by using a taylor expansion of the equations that define the two step estimator for polychoric correlations the asymptotic covariance matrix for the estimated correlations can be derived in a simple and straightforward way

matrix estimation by universal singular value thresholding consider the problem of estimating the entries of a large matrix when the observed entries are noisy versions of a small random fraction of the original entries this problem has received widespread attention in recent times especially after the pioneering works of emmanuel candes and collaborators this paper introduces a simple estimation procedure called universal singular value thresholding usvt that works for any matrix that has a little bit of structure surprisingly this simple estimator achieves the minimax error rate up to a constant factor the method is applied to solve problems related to low rank matrix estimation blockmodels distance matrix completion latent space models positive definite matrix completion graphon estimation and generalized bradley terry models for pairwise comparison

filtering s coupled algebraic riccati equations for discrete time markov jump systems abstract this paper deals with a set of s coupled algebraic riccati equations that arises in the study of filtering of discrete time linear jump systems with the markov chain in a general borel space s by s coupled it is meant that the algebraic riccati equations are coupled via an integral over s conditions for the existence and uniqueness of a positive semi definite solution to the filtering s coupled algebraic riccati equations are obtained in terms of the concepts of stochastic detectability and stochastic stabilizability this result is then applied to solve the infinite horizon minimum mean square linear markov jump filtering problem the obtained results generalize previous ones in the literature which considered only the case of the markov chain taking values in a finite state space

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

brief paper static output feedback stabilization of discrete time markovian jump linear systems a system augmentation approach this paper studies the static output feedback sof stabilization problem for discrete time markovian jump systems from a novel perspective the closed loop system is represented in a system augmentation form in which input and gain output matrices are separated by virtue of the system augmentation a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities which possess a monotonic structure for a linearized computation and a convergent iteration algorithm is given to solve such inequalities in addition a special property of the feasible solutions enables one to further improve the solvability via a simple d k type optimization on the initial values an extension to mode independent sof stabilization is provided as well compared with some existing approaches to sof synthesis the proposed one has several advantages that make it specific for markovian jump systems the effectiveness and merit of the theoretical results are shown through some numerical examples

partial identification of latent correlations with binary data the tetrachoric correlation is a popular measure of association for binary data and estimates the correlation of an underlying normal latent vector however when the underlying vector is not normal the tetrachoric correlation will be different from the underlying correlation since assuming underlying normality is often done on pragmatic and not substantial grounds the estimated tetrachoric correlation may therefore be quite different from the true underlying correlation that is modeled in structural equation modeling this motivates studying the range of latent correlations that are compatible with given binary data when the distribution of the latent vector is partly or completely unknown we show that nothing can be said about the latent correlations unless we know more than what can be derived from the data we identify an interval constituting all latent correlations compatible with observed data when the marginals of the latent variables are known also we quantify how partial knowledge of the dependence structure of the latent variables affect the range of compatible latent correlations implications for tests of underlying normality are briefly discussed

stabilization of markovian systems via probability rate synthesis and output feedback this technical note is concerned with the stabilization problem of markovian jump linear systems via designing switching probability rate matrices and static output feedback gains a novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of markovian jump linear systems based on this a necessary and sufficient condition is provided for the existence of desired controller gains and probability rate matrices extensions to the polytopic uncertain case are also provided all the conditions are formulated in terms of linear matrix inequalities with some equality constraints which can be solved by two modified cone complementarity linearization algorithms examples are given to show the effectiveness of the proposed method

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

on the estimation of polychoric correlations and their asymptotic covariance matrix a general theory for parametric inference in contingency tables is outlined estimation of polychoric correlations is seen as a special case of this theory the asymptotic covariance matrix of the estimated polychoric correlations is derived for the case when the thresholds are estimated from the univariate marginals and the polychoric correlations are estimated from the bivariate marginals for given thresholds computational aspects are also discussed

high dimensional exploratory item factor analysis by a metropolis hastings robbins monro algorithm a metropolis hastings robbins monro mh rm algorithm for high dimensional maximum marginal likelihood exploratory item factor analysis is proposed the sequence of estimates from the mh rm algorithm converges with probability one to the maximum likelihood solution details on the computer implementation of this algorithm are provided the accuracy of the proposed algorithm is demonstrated with simulations as an illustration the proposed algorithm is applied to explore the factor structure underlying a new quality of life scale for children it is shown that when the dimensionality is high mh rm has advantages over existing methods such as numerical quadrature based em algorithm extensions of the algorithm to other modeling frameworks are discussed

stochastic stability of jump discrete time linear systems with markov chain in a general borel space necessary and sufficient conditions for stochastic stability ss of discrete time linear systems subject to markov jumps in the parameters are considered assuming that the markov chain takes values in a general borel space s it is shown that ss is equivalent to the spectrum radius of a bounded linear operator in a banach space being less than 1 or to the existence of a solution of a lyapunov type equation these results generalize several previous results in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

on exponential almost sure stability of random jump systems this paper is concerned with a class of random jump systems represented by transition operators which includes switched linear systems with strictly stationary switching signals in infinite modes space as its special case a series of necessary and sufficient conditions are established for almost sure stability of this class of random jump systems under different scenarios the stability criteria obtained are further extended to markov jump linear systems with infinite states and hence a unified approach to describing the almost sure stability of mjlss is addressed under this context all the results in the work are developed for both the continuous and discrete time systems

exponential stability for discrete time infinite markov jump systems this technical note addresses a class of discrete time stochastic systems with infinite markov jump parameter first of all spectral criterion and lyapunov type criteria are presented for the exponential stability of considered systems further under the condition of strong detectability a barbashin krasovskii stability theorem is shown in terms of a generalized lyapunov equation with a positive semi definite term as an application of the proposed lyapunov stability criterion a sufficient condition of ell 2 input state stability is derived for the infinite markov jump systems disturbed by finite energy random disturbance

on structural equation modeling with data that are not missing completely at random a general latent variable model is given which includes the specification of a missing data mechanism this framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data here missing completely at random is not a prerequisite for unbiased estimation in large samples as when using the traditional listwise or pairwise present data approaches the theory is connected with old and new results in the area of selection and factorial invariance it is pointed out that in many applications maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software such as lisrel and liscomp several sets of artifical data are generated within the general model framework the proposed estimator is compared to the two traditional ones and found superior

stability of switched systems on randomly switching durations with random interaction matrices in this paper we investigate the almost sure stability of switched systems on randomly switching durations simultaneously with randomly switching interaction matrices we not only allow the interaction matrix on each switching duration to take values randomly from either a countable an uncountable or even an unbounded state space but also allow the corresponding probability density function to be time varying with the switching we provide an example to show the difference between the almost sure stability and the moment stability then we establish several practical stability criteria for switched systems which may have linear or nonlinear subsystems these stability criteria also enable us to find suitable conditions for realizing almost sure synchronization in complex networks such as small world networks with both randomly switching durations and a few switching couplings that take values randomly in either an uncountable or an unbounded state space