conewise linear systems non zenoness and observability conewise linear systems are dynamical systems in which the state space is partitioned into a finite number of nonoverlapping polyhedral cones on each of which the dynamics of the system is described by a linear differential equation this class of dynamical systems represents a large number of piecewise linear systems most notably linear complementarity systems with the p property and their generalizations to affine variational systems which have many applications in engineering systems and dynamic optimization the challenges of dealing with this type of hybrid system are due to two major characteristics mode switchings are triggered by state evolution and states are constrained in each mode in this paper we first establish the absence of zeno states in such a system based on this fundamental result we then investigate and relate several state observability notions short time and t time or finite time local global observability for the short time observability notions constructive finitely verifiable algebraic both sufficient and necessary conditions are derived due to their long time mode transitional behavior which is very difficult to predict only partial results are obtained for the t time observable states nevertheless we completely resolve the t time local observability for the bimodal conewise linear system for finite t and provide numerical examples to illustrate the difficulty associated with the long time observability

nonsmooth lyapunov pairs for infinite dimensional first order differential inclusions the main objective of this paper is to provide new explicit criteria to characterize weak lower semicontinuous lyapunov pairs or functions associated to first order differential inclusions in hilbert spaces these inclusions are governed by a lipschitzian perturbation of a maximally monotone operator the dual criteria we give are expressed by means of the proximal and basic subdifferentials of the nominal functions while primal conditions are described in terms of the contingent directional derivative we also propose a unifying review of many other criteria given in the literature our approach is based on advanced tools of variational analysis and generalized differentiation

nonsmooth lyapunov pairs for differential inclusions governed by operators with nonempty interior domain the general theory of lyapunov stability of first order differential inclusions in hilbert spaces has been studied by the authors in the previous paper adly et al in nonlinear anal 75 3 985 1008 2012 this new contribution focuses on the case when the interior of the domain of the maximally monotone operator governing the given differential inclusion is nonempty this includes in a natural way the finite dimensional case the current setting leads to simplified more explicit criteria and permits some flexibility in the choice of the generalized subdifferentials some consequences of the viability of closed sets are given our analysis makes use of standard tools from convex and variational analysis

differential variational inequalities this paper introduces and studies the class of differential variational inequalities dvis in a finite dimensional euclidean space the dvi provides a powerful modeling paradigm for many applied problems in which dynamics inequalities and discontinuities are present examples of such problems include constrained time dependent physical systems with unilateral constraints differential nash games and hybrid engineering systems with variable structures the dvi unifies several mathematical problem classes that include ordinary differential equations odes with smooth and discontinuous right hand sides differential algebraic equations daes dynamic complementarity systems and evolutionary variational inequalities conditions are presented under which the dvi can be converted either locally or globally to an equivalent ode with a lipschitz continuous right hand function for dvis that cannot be so converted we consider their numerical resolution via an euler time stepping procedure which involves the solution of a sequence of finite dimensional variational inequalities borrowing results from differential inclusions dis with upper semicontinuous closed and convex valued multifunctions we establish the convergence of such a procedure for solving initial value dvis we also present a class of dvis for which the theory of dis is not directly applicable and yet similar convergence can be established finally we extend the method to a boundary value dvi and provide conditions for the convergence of the method the results in this paper pertain exclusively to systems with index not exceeding two and which have absolutely continuous solutions

heuristics of instability and stabilization in model selection in model selection usually a best predictor is chosen from a collection hat mu cdot s of predictors where hat mu cdot s is the minimum least squares predictor in a collection mathsf u s of predictors here s is a complexity parameter that is the smaller s the lower dimensional smoother the models in mathsf u s if mathsf l is the data used to derive the sequence hat mu cdot s the procedure is called unstable if a small change in mathsf l can cause large changes in hat mu cdot s with a crystal ball one could pick the predictor in hat mu cdot s having minimum prediction error without prescience one uses test sets cross validation and so forth the difference in prediction error between the crystal ball selection and the statistician s choice we call predictive loss for an unstable procedure the predictive loss is large this is shown by some analytics in a simple case and by simulation results in a more complex comparison of four different linear regression methods unstable procedures can be stabilized by perturbing the data getting a new predictor sequence hat mu cdot s and then averaging over many such predictor sequences

viscosity solutions for hamilton jacobi equations with unbounded nonlinear term a simplified approach abstract in a previous paper the author defined a notion for hamilton jacobi equations with an unbounded nonlinear term ax du and for such solutions proved existence and uniqueness results here we define an equivalent notion of solution for such equations which in addition has the advantage of being simpler and more intuitive

parsimonious covariance matrix estimation for longitudinal data this article proposes a data driven method to identify parsimony in the covariance matrix of longitudinal data and to exploit any such parsimony to produce a statistically efficient estimator of the covariance matrix the approach parameterizes the covariance matrix through the cholesky decomposition of its inverse for longitudinal data this is a one step ahead predictive representation and the cholesky factor is likely to have off diagonal elements that are zero or close to zero a hierarchical bayesian model is used to identify any such zeros in the cholesky factor similar to approaches that have been successful in bayesian variable selection the model is estimated using a markov chain monte carlo sampling scheme that is computationally efficient and can be applied to covariance matrices of high dimension it is demonstrated through simulations that the proposed method compares favorably in terms of statistical efficiency with a highly regarded competing approach the estimator is applied to three

oracle estimation of parametric models under boundary constraints in many classical estimation problems the parameter space has a boundary in most cases the standard asymptotic properties of the estimator do not hold when some of the underlying true parameters lie on the boundary however without knowledge of the true parameter values confidence intervals constructed assuming that the parameters lie in the interior are generally over conservative a penalized estimation method is proposed in this article to address this issue an adaptive lasso procedure is employed to shrink the parameters to the boundary yielding oracle inference which adapt to whether or not the true parameters are on the boundary when the true parameters are on the boundary the inference is equivalent to that which would be achieved with a priori knowledge of the boundary while if the converse is true the inference is equivalent to that which is obtained in the interior of the parameter space the method is demonstrated under two practical scenarios namely the frailty survival model and linear regression with order restricted parameters simulation studies and real data analyses show that the method performs well with realistic sample sizes and exhibits certain advantages over standard methods

invariant sets and lyapunov pairs for differential inclusions with maximal monotone operators we give different conditions for the invariance of closed sets with respect to differential inclusions governed by a maximal monotone operator defined on hilbert spaces which is subject to a lipschitz continuous perturbation depending on the state these sets are not necessarily weakly closed as in 3 4 while the invariance criteria are still written by using only the data of the system so no need to the explicit knowledge of neither the solution of this differential inclusion nor the semi group generated by the maximal monotone operator these invariant viability results are next applied to derive explicit criteria for a lyapunov pairs of lower semi continuous not necessarily weakly lsc functions associated to these differential inclusions the lack of differentiability of the candidate lyapunov functions and the consideration of general invariant sets possibly not convex or smooth are carried out by using techniques from nonsmooth analysis

stability of dynamical systems with competitive controls the degenerate case abstract we study the stability of a dynamical system with two competitive controls to a general closed set the stability is proven to be equivalent to the continuity on such set of the value function of a differential game with maximum cost functional the existence of a suitably defined and continuous lyapunov function is proven to imply the stability our lyapunov function satisfies a differential inequality in the sense of the theory of viscosity solutions

cal h _ infty control of nonlinear systems differential games and viscosity solutions dealing with disturbances is one of the most important questions for controlled systems cal h infty optimal control theory is a deterministic way to tackle the problem in the presence of unfavorable disturbances the theory of differential games and the study of the associated hamilton jacobi isaacs equation appear to be basic tools of the theory we consider a general nonlinear system and prove that the existence of a continuous local viscosity supersolution of the isaacs equation corresponding to the cal h infty control problem is sufficient for its solvability we also show that the existence of a lower semicontinuous viscosity supersolution is necessary

lyapunov functions for infinite dimensional systems abstract we study lyapunov functions for infinite dimensional dynamical systems governed by general maximal monotone operators we obtain a characterization of lyapunov pairs by means of the associated hamilton jacobi partial differential equations whose solutions are meant in the viscosity sense as evolved in works of tataru and crandall lions our approach also leads to a new sufficient condition for lyapunov pairs generalizing a classical result of pazy

fixed and random effects selection in linear and logistic models we address the problem of selecting which variables should be included in the fixed and random components of logistic mixed effects models for correlated data a fully bayesian variable selection is implemented using a stochastic search gibbs sampler to estimate the exact model averaged posterior distribution this approach automatically identifies subsets of predictors having nonzero fixed effect coefficients or nonzero random effects variance while allowing uncertainty in the model selection process default priors are proposed for the variance components and an efficient parameter expansion gibbs sampler is developed for posterior computation the approach is illustrated using simulated data and an epidemiologic example

the e ms algorithm model selection with incomplete data we propose a procedure associated with the idea of the e m algorithm for model selection in the presence of missing data the idea extends the concept of parameters to include both the model and the parameters under the model and thus allows the model to be part of the e m iterations we develop the procedure known as the e ms algorithm under the assumption that the class of candidate models is finite some special cases of the procedure are considered including e ms with the generalized information criteria gic and e ms with the adaptive fence af jiang et al we prove numerical convergence of the e ms algorithm as well as consistency in model selection of the limiting model of the e ms convergence for e ms with gic and e ms with af we study the impact on model selection of different missing data mechanisms furthermore we carry out extensive simulation studies on the finite sample performance of the e ms with comparisons to other procedures the methodology is also illustrated on a real dat

differential games and nonlinear boldmath cal h_ infty control in infinite dimensions this paper studies the cal h infty control problem for a nonlinear unbounded infinite dimensional system with state constraints we characterize the solvability of the problem by means of a hamilton jacobi isaacs hji equation proving that the cal h infty problem can be solved if and only if the hji equation has a positive definite viscosity supersolution vanishing and continuous at the origin in order to do so the standard definition of the cal h infty problem has to be relaxed by using the theory of differential games we apply our results to the one phase stefan problem

joint selection in mixed models using regularized pql abstractthe application of generalized linear mixed models presents some major challenges for both estimation due to the intractable marginal likelihood and model selection as we usually want to jointly select over both fixed and random effects we propose to overcome these challenges by combining penalized quasi likelihood pql estimation with sparsity inducing penalties on the fixed and random coefficients the resulting approach referred to as regularized pql is a computationally efficient method for performing joint selection in mixed models a key aspect of regularized pql involves the use of a group based penalty for the random effects sparsity is induced such that all the coefficients for a random effect are shrunk to zero simultaneously which in turn leads to the random effect being removed from the model despite being a quasi likelihood approach we show that regularized pql is selection consistent that is it asymptotically selects the true set of fixed and random effects in the setti

model averaging and weight choice in linear mixed effects models this article studies model averaging for linear mixed effects models we establish an unbiased estimator of the squared risk for the model averaging and use the estimator as a criterion for choosing weights the resulting model average estimator is proved to be asymptotically optimal under some regularity conditions simulation experiments show it is superior or comparable to estimators based on the final models selected by the commonly used methods and some existing averaging procedures the proposed procedure is applied to data from an aids clinic trial

joint variable selection for fixed and random effects in linear mixed effects models it is of great practical interest to simultaneously identify the important predictors that correspond to both the fixed and random effects components in a linear mixed effects lme model typical approaches perform selection separately on each of the fixed and random effect components however changing the structure of one set of effects can lead to different choices of variables for the other set of effects we propose simultaneous selection of the fixed and random factors in an lme model using a modified cholesky decomposition our method is based on a penalized joint log likelihood with an adaptive penalty for the selection and estimation of both the fixed and random effects it performs model selection by allowing fixed effects or standard deviations of random effects to be exactly zero a constrained expectation maximization algorithm is then used to obtain the final estimates it is further shown that the proposed penalized estimator enjoys the oracle property in that asymptotically it performs as well as if the true model was known beforehand we demonstrate the performance of our method based on a simulation study and a real data example

maximum likelihood computations with repeated measures application of the em algorithm abstract the purpose of this article is to consider the use of the em algorithm dempster laird and rubin 1977 for both maximum likelihood ml and restricted maximum likelihood reml estimation in a general repeated measures setting using a multivariate normal data model with linear mean and covariance structure anderson 1973 several models and methods of analysis have been proposed in recent years for repeated measures data ware 1985 presented an overview because the em algorithm is a general purpose iterative method for computing ml estimates with incomplete data it has often been used in this particular setting dempster et al 1977 andrade and helms 1984 jennrich and schluchter 1985 there are two apparently different approaches to using the em algorithm in this setting in one application each experimental unit is observed under a standard protocol specifying measurements at each of n occasions or under n conditions and incompleteness implies that the number of measurements actua

the effect of covariance structure on variance estimation in balanced growth curve models with random parameters abstract intuition suggests that altering the covariance structure of a parametric model for repeated measures data alters the variances of the model s estimated mean parameters the purpose of this article is to sharpen such intuition for a family of growth curve models with differing numbers of random effects for the individual sampling units and with a fixed structure on the mean for every member of this family the maximum likelihood ml estimator of the fixed effects is identical to the ordinary least squares ols estimator in addition simple closed form ml and restricted maximum likelihood estimators for the variance and covariance parameters exist for every member as a consequence closed form expressions for the estimated variance covariance matrix of the ols estimator of the fixed effects also exist for the entire family we derive explicit relationships between the variance and covariance parameter estimators from different members of the family and thereby extend some familiar results fo

fixed and random effects selection in mixed effects models summary we consider selecting both fixed and random effects in a general class of mixed effects models using maximum penalized likelihood mpl estimation along with the smoothly clipped absolute deviation scad and adaptive least absolute shrinkage and selection operator alasso penalty functions the mpl estimates are shown to possess consistency and sparsity properties and asymptotic normality a model selection criterion called the icq statistic is proposed for selecting the penalty parameters ibrahim zhu and tang 2008 journal of the american statistical association 103 1648 1658 the variable selection procedure based on icq is shown to consistently select important fixed and random effects the methodology is very general and can be applied to numerous situations involving random effects including generalized linear mixed models simulation studies and a real data set from a yale infant growth study are used to illustrate the proposed methodology

on the degrees of freedom of the lasso we study the effective degrees of freedom of the lasso in the framework of stein s unbiased risk estimation sure we show that the number of nonzero coefficients is an unbiased estimate forthe degrees of freedom of the lasso a conclusion that requires no special assumption on the predictors in addition the unbiased estimator is shown to be asymptotically consistent with these results on hand various model selection criteria cp aic and bic are available which along with the lars algorithm provide a principled and efficient approach to obtaining the optimal lasso fit with the computational effort of a single ordinary least squares fit

viscosity solutions of hamilton jacobi equations with unbounded nonlinear terms abstract the aim of this paper is to introduce a new definition of viscosity solutions for hamilton jacobi equations in infinite dimensions with unbounded nonlinear terms we prove existence and uniqueness results under usual assumptions regarding the bounded part of the hamiltonian

flexible estimation of covariance function by penalized spline with application to longitudinal family data longitudinal data are routinely collected in biomedical research studies a natural model describing longitudinal data decomposes an individual s outcome as the sum of a population mean function and random subject specific deviations when parametric assumptions are too restrictive methods modeling the population mean function and the random subject specific functions nonparametrically are in demand in some applications it is desirable to estimate a covariance function of random subject specific deviations in this work flexible yet computationally efficient methods are developed for a general class of semiparametric mixed effects models where the functional forms of the population mean and the subject specific curves are unspecified we estimate nonparametric components of the model by penalized spline p spline biometrics 2001 57 253 259 and reparameterize the random curve covariance function by a modified cholesky decomposition biometrics 2002 58 121 128 which allows for unconstrained estimation of a positive semidefinite matrix to provide smooth estimates we penalize roughness of fitted curves and derive closed form solutions in the maximization step of an em algorithm in addition we present models and methods for longitudinal family data where subjects in a family are correlated and we decompose the covariance function into a subject level source and observation level source we apply these methods to the multi level framingham heart study data to estimate age specific heritability of systolic blood pressure nonparametrically copyright 2011 john wiley sons ltd

can the strengths of aic and bic be shared a conflict between model indentification and regression estimation a traditional approach to statistical inference is to identify the true or best model first with little or no consideration of the specific goal of inference in the model identification stage can the pursuit of the true model also lead to optimal regression estimation in model selection it is well known that bic is consistent in selecting the true model and aic is minimax rate optimal for estimating the regression function a recent promising direction is adaptive model selection in which in contrast to aic and bic the penalty term is data dependent some theoretical and empirical results have been obtained in support of adaptive model selection but it is still not clear if it can really share the strengths of aic and bic model combining or averaging has attracted increasing attention as a means to overcome the model selection uncertainty can bayesian model averaging be optimal for estimating the regression function in a minimax sense we show that the answers to these questions are basically in the negative for any model selection criterion to be consistent it must behave suboptimally for estimating the regression function in terms of minimax rate of covergence and bayesian model averaging cannot be minimax rate optimal for regression estimation

conditional akaike information for mixed effects models summary this paper focuses on the akaike information criterion aic for linear mixed effects models in the analysis of clustered data we make the distinction between questions regarding the population and questions regarding the particular clusters in the data we show that the aic in current use is not appropriate for the focus on clusters and we propose instead the conditional akaike information and its corresponding criterion the conditional aic caic the penalty term in caic is related to the effective degrees of freedom p for a linear mixed model proposed by hodges sargent 2001 p reflects an intermediate level of complexity between a fixed effects model with no cluster effect and a corresponding model with fixed cluster effects the caic is defined for both maximum likelihood and residual maximum likelihood estimation a pharmacokinetics data appli cation is used to illuminate the distinction between the two inference settings and to illustrate the use of the conditional aic in model selection

the schwarz criterion and related methods for normal linear models in this paper we derive schwarz s information criterion and two modifications for choosing fixed effects in normal linear mixed models the first modification allows an arbitrary possibly informative prior for the parameter of interest replacing this prior with the normal unit information prior of kass wasserman 1995 and the generalised cauchy prior of jeffreys 1961 yields the usual schwarz criterion and a second modification respectively under the null hypothesis these criteria approximate bayes factors using the corresponding priors to increased accuracy in regression the second modification also corresponds asymptotically to the bayes factors of zellner siow 1980 and o hagan 1995 and is similar to the bayes factor of berger pericchi 1996 in mixed models the effective sample size term in schwarz s formula is ambiguous because of correlation between observations we propose an appropriate generalisation of schwarz s approximation and apply our results to evaluate a large class of models for repeated neuron area measurements in alcoholic and suicidal patients

characterization of lyapunov pairs in the nonlinear case and applications abstract the paper presents a characterization of the lyapunov pairs for a general initial value problem with a possibly multivalued m accretive operator on an arbitrary banach space by means of the contingent derivative related to the operator the proof is based on tangency and flow invariance arguments combined with a priori estimates and approximation the abstract results are applied to obtain precise a priori estimates for the mild solutions they readily lead to the existence of global solutions and various controllability properties important lyapunov pairs are pointed out in connection with specific problems

a strongly consistent procedure for model selection in a regression problem summary we consider the multiple regression model yn xn en where yn and en are n vector random variables xn is an n x m matrix and 83 is an m vector of unknown regression parameters each component of 3 may be zero or nonzero which gives rise to 2 possible models for multiple regression we provide a decision rule for the choice of a model which is strongly consistent for the true model as n oo the result is proved under certain mild conditions for instance without assuming normality of the distribution of the components of en

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

prime knots and tangles a study is made of a method of proving that a classical knot or link is prime the method consists of identifying together the boundaries of two prime tangles examples and ways of constructing prime tangles are explored introduction this paper explores the idea of the prime tangle that was briefly introduced in kl it is here shown that summing together two prime tangles always produces a prime knot or link here a tangle is just two arcs spanning a 3 ball and such a tangle is prime if it contains no knotted ball pair and its arcs cannot be separated by a disc a few prototype examples of prime tangles are given figure 2 together with ways of using them to create infinitely many more theorem 3 then usage of the prime tangle idea becomes a powerful machine nicely complementing other methods in the production of prime knots and links finally it is shown theorem 5 that the idea of the prime tangle has a very natural interpretation in terms of double branched covers the paper should be interpreted as being in either the p l or smooth category with the exception of the section on double branched covers all the methods used are the straightforward innermost disc techniques of the elementary theory of 3 manifolds none of the proofs is difficult the paper aims for significance rather than sophistication indeed various possible generalizations of the prime tangle have not been developed e g n arcs for n 2 or arcs in a ball with holes meeting each boundary component in four points in order to avoid unnecessary complication the author wishes to record his gratitude to the university of california at santa barbara for providing opportunity facilities and inspiration for the writing of this

simultaneous regression shrinkage variable selection and supervised clustering of predictors with oscar variable selection can be challenging particularly in situations with a large number of predictors with possibly high correlations such as gene expression data in this article a new method called the oscar octagonal shrinkage and clustering algorithm for regression is proposed to simultaneously select variables while grouping them into predictive clusters in addition to improving prediction accuracy and interpretation these resulting groups can then be investigated further to discover what contributes to the group having a similar behavior the technique is based on penalized least squares with a geometrically intuitive penalty function that shrinks some coefficients to exactly zero additionally this penalty yields exact equality of some coefficients encouraging correlated predictors that have a similar effect on the response to form predictive clusters represented by a single coefficient the proposed procedure is shown to compare favorably to the existing shrinkage and variable selection techniques in terms of both prediction error and model complexity while yielding the additional grouping information

lyapunov stability of complementarity and extended systems a linear complementarity system lcs is a piecewise linear dynamical system consisting of a linear time invariant ordinary differential equation ode parameterized by an algebraic variable that is required to be a solution to a finite dimensional linear complementarity problem lcp whose constant vector is a linear function of the differential variable continuing the authors recent investigation of the lcs from the combined point of view of system theory and mathematical programming this paper addresses the important system theoretic properties of exponential and asymptotic stability for an lcs with a c 1 state trajectory the novelty of our approach lies in our employment of a quadratic lyapunov function that involves the auxiliary algebraic variable of the lcs when expressed in the state variable alone the lyapunov function is piecewise quadratic and thus nonsmooth the nonsmoothness feature invalidates standard stability analysis that is based on smooth lyapunov functions in addition to providing sufficient conditions for exponential stability we establish a generalization of the well known lasalle invariance theorem for the asymptotic stability of a smooth dynamical system to the lcs which is intrinsically a nonsmooth system sufficient matrix theoretic copositivity conditions are introduced to facilitate the verification of the stability properties properly specialized the latter conditions are satisfied by a passive like lcs and certain hybrid linear systems having common quadratic lyapunov functions we provide numerical examples to illustrate the stability results we also develop an extended local exponential stability theory for nonlinear complementarity systems and differential variational inequalities based on a new converse theorem for odes with b differentiable right hand sides the latter theorem asserts that the existence of a b differentiable lyapunov function is a necessary and sufficient condition for the exponential stability of an equilibrium of such a differential system

penalized nonlinear mixed effects model to identify biomarkers that predict disease progression precise modeling of disease progression in neurodegenerative disorders may enable early intervention before clinical manifestation of a disease which is crucial since early intervention at the premanifest stage is expected to be more effective neuroimaging biomarkers are indicative of the underlying disease pathology and may be used to predict future disease occurrence at the premanifest stage as observed in many pivotal studies longitudinal measurements of clinical outcomes such as motor or cognitive symptoms often present nonlinear sigmoid shapes over time where the inflection points of the trajectories mark a meaningful time in disease progression therefore to identify neuroimaging biomarkers predicting disease progression we propose a nonlinear mixed effects model based on a sigmoid function to predict longitudinal clinical outcomes and associate a linear combination of neuroimaging biomarkers with subject specific inflection points based on an expectation maximization em algorithm we propose a method that can fit a nonlinear model with many potentially correlated biomarkers for random inflection points while achieving computational stability variable selection is introduced in the algorithm in order to identify important biomarkers of disease progression and to reduce prediction variability we apply the proposed method to the data from the predictors of huntington s disease study to select brain subcortical regional volumes predictive of the inflection points of the motor and cognitive function trajectories our results reveal that brain atrophy in the striatum and expansion of the ventricular system are highly predictive of the inflection points furthermore these inflection points may precede clinically defined disease onset by as early as a decade and thus may be useful biomarkers as early signs of huntington s disease onset

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

fence methods for mixed model selection many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure asymptotic properties for these types of procedures in settings like linear regression and arma time series have been studied but these do not naturally extend to nonstandard situations such as mixed effects models where simple definition of the sample size is not meaningful this paper introduces a new class of strategies known as fence methods for mixed model selection which includes linear and generalized linear mixed models the idea involves a procedure to isolate a subgroup of what are known as correct models of which the optimal model is a member this is accomplished by constructing a statistical fence or barrier to carefully eliminate incorrect models once the fence is constructed the optimal model is selected from among those within the fence according to a criterion which can be made flexible in addition we propose two variations of the fence the first is a stepwise procedure to handle situations of many predictors the second is an adaptive approach for choosing a tuning constant we give sufficient conditions for consistency of fence and its variations a desirable property for a good model selection procedure the methods are illustrated through simulation studies and real data analysis

sparse pairwise likelihood estimation for multivariate longitudinal mixed models abstractit is becoming increasingly common in longitudinal studies to collect and analyze data on multiple responses for example in the social sciences we may be interested in uncovering the factors driving mental health of individuals over time where mental health is measured using a set of questionnaire items one approach to analyzing such multi dimensional data is multivariate mixed models an extension of the standard univariate mixed model to handle multiple responses estimating multivariate mixed models presents a considerable challenge however let alone performing variable selection to uncover which covariates are important in driving each response motivated by composite likelihood ideas we propose a new approach for estimation and fixed effects selection in multivariate mixed models called approximate pairwise likelihood estimation and shrinkage aples the method works by constructing a quadratic approximation to each term in the pairwise likelihood function and then augmenting this ap

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

viscosity solutions for a class of hamilton jacobi equations in hilbert spaces we study hamilton jacobi equations with an unbounded term in hilbert spaces we introduce a new variant of the notion of viscosity solution for a class of hamilton jacobi equations and obtain comparison and existence results for viscosity solutions we also examine the usefulness of the notion of viscosity solution in optimal control

random effects selection in linear mixed models nous presentons le probleme pratique important de la selection des effets aleatoires dans un modele lineaire mixte un modele bayesien hierarchique est utilise pour identifier tout effet aleatoire devariance nulle l approche proposee reparametrise le modele mixte de telle sorte que les fonctions des parametres de covariance de la distribution des effets aleatoires soient incorporees comme des coefficients de regression pour des variables latentes normales nous permettons aux effets aleatoires de sortir du modele en choisissant des melanges d a priori avec des masses ponctuelles en zero pour les variances des effets aleatoires du fait de la reparametrisation le modele prend une structure lineaire conditionnelle qui facilite l utilisation de lois a priori conjuguees et normales nous demontrons que les calculs a posteriori peuvent etre effectues via un algorithme simple et efficace de monte carlo par chaine de markov les methodes sont illustrees par des donnees simulees et par des donnees reelles d exposition prenatale au polychlorobiphenile et des donnees sur le developpement psychomoteur des enfants

mixtures of g priors for bayesian variable selection zellner s g prior remains a popular conventional prior for use in bayesian variable selection despite several undesirable consistency issues in this article we study mixtures of g priors as an alternative to default g priors that resolve many of the problems with the original formulation while maintaining the computational tractability that has made the g prior so popular we present theoretical properties of the mixture g priors and provide real and simulated examples to compare the mixture formulation with fixed g priors empirical bayes approaches and other default procedures please see arnold zellner s letter and the author s response

variable selection in linear mixed effects models this paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models we propose a class of nonconcave penalized profile likelihood methods for selecting and estimating important fixed effects to overcome the difficulty of unknown covariance matrix of random effects we propose to use a proxy matrix in the penalized profile likelihood we establish conditions on the choice of the proxy matrix and show that the proposed procedure enjoys the model selection consistency where the number of fixed effects is allowed to grow exponentially with the sample size we further propose a group variable selection strategy to simultaneously select and estimate important random effects where the unknown covariance matrix of random effects is replaced with a proxy matrix we prove that with the proxy matrix appropriately chosen the proposed procedure can identify all true random effects with asymptotic probability one where the dimension of random effects vector is allowed to increase exponentially with the sample size monte carlo simulation studies are conducted to examine the finite sample performance of the proposed procedures we further illustrate the proposed procedures via a real data example

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control