a note on the quadratic exponential binary distribution summary the joint distribution of p binary variables is studied in the quadratic exponential form containing only main effects and two factor interactions in the log probabilities approximate versions of marginalized forms of the distribution are studied based on taylor expansion and a number of conclusions drawn

autoregressive and cross lagged model for bivariate non commensurate outcomes autoregressive and cross lagged models have been widely used to understand the relationship between bivariate commensurate outcomes in social and behavioral sciences but not much work has been carried out in modeling bivariate non commensurate e g mixed binary and continuous outcomes simultaneously we develop a likelihood based methodology combining ordinary autoregressive and cross lagged models with a shared subject specific random effect in the mixed model framework to model two correlated longitudinal non commensurate outcomes the estimates of the cross lagged and the autoregressive effects from our model are shown to be consistent with smaller mean squared error than the estimates from the univariate generalized linear models inclusion of the subject specific random effects in the proposed model accounts for between subject variability arising from the omitted and or unobservable but possibly explanatory subject level predictors our model is not restricted to the case with equal number of events per subject and it can be extended to different types of bivariate outcomes we apply our model to an ecological momentary assessment study with complex dependence and sampling data structures specifically we study the dependence between the condom use and sexual satisfaction based on the data reported in a longitudinal study of sexually transmitted infections we find negative cross lagged effect between these two outcomes and positive autoregressive effect within each outcome copyright 2017 john wiley sons ltd

brief paper adaptive control in robotic systems with h tracking performance the problem of the adaptive model reference tracking control with a guaranteed h performance is solved for rigid robotic systems with unknown parameters and external disturbances a novel model for disturbance signals is introduced to improve the ability of disturbance rejection in the proposed robotic adaptive tracking control design the proposed h adaptive tracking control design consists of an adaptive disturbance attenuation algorithm and an adaptive internal model compensation algorithm so that the tracking error can asymptotically converge to zero in the presence of disturbances the proposed h adaptive tracking control is smooth as well as global and suitable for practical robotic control design finally a simulation example is given to exhibit the tracking performance of a two link robotic manipulator with the proposed h adaptive control algorithm

pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data abstract we show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model under the approximating model simple sufficient statistics exist for the subject specific parameters introduced to capture the unobserved heterogeneity between subjects the latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors by conditioning on the sufficient statistics we derive a pseudo conditional likelihood estimator of the structural parameters of the dynamic logit model which is simple to compute asymptotic properties of this estimator are studied in detail simulation results show that the estimator is competitive in terms of efficiency with estimators recently proposed in the econometric literature

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

binary models for marginal independence summary log linear models are a classical tool for the analysis of contingency tables in particular the subclass of graphical log linear models provides a general framework for modelling conditional independences however with the exception of special structures marginal independence hypotheses cannot be accommodated by these traditional models focusing on binary variables we present a model class that provides a framework for modelling marginal independences in contingency tables the approach that is taken is graphical and draws on analogies with multivariate gaussian models for marginal independence for the graphical model representation we use bidirected graphs which are in the tradition of path diagrams we show how the models can be parameterized in a simple fashion and how maximum likelihood estimation can be performed by using a version of the iterated conditional fitting algorithm finally we consider combining these models with symmetry restrictions

mini max integral sliding mode control for multimodel linear uncertain systems an original linear time varying system with matched and unmatched disturbances and uncertainties is replaced by a finite set of dynamic models such that each one describes a particular uncertain case including exact realizations of possible dynamic equations as well as external unmatched bounded disturbances such a tradeoff between an original uncertain linear time varying dynamic system and a corresponding higher order multimodel system containing only matched uncertainties leads to a linear multi model system with known unmatched bounded disturbances and unknown matched disturbances as well each model from a given finite set is characterized by a quadratic performance index the developed minimax integral sliding mode control strategy gives an optimal minimax linear quadratic lq control with additional integral sliding mode term the design of this controller is reduced to a solution of an equivalent mini max lq problem that corresponds to the weighted performance indices with weights from a finite dimensional simplex the additional integral sliding mode controller part completely dismisses the influence of matched uncertainties from the initial time instant two numerical examples illustrate this study

optimization over the efficient set abstract in this paper we study the problem of optimizing a linear function over the set of efficient solutions for a vector maximization problem this problem arises whenever a linear function is available which acts as a criterion for measuring the importance of or for discriminating among the efficient alternatives that are available using the concepts of an efficient direction and of a direction of recession we develop necessary and sufficient conditions for this problem to be unbounded we also present necessary and sufficient conditions for efficient and for arbitrary solutions of the underlying vector maximization problem to be optimal solutions for this problem some of these conditions are geometric in nature others algebraic the algebraic conditions suggest potential computational procedures for finding an optimal solution to the problem finally we give conditions under which the set of optimal solutions possesses certain special properties

likelihood methods for incomplete longitudinal binary responses with incomplete categorical covariates summary we consider longitudinal studies in which the outcome observed over time is binary and the covariates of interest are categorical with no missing responses or covariates one specifies a multinomial model for the responses given the covariates and uses maximum likelihood to estimate the parameters unfortunately incomplete data in the responses and covariates are a common occurrence in longitudinal studies here we assume the missing data are missing at random rubin 1976 biometrika63 581 592 since all of the missing data responses and covariates are categorical a useful technique for obtaining maximum likelihood parameter estimates is the em algorithm by the method of weights proposed in ibrahim 1990 journal of the american statistical association85 765 769 in using the em algorithm with missing responses and covariates one specifies the joint distribution of the responses and covariates here we consider the parameters of the covariate distribution as a nuisance in data sets where the percentage of missing data is high the estimates of the nuisance parameters can lead to highly unstable estimates of the parameters of interest we propose a conditional model for the covariate distribution that has several modeling advantages for the em algorithm and provides a reduction in the number of nuisance parameters thus providing more stable estimates in finite samples

nonlinear h control around periodic orbits abstract in this paper we study the nonlinear h control of systems with periodic orbits we develop the notion of an induced l 2 gain so called nonlinear h norm for systems where the no disturbance behavior of the system is a periodic orbit and provide conditions under which the induced l 2 gain of the system around the orbit can be made less than a specified value by state feedback this work is a natural extension of results on nonlinear h control of nonlinear systems in a neighborhood of a stable equilibrium point to the periodic orbit case synthesis of a nonlinear h state feedback controller is facilitated by the use of transverse coordinates and in particular the transverse linearization of the system

h control of linear time varying systems a state space approach in this paper the standard problem of h infty control theory for finite dimensional linear time varying continuous time plants is considered the problem is given a real number gamma 0 f

multivariate logistic models for incomplete binary responses abstract in this article we describe a likelihood based regression model appropriate for analyzing incomplete multivariate binary responses we focus on marginal models that is models where the marginal mean or expectation of the binary response is related to a set of covariates the association between the binary responses is modeled in terms of conditional log odds ratios when the nonresponse mechanism is ignorable it is not necessary to specify a nonresponse model and valid inferences can be obtained provided that the likelihood for the responses has been correctly specified but when the nonresponse mechanism is nonignorable valid inferences can only be obtained by incorporating a model for nonresponse an unresolved issue with nonignorable models concerns the identifiability of the parameters so far no general and practically useful necessary and sufficient conditions for identifiability are available here we suggest some simple procedures for examining the identifiability status of nonign

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

association models for a multivariate binary response models for a multivariate binary response are parameterized by univariate marginal probabilities and dependence ratios of all orders the w order dependence ratio is the joint success probability of w binary responses divided by the joint success probability assuming independence this parameterization supports likelihood based inference for both regression parameters relating marginal probabilities to explanatory variables and association model parameters relating dependence ratios to simple and meaningful mechanisms five types of association models are proposed where responses are 1 independent given a necessary factor for the possibility of a success 2 independent given a latent binary factor 3 independent given a latent beta distributed variable 4 follow a markov chain and 5 follow one of two first order markov chains depending on the realization of a binary latent factor these models are illustrated by reanalyzing three data sets foremost a set of binary time series on auranofin therapy against arthritis likelihood based approaches are contrasted with approaches based on generalized estimating equations association models specified by dependence ratios are contrasted with other models for a multivariate binary response that are specified by odds ratios or correlation coefficients

testing covariance structure in multivariate models application to family disease data abstract recent interest in modeling multivariate responses for members of groups has emphasized the need for testing goodness of fit here we describe a way to test the covariance structure of a multivariate distribution parameterized by a vector the idea is to extend this distribution the null distribution to a more general distribution that depends on an additional scalar and a specific quadratic function of the response vector chosen to capture features of an alternative covariance structure when 0 the more general distribution reduces to the null one standard likelihood theory yields a score test for 0 that is a test of fit of the null distribution the score statistic is the standardized difference between observed and expected values of the quadratic function where the expectation is taken with respect to the null distribution with replaced by its maximum likelihood estimate applying the methods to case control data on familial cancers of the ovary and breast we illu

a computational study for bilevel quadratic programs using semidefinite relaxations abstract in this paper we deal with bilevel quadratic programming problems with binary decision variables in the leader problem and convex quadratic programs in the follower problem for this purpose we transform the bilevel problems into equivalent quadratic single level formulations by replacing the follower problem with the equivalent karush kuhn tucker kkt conditions then we use the single level formulations to obtain mixed integer linear programming milp models and semidefinite programming sdp relaxations thus we compute optimal solutions and upper bounds using linear programming lp and sdp relaxations our numerical results indicate that the sdp relaxations are considerably tighter than the lp ones consequently the sdp relaxations allow finding tight feasible solutions for the problem especially when the number of variables in the leader problem is larger than in the follower problem moreover they are solved at a significantly lower computational cost for large scale instances

optimality conditions for minimization over the weakly or properly efficient set abstract the paper deals with the optimization problem of a nonlinear real function over the weakly or properly efficient set associated to a convex multi objective program in banach spaces abstract optimality conditions are obtained via derivatives for set valued functions in the strict convex case these conditions lead to a nonlinear system involving the classical derivatives up to the second order

bayesian semiparametric regression for longitudinal binary processes with missing data longitudinal studies with binary repeated measures are widespread in biomedical research marginal regression approaches for balanced binary data are well developed whereas for binary process data where measurement times are irregular and may differ by individuals likelihood based methods for marginal regression analysis are less well developed in this article we develop a bayesian regression model for analyzing longitudinal binary process data with emphasis on dealing with missingness we focus on the settings where data are missing at random mar which require a correctly specified joint distribution for the repeated measures in order to draw valid likelihood based inference about the marginal mean to provide maximum flexibility the proposed model specifies both the marginal mean and serial dependence structures using nonparametric smooth functions serial dependence is allowed to depend on the time lag between adjacent outcomes as well as other relevant covariates inference is fully bayesian using simulations we show that adequate modeling of the serial dependence structure is necessary for valid inference of the marginal mean when the binary process data are mar longitudinal viral load data from the hiv epidemiology research study are analyzed for illustration

on marginal and conditional parameters in logistic regression models a fundamental research question is how much a variation in a covariate influences a binary response variable in a logistic regression model both directly or through mediators we derive the exact formula linking the parameters of marginal and conditional regression models with binary mediators when no conditional independence assumptions can be made the formula has the appealing property of being the sum of terms that vanish whenever parameters of the conditional models vanish thereby recovering well known results as particular cases it also permits to quantify the distortion induced by omission of some relevant covariates opening the way to sensitivity analysis also in this case as the parameters of the conditional models are multiplied by terms that are always positive or bounded the formula may be used to construct reasonable bounds on the parameters of interest we assume that conditionally on a set of covariates the data generating process can be represented by a directed acyclic graph we also show how the results here presented lead to the extension of path analysis to a system of binary random variables

brief paper a neural network solution for fixed final time optimal control of nonlinear systems in this paper fixed final time optimal control laws using neural networks and hjb equations for general affine in the input nonlinear systems are proposed the method utilizes kronecker matrix methods along with neural network approximation over a compact set to solve a time varying hjb equation the result is a neural network feedback controller that has time varying coefficients found by a priori offline tuning convergence results are shown the results of this paper are demonstrated on an example

marginal modelling of multivariate categorical data this paper describes likelihood methods of analysis for multivariate categorical data the joint distribution is specified in terms of marginal mean functions and pairwise and higher order association measures for the association the emphasis is on global odds ratios the method allows flexible formulation of a broad class of designs such as repeated measurements longitudinal studies interrater agreement and cross over trials the proposed model can be used for parameter estimation and hypothesis testing simple fitting algorithms are proposed the method is illustrated using a data example

a likelihood based method for analysing longitudinal binary responses summary in this paper we discuss a likelihood based method for analysing correlated binary responses based on a multivariate model it is related to the pseudo maximum likelihood approach suggested recently by zhao prentice 1990 their parameterization results in a simple pairwise model in which the association between responses is modelled in terms of correlations while the present paper uses conditional log odds ratios with this approach higher order associations can be incorporated in a natural way one important advantage of this parameterization is that the maximum likelihood estimates of the marginal mean parameters are robust to misspecification of the time dependence we describe an iterative two stage procedure for obtaining the maximum likelihood estimates two examples are presented to illustrate this methodology

efficiency and proper efficiency in vector maximization with respect to cones abstract vector maximization problems arise when more than one objective function is to be maximized over a given feasibility region the concepts of efficiency and proper efficiency have played a useful role in the analysis of such problems recently these concepts have been extended to vector maximization problems in which the underlying domination cone is a convex cone in this paper efficient and properly efficient solutions for the vector maximization problem in which the underlying domination cone is any nontrivial closed convex cone are examined differences between properly and improperly efficient solutions are established characterizations of efficient and properly efficient solutions are presented and conditions under which efficient solutions exist and fail to exist are derived

a note on pseudolikelihood constructed from marginal densities for likelihood based inference involving distributions in which high dimensional dependencies are present it may be useful to use approximate likelihoods based for example on the univariate or bivariate marginal distributions the asymptotic properties of formal maximum likelihood estimators in such cases are outlined in particular applications in which only a single q x i vector of observations is observed are examined conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied some examples are analysed in detail

nonlinear h control of nonsmooth time varying systems with application to friction mechanical manipulators nonlinear h controller synthesis is developed for nonsmooth time varying systems via measurement feedback a local h controller is derived by means of a certain perturbation of the differential riccati equations appearing in solving the h control problem for the linearized system when these unperturbed equations have bounded positive semidefinite solutions stabilizability and detectability properties of the control system are thus ensured by the existence of the proper solutions of the unperturbed differential riccati equations and hence the proposed synthesis procedure obviates an extra formidable in the nonlinear case work on verification of these properties theoretical results are applied to a position tracking control problem and particularly a regulation problem for mechanical systems with friction performance issues of the nonlinear h tracking controller are illustrated in a simulation study made for a two degrees of freedom robot manipulator

generalization of the mantel haenszel estimating function for sparse clustered binary data we extend the mantel haenszel estimating function to estimate both the intra cluster pairwise correlation and the main effects for sparse clustered binary data we propose both a composite likelihood approach and an estimating function approach for the analysis of such data the proposed estimators are consistent and asymptotically normally distributed simulation results demonstrate that the two approaches are comparable in terms of bias and efficiency however the estimating equation approach is computationally simpler analysis of the georgia high blood pressure survey is used for illustration

analysis of serially correlated data using quasi least squares summary quasi least squares qls a marginal statistical approach via generalized estimating equations that is described in the balanced data setting by chaganty 1997 journal of statistical planning and inference 63 39 54 allows for application of a wide range of working correlation structures when analyzing serially correlated data we extend the application of qls to serially correlated unequally spaced and unbalanced data using three useful working correlation models the firstorder autoregressive ar 1 the markov and the generalized markov structure described by nuniez anton and woodworth 1994 biometrics 50 445 456 we compare qls and the original formulation of the generalized estimating equation approach gee for these structures demonstrating that i infeasibility of the gee correlation parameter estimates can be a problem ii it is difficult to obtain consistent moment estimates of the correlation parameters for the generalized markov structure and iii the use of qls can lead to reduced mean square error of the estimate of the regression parameter for small samples of moderately correlated data to choose between alternative correlation models we propose a criterion that is based on the principle of generalized least squares finally data for which the generalized markov structure is appropriate are analyzed to demonstrate the use of qls in selecting a suitable working correlation structure and identifying in this paper we apply a statistical method based on the generalized estimating equation approach of liang and zeger 1986 to the analysis of longitudinal data that may be difficult to analyze using other established methods we consider repeated measures data collected by taking measurements of an outcome variable and associated covariates on each of a group of independent subjects our primary data analysis goal is to identify important covariates and to explain their effect on the marginal mean of the outcome variable while also accounting for the correlation among observations on each subject accomplishing this research objective may be difficult due to certain conditions that are typical in longitudinal studies the timing and total number of measurements taken may vary from subject to subject so that the data may be unbalanced and unequally spaced the outcome variable may not be normally distributed the intrasubject correlation may be described using a time dependent pattern for example the correlation between two measurements may decrease as they become more

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

weak linear bilevel programming problems existence of solutions via a penalty method we are concerned with a class of weak linear bilevel programs with nonunique lower level solutions for such problems we give via an exact penalty method an existence theorem of solutions then we propose an algorithm

nonlinear h sub spl infin control of time varying systems a unified distribution based formalism for continuous and sampled data measurement feedback design nonlinear h sub spl infin controller synthesis is presented for time varying systems via sampled data measurement feedback the h sub spl infin control problem for a nonlinear system with a sampled data measurement output is shown to be equivalent to the h sub spl infin control problem for a certain nonlinear system with a time continuous measurement output special mathematical tools are developed to straightforwardly derive a local solution of the sampled data measurement feedback smf h sub spl infin control problem from that of the time continuous measurement feedback cmf h sub spl infin control problem

on the approximation of the quadratic exponential distribution in a latent variable context summary following cox wermuth 1994 2002 we show that the distribution of a set of binary observable variables induced by a certain discrete latent variable model may be approximated by a quadratic exponential distribution this discrete latent variable model is equivalent to the latent class version of the two parameter logistic model of birnbaum 1968 which may be seen as a generalized version of the rasch model rasch 1960 1961 on the basis of this result we develop an approximate maximum likelihood estimator of the item parameters of the two parameter logistic model which is very simply implemented the proposed approach is illustrated through an example based on a dataset on educational assessment

order restricted inference for multivariate binary data with application to toxicology in many applications researchers collect multivariate binary response data under two or more naturally ordered experimental conditions in such situations one is often interested in using all binary outcomes simultaneously to detect an ordering among the experimental conditions to make such comparisons we develop a general methodology for testing for the multivariate stochastic order between k 2 multivariate binary distributions our proposed test uses order restricted estimators which according to our simulation study are more efficient than the unrestricted estimators in terms of their mean squared error we compared the power of the proposed test with that of several alternative tests including procedures that combine individual univariate tests for order such as union intersection tests and a bonferroni based test we also compared the proposed test with an unrestricted hotelling t2 type test our simulations suggest that the proposed method competes well with these alternatives the gain i

an exact penalty on bilevel programs with linear vector optimization lower level we are interested in a class of linear bilevel programs where the upper level is a linear scalar optimization problem and the lower level is a linear multi objective optimization problem we approach this problem via an exact penalty method then we propose an algorithm illustrated by numerical examples

pseudolikelihood modeling of multivariate outcomes in developmental toxicology abstract the primary goal of this article is to determine benchmark doses based on the ethylene glycol study which comprises data from a developmental toxicity study in mice because the data involve a vector of malformation indicators a flexible model for multivariate clustered data is required an exponential family model is considered and pseudolikelihood based inferential tools are proposed hence avoiding excessive computational requirements

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

an approximation to maximum likelihood estimates in reduced models summary an approximation to the maximum likelihood estimates of the parameters in a model can be obtained from the corresponding estimates and information matrices in an extended model i e a model with additional parameters the approximation is close provided that the data are consistent with the first model applications are described to log linear models for discrete data to models for multivariate normal distributions with special covariance matrices and to mixed discrete continuous models

on l sub 2 and l sub infinity stability approaches for the robust control of robot manipulators robustness results were recently obtained for the linear and nonlinear control of robot manipulators using the l sub 2 and l sub infinity stability approaches respectively critical remarks on these approaches and further investigations are presented in order to investigate l sub 2 stability it is shown that additional assumptions have to be made and a reformulation of the control problem has to be carried out

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research