invariant subspaces dilation theory and the structure of the predual of a dual algebra i on etudie la structure des preduaux d algebres d operateurs on obtient un nouveau theoreme de sous espace invariant on trouve des proprietes concernant le treillis sous espace invariant de l operateur decalage de bergman

doubly robust estimates for binary longitudinal data analysis with missing response and missing covariates longitudinal studies often feature incomplete response and covariate data likelihood based methods such as the expectation maximization algorithm give consistent estimators for model parameters when data are missing at random mar provided that the response model and the missing covariate model are correctly specified however we do not need to specify the missing data mechanism an alternative method is the weighted estimating equation which gives consistent estimators if the missing data and response models are correctly specified however we do not need to specify the distribution of the covariates that have missing values in this article we develop a doubly robust estimation method for longitudinal data with missing response and missing covariate when data are mar this method is appealing in that it can provide consistent estimators if either the missing data model or the missing covariate model is correctly specified simulation studies demonstrate that this method performs well in a variety of situations

nonmonotone systems decomposable into monotone systems with negative feedback motivated by the work of angeli and sontag 1 and enciso and sontag 7 in control theory we show that certain flnite and inflnite dimensional semi dynamical systems with negative feedback can be decomposed into a monotone open loop system with inputs and a decreasing output function the original system is reconstituted by plugging the output into the input employing a technique of gouz 9 and cosner 5 of imbedding the system into a larger symmetric monotone system we are able to obtain information on the asymptotic behavior of solutions including existence of positively invariant sets and global convergence

missing data methods for generalized linear models a comparative review missing data is a major issue in many applied problems especially in the biomedical sciences we review four common approaches for inference in generalized linear models glms with missing covariate data maximum likelihood ml multiple imputation mi fully bayesian fb and weighted estimating equations wees there is considerable interest in how these four methodologies are related the properties of each approach the advantages and disadvantages of each methodology and computational implementation we examine data that are missing at random and nonignorable missing for ml we focus on techniques using the em algorithm and in particular discuss the em by the method of weights and related procedures as discussed by ibrahim for mi we examine the techniques developed by rubin for fb we review approaches considered by ibrahim et al for wee we focus on the techniques developed by robins et al we use a real dataset and a detailed simulation study to compare the four methods

factorization theorems and the structure of operators on hilbert space soit 7b h un espace de hilbert complexe et soit 7b l 7b h l algebre des operateurs lineaires bornes agissant sur 7b h on demontre des theoremes de factorisation on etudie la structure des operateurs sur 7b h

median regression models for longitudinal data with dropouts summary recently median regression models have received increasing attention when continuous responses follow a distribution that is quite different from a normal distribution usual mean regression models may fail to produce efficient estimators whereas median regression models may perform satisfactorily in this article we discuss using median regression models to deal with longitudinal data with dropouts weighted estimating equations are proposed to estimate the median regression parameters for incomplete longitudinal data where the weights are determined by modeling the dropout process consistency and the asymptotic distribution of the resultant estimators are established the proposed method is used to analyze a longitudinal data set arising from a controlled trial of hiv disease volberding et al 1990 the new england journal of medicine 322 941 949 simulation studies are conducted to assess the performance of the proposed method under various situations an extension to estimation of the association parameters is outlined

robustness of a parametric model for informatively censored bivariate longitudinal data under misspecification of its distributional assumptions a simulation study repeated measurements of surrogate markers are frequently used to track disease progression but these series are often prematurely terminated due to disease progression or death analysing such data through standard likelihood based approaches can yield severely biased estimates if the censoring mechanism is non ignorable motivated by this problem we have proposed the bivariate joint multivariate random effects jmre model which has shown that when correctly specified it performs well in terms of bias reduction and precision the bivariate jmre model is fully parametric and belongs to the class of shared parameters joint models where a survival model for the dropouts and a mixed model for the markers evolution are linked through a multivariate normal distribution of random effects as in every parametric model robustness under violations of its distributional assumptions is of great importance in this study we generated 500 simulated data sets assuming that random effects jointly follow a heavy tailed distribution two skewed distributions or a mixture of two normal distributions moreover we generated data where level 1 errors or residuals in the survival part of the model follow a skewed distribution further sensitivity analysis on the effects of reduced sample size increased level 1 variances and altered fixed effects values was also performed we found that fixed effects estimates are almost unaffected but their standard errors ses may be underestimated especially under heavily skewed distributions the proposed model seems robust enough but its performance on smaller data sets or under more extreme departures of its assumptions needs further investigation

operator valued typically real functions induced by a contraction let h be a complex hilbert space and let l h denote the algebra of all bounded linear operators on h letf z n 0 znanbe an operator valued analytic function whose coefficients are bounded operators in l h forzin the open unit disc d and the series is convergent in the strong operator topology in this paper we discuss operator valued typically real functionsf z n 0 znanwhich generalize complex valued typically real functions we characterize operator valued typically real functions and study such functionsf z induced by a contraction on h in addition we considerm n tuple operator valued typically real functions and positively real functions finally we charaterize operator valued typically real functions in the finite dimensional cases

on the hyperinvariant subspace problem iii abstract in two recent papers foias and pearcy j funct anal in press hamid et al indiana univ math j to appear the authors reduced the hyperinvariant subspace problem for operators on hilbert space to the question whether every c 00 bcp operator that is quasidiagonal and has spectrum the unit disc has a nontrivial hyperinvariant subspace n h s in this note we continue this study by showing with the help of a new equivalence relation that every operator whose spectrum is uncountable as well as every nonalgebraic operator with finite spectrum has a hyperlattice i e lattice of hyperinvariant subspaces that is isomorphic to the hyperlattice of a c 00 quasidiagonal bcp operator whose spectrum is the closed unit disc

shift type invariant subspaces of contractions abstract using the sz nagy foias functional model it was shown in l kerchy injection of unilateral shifts into contractions with non vanishing unitary asymptotes acta sci math szeged 61 1995 443 476 that under certain conditions on a contraction t the natural embedding of a hardy space of vector valued functions into the corresponding l 2 space can be factored into the product of two transformations intertwining t with a unilateral shift and with an absolutely continuous unitary operator respectively the norm estimates in the factorization theorem of this paper are sharpened to their best possible form by essential improvements in the proof as a consequence we obtain that if the residual set of a contraction covers the whole unit circle then those invariant subspaces where the restriction is similar to the unilateral shift with a similarity constant arbitrarily close to 1 span the whole space furthermore the hyperinvariant subspace problem for asymptotically non vanishing contractions is reduced to these special circumstances

invariant subspaces for operators whose spectra are caratheodory regions abstract in this paper it is shown that if an operator t satisfies p t p t for every polynomial p and the polynomially convex hull of t is a caratheodory region whose accessible boundary points lie in rectifiable jordan arcs on its boundary then t has a nontrivial invariant subspace as a corollary it is also shown that if t is a hyponormal operator and the outer boundary of t has at most finitely many prime ends corresponding to singular points on d and has a tangent at almost every point on each jordan arc then t has a nontrivial invariant subspace

every missingness not at random model has a missingness at random counterpart with equal fit over the last decade a variety of models to analyse incomplete multivariate and longitudinal data have been proposed many of which allowing for the missingness to be not at random in the sense that the unobserved measurements influence the process governing missingness in addition to influences coming from observed measurements and or covariates the fundamental problems that are implied by such models to which we refer as sensitivity to unverifiable modelling assumptions has in turn sparked off various strands of research in what is now termed sensitivity analysis the nature of sensitivity originates from the fact that a missingness not at random mnar model is not fully verifiable from the data rendering the empirical distinction between mnar and missingness at random mar where only covariates and observed outcomes influence missingness difficult or even impossible unless we are willing to accept the posited mnar model in an unquestioning way we show that the empirical distinction between mar and mnar is not possible in the sense that each mnar model fit to a set of observed data can be reproduced exactly by an mar counterpart of course such a pair of models will produce different predictions of the unobserved outcomes given the observed outcomes theoretical considerations are supplemented with an illustration that is based on the slovenian public opinion survey which has been analysed before in the context of sensitivity analysis

on c00 contractions with dominating spectrum abstract this paper concerns the structure of the predual of certain singly generated operator algebras it is shown that if t acts on a finite dimensional space then in the predual of the algebra generated by t and the identity convex combinations of point evaluations can be written in the form x x for some x second it is shown that if t is a c00 contraction whose spectrum intersected with the unit disc is dominating then t belongs to the class a 0

conditional mixed models adjusting for non ignorable drop out with administrative censoring in longitudinal studies in this paper a class of conditional mixed models is proposed to adjust for non ignorable drop out while also accommodating unequal follow up due to staggered entry and administrative censoring in longitudinal studies conditional linear and quadratic models which model subject specific slopes as linear or quadratic functions of the time to drop out as well as pattern mixture models are both special cases of this approach we illustrate these models and compare them with the usual maximum likelihood approach assuming ignorable drop out using data from a multi centre randomized clinical trial of renal disease simulations under various scenarios where the drop out mechanism is ignorable and non ignorable are employed to evaluate the performance of these models

on the structure of contraction operators with applications to invariant subspaces on ameliore certaines conditions suffisantes pour un membre de la classe a d 0 on obtient de nouvelles conditions suffisantes pour qu une contraction sur un espace de hilbert dont le spectre contient le cercle unite ait des sous espaces invariants non triviaux

two banach space methods and dual operator algebras abstract in this paper we present several new slightly nonlinear variants of the bipolar and the open mapping theorems in banach spaces which we abstracted from the recent developments in the theory of dual operator algebras a new application of our techniques to the theory of operator algebras is also given

synchronization of goodwin s oscillators under boundedness and nonnegativeness constraints for solutions in the recent paper by hamadeh et al 2012 an elegant analytic criterion for incremental output feedback passivity iofp of cyclic feedback systems cfs has been reported assuming that the constituent subsystems are incrementally output strictly passive iosp this criterion was used to prove that a network of identical cfs can be synchronized under sufficiently strong linear diffusive coupling a very important class of cfs consists of biological oscillators named after brian goodwin and describing self regulated chains of enzymatic reactions where the product of each reaction catalyzes the next reaction while the last product inhibits the first reaction in the chain goodwin s oscillators are used in particular to model the dynamics of genetic circadian pacemakers hormonal cycles and some metabolic pathways in this technical note we point out that for goodwin s oscillators where the individual reactions have nonlinear e g mikhaelis menten kinetics the synchronization criterion obtained by hamadeh et al cannot be directly applied this criterion relies on the implicit assumption of the solution boundedness dictated also by the chemical feasibility the state variables stand for the concentrations of chemicals furthermore to test the synchronization condition one needs to know an explicit bound for a solution which generally cannot be guaranteed under linear coupling at the same time we show that these restrictions can be avoided for a nonlinear synchronization protocol where the control inputs are saturated by a special nonlinear function belonging to a wide class which guarantees nonnegativity of the solutions and allows to get explicit ultimate bounds for them we prove that oscillators synchronize under such a protocol provided that the couplings are sufficiently strong

an index of local sensitivity to nonignorable drop out in longitudinal modelling in longitudinal studies with potentially nonignorable drop out one can assess the likely effect of the nonignorability in a sensitivity analysis troxel et al proposed a general index of sensitivity to nonignorability or isni to measure sensitivity of key inferences in a neighbourhood of the ignorable missing at random mar model they derived detailed formulas for isni in the special case of the generalized linear model with a potentially missing univariate outcome in this paper we extend the method to longitudinal modelling we use a multivariate normal model for the outcomes and a regression model for the drop out process allowing missingness probabilities to depend on an unobserved response the computation is straightforward and merely involves estimating a mixed effects model and a selection model for the drop out together with some simple arithmetic calculations we illustrate the method with three examples

every missing not at random model has got a missing at random counterpart with equal fit over the last decade a variety of models to analyze incomplete multivariate and longitudinal data have been proposed many of which allowing for the missingness to be not at random mnar in the sense that the unobserved measurements influence the process governing missingness in addition to influences coming from observed measurements and or covariates the fundamental problems implied by such models to which we refer as sensitivity to unverifiable modeling assumptions has in turn sparked off various strands of research in what is now termed sensitivity analysis the nature of sensitivity originates from the fact that an mnar model is not fully verifiable from the data rendering the empirical distinction between mnar and random missingness mar where only covariates and observed outcomes influence missingness hard or even impossible unless one is prepared to accept the posited mnar model in an unquestioning way in this paper we show that the empirical distinction between mar and mnar is not possible in the sense that each mnar model fit to a set of observed data can be reproduced exactly by an mar counterpart of course such a pair of models will produce different predictions of the unobserved outcomes given the observed ones theoretical considerations are supplemented with an illustration based on the slovenian public opinion survey analyzed before in the context of sensitivity analysis missing data can be seen as latent variables such a view allows extension of our results to other forms of coarsening such as grouping and censoring in addition the technology applies to random effects models where a parametric form for the random effects can be replaced by certain other parametric and non parametric form without distorting the model s fit latent classes latent variables etc

dilation theory and systems of simultaneous equations in the predual of an operator algebra ii 1 this note is a continuation of our earlier paper 3 in which we developed a dilation theory for a certain class of contraction operators acting on a separable infinite dimensional complex hilbert space the notation and terminology in what follows is taken from 3 for the convenience of the reader we recall a few pertinent definitions the algebra of bounded linear operators on is denoted by y if t se 2c the ultraweakly closed algebra generated by t and l e is denoted by dr we recall that d r can be identified with the dual space of the quotient space q r z c where zc denotes the ideal of trace class operators in 5 24 and is the preannihilator of d r in z c under the pairing

sensitivity analysis of longitudinal normal data with drop outs we propose to perform a sensitivity analysis to evaluate the extent to which results from a longitudinal study can be affected by informative drop outs the method is based on a selection model where the parameter relating the dropout probability to the current observation is not estimated but fixed to a set of values this allows to evaluate several hypotheses for the degree of informativeness of the drop out process expectation and variance of missing data conditional on the drop out time are computed and a stochastic em algorithm is used to obtain maximum likelihood estimates simulations show that when the drop out parameter is correctly specified unbiased estimates of the other parameters are obtained and coverage percentages of their confidence intervals are close to their theoretical value more interestingly misspecification of the drop out parameter does not considerably alter these results this method was applied to a randomized clinical trial designed to demonstrate non inferiority of an inhaled corticosteroid in terms of bone density compared with a reference treatment sensitivity analysis showed that the conclusion of non inferiority was robust against different hypotheses for the drop out process

on the structure of contraction operators ii soit 7b h un espace de hilbert complexe separable de dimension infinie et 7b l 7b h l algebre de tous les operateurs lineaires bornes sur 7b h soit d le disque unite ouvert dans c d et n est l ensemble des entiers positifs il existe r 6 tel que chaque contraction t dans 7b l 7b h avec c t soit a un sous espace hyperinvariant non trivial soit appartient a la classe a 1 r

the slice map problem and approximation properties we show that a weakly closed subspace j of the bounded operators bh on an infinite dimensional hilbert space h has property s the fubini product lt l for all weakly closed subspaces t b h if and only if j satisfies a certain approximation property which we call the weak approximation property the weak approximation property is implied by but does not imply the weak completely bounded approximation property moreover if j has the weak approximation property then the predual j has the approximation property for banach spaces we also prove analagous results for property s and variations of property s for c algebras as an application of our characterization of subspaces with property s we show that the reflexive algebra tensor product formula alg l1 alg l2 alg l1 l2 is not always valid in fact we show that for each of the types ii1 ii and iii 0 1 there is a separably acting factor m alg l1 of that type and a reflexive algebra a alg l2 such that alg l1 alg l2 is strictly contained in alg l1 l2

using hierarchical likelihood for missing data problems most statistical solutions to the problem of statistical inference with missing data involve integration or expectation this can be done in many ways directly or indirectly analytically or numerically deterministically or stochastically missing data problems can be formulated in terms of latent random variables so that hierarchical likelihood methods of lee nelder 1996 can be applied to missing value problems to provide one solution to the problem of integration of the likelihood the resulting methods effectively use a laplace approximation to the marginal likelihood with an additional adjustment to the measures of precision to accommodate the estimation of the fixed effects parameters we first consider missing at random cases where problems are simpler to handle because the integration does not need to involve the missing value mechanism and then consider missing not at random cases we also study tobit regression and refit the missing not at random selection model to the antidepressant trial data analyzed in diggle kenward 1994

weighted generalized estimating functions for longitudinal response and covariate data that are missing at random longitudinal studies often feature incomplete response and covariate data it is well known that biases can arise from naive analyses of available data but the precise impact of incomplete data depends on the frequency of missing data and the strength of the association between the response variables and covariates and the missing data indicators various factors may influence the availability of response and covariate data at scheduled assessment times and at any given assessment time the response may be missing covariate data may be missing or both response and covariate data may be missing here we show that it is important to take the association between the missing data indicators for these two processes into account through joint models inverse probability weighted generalized estimating equations offer an appealing approach for doing this here we develop these equations for a particular model generating intermittently missing at random data empirical studies demonstrate that the consistent e

sensitivity analysis for nonrandom dropout a local influence approach diggle and kenward 1994 applied statistics 43 49 93 proposed a selection model for continuous longitudinal data subject to nonrandom dropout it has provoked a large debate about the role for such models the original enthusiasm was followed by skepticism about the strong but untestable assumptions on which this type of model invariably rests since then the view has emerged that these models should ideally be made part of a sensitivity analysis this paper presents a formal and flexible approach to such a sensitivity assessment based on local influence cook 1986 journal of the royal statistical society series b 48 133 169 the influence of perturbing a missing at random dropout model in the direction of nonrandom dropout is explored the method is applied to data from a randomized experiment on the inhibition of testosterone production in rats

robust estimation in mixed linear models with non monotone missingness we introduce a model to account for abrupt changes among repeated measures with non monotone missingness development of likelihood inferences for such models is hard because it involves intractable integration to obtain the marginal likelihood we use hierarchical likelihood to overcome such difficulty abrupt changes among repeated measures can be well described by introducing random effects in the dispersion a simulation study shows that the resulting estimator is efficient robust against misspecification of fatness of tails for illustration we use a schizophrenic behaviour data presented by rubin and wu

a contribution to the structure theory of operators in the class a soit 7b h un espace de hilbert separable et soit t une contraction agissant sur 7b h on suppose que t est absolument continu soit 7b a t l etoile fermee algebre faible engendree par t si t a on dit que t appartient a la classe a 1 si pour chaque fonctionnelle etoile continue faible sur 7b a t il existe des vecteurs n y 7b h satisfaisant a a 7b a t on montre que chaque operateur t tel que t a et soit t n 0 soit t n o avec 1 n appartient a a 1

selection models for repeated measurements with non random dropout an illustration of sensitivity the outcome based selection model of diggle and kenward for repeated measurements with non random dropout is applied to a very simple example concerning the occurrence of mastitis in dairy cows in which the occurrence of mastitis can be modelled as a dropout process it is shown through sensitivity analysis how the conclusions concerning the dropout mechanism depend crucially on untestable distributional assumptions this example is exceptional in that from a simple plot of the data two outlying observations can be identified that are the source of the apparent evidence for non random dropout and also provide an explanation of the behaviour of the sensitivity analysis it is concluded that a plausible model for the data does not require the assumption of non random dropout

partial and latent ignorability in missing data problems summary when an assumption of missing at random is untenable it becomes necessary to model missingdata indicators which carry information about the parameters of the complete data population within a given application however researchers may believe that some aspects of missingness are ignorable but others are not we argue that there are two different ways to formalize the notion that only part of the missingness is ignorable these approaches correspond to assumptions that we call partially missing at random and latently missing at random we explain these concepts and apply them in a latent class analysis of survey questions with item nonresponse

global state synchronization in networks of cyclic feedback systems this technical note studies global asymptotic state synchronization in networks of identical systems conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback structure are deduced using incremental dissipativity theory the method takes advantage of the incremental passivity properties of the constituent subsystems of the network nodes to reformulate the synchronization problem as one of achieving incremental passivity by coupling the method can be used in the framework of contraction theory to constructively build a contracting metric for the incremental system the result is illustrated for a network of biochemical oscillators

compression of quasianalytic spectral sets of cyclic contractions the class l0 h of cyclic quasianalytic contractions was studied in kerchy 2011 12 the subclass l1 h consists of those operators t in l0 h whose quasianalytic spectral set t covers the unit circle t the contractions in l1 h have rich invariant subspace lattices in this paper it is shown that for every operator t l0 h there exists an operator t1 l1 h commuting with t thus the hyperinvariant subspace problems for the two classes are equivalent the operator t1 is found as an h function of t the existence of an appropriate function compressing t to the whole circle is proved using potential theoretic tools by constructing a suitable regular compact set on t with absolutely continuous equilibrium measure

l1 factorization forc00 contractions with isometric functional calculus abstract let t be an absolutely continuous contraction acting on a hilbert space h for x y h define x t y l 1 t by its fourier coefficients x t y n t n x y if n n x n t w l 1 h 1 0 w t x n l 1 h 1 0 0 w h implies that lim n x n t w l 1 0 w h using known factorization techniques we exhibit a borel set t such that for any f l 1 t there exist x y h such that f x t y t in the case where t a c 00 this leads to a simple proof of the fact that for every f l 1 t there exists x y h such that f x t y in this case we also show using dilation theory in the unit disk that every strictly positive lower semicontinuous function l 1 t can be written in the form x t x examples show that this is the best possible result for the class a c 00

notes on invariant subspaces the main purpose of this article is to give an approach to the recent invariant subspace theorem of brown chevreau and pearcy every contraction on a hubert space whose spectrum contains the unit circle has nontrivial invariant subspaces our proof incorporates several of the recent ideas tying together function theory and operator theory 1 i n t r o d u c t i o n the jordan structure theorem for finite matrices has been known now for over one hundred years and its usefulness can hardly be overstated it says that every square matrix a over the complex numbers c is similar to another matrix b i e b xax for some invertible matrix x which is a direct sum of jordan cells that is b can be written in block form bx 0 0 b o 0 bk and each bt has the form a 0 0

analysis of interconnected oscillators by dissipativity theory this paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension oscillators are regarded as open systems that satisfy a particular dissipation inequality it is shown that this characterization has implications for the global stability analysis of limit cycle oscillations i in isolated oscillators ii in interconnections of oscillators and iii for the global synchrony analysis in interconnections of identical oscillators

parameterization and bayesian modeling progress in statistical computation often leads to advances in statistical modeling for example it is surprisingly common that an existing model is reparameterized solely for computational purposes but then this new configuration motivates a new family of models that is useful in applied statistics one reason why this phenomenon may not have been noticed in statistics is that reparameterizations do not change the likelihood in a bayesian framework however a transformation of parameters typically suggests a new family of prior distributions we discuss examples in censored and truncated data mixture modeling multivariate imputation stochastic processes and multilevel models