bayesian analysis of dichotomous quantal response models abstract qualitative response models qrm s are analyzed from the bayesian point of view using diffuse and informative prior distributions exact finite sample bayesian and large sample bayesian and non bayesian estimation results are compared in addition the paper provides 1 plots and discussion of the properties of likelihood functions for qrm s 2 posterior distributions for logit models derivatives and elasticities 3 bayesian prediction procedures for qrm s 4 new estimates for the median and other fractiles of the logistic distribution 5 posterior odds ratios for model selection problems and 6 comparisons of two alternative monte carlo numerical integration procedures it is concluded that asymptotic approximations are not accurate for small to moderate sized samples even when only a single input variable is used and that operational bayesian methods are available for providing both exact small sample and large sample approximate inferences for drm s

quadratic stabilizability of uncertain linear systems existence of a nonlinear stabilizing control does not imply existence of a linear stabilizing control this note is concerned with the problem of stabilizing an uncertain linear system via state feedback control an uncertain system which admits a stabilizing state feedback control and some associated quadratic lyapunov function is said to be quadratically stabilizable in a number of recent papers conditions are given under which quadratic stabilizability via nonlinear control implies quadratic stabilizability via linear control these papers restrict the manner in which the uncertain parameters are permitted to enter structurally into the state equation in order to establish this result this note presents an example which shows that this implication is not true for more general uncertain linear systems to this end we describe an uncertain linear system which is quadratically stabilizable via nonlinear control but not quadratically stabilizable via linear control

forecasting multivariate realized stock market volatility we present a new matrix logarithm model of the realized covariance matrix of stock returns the model uses latent factors which are functions of lagged volatility lagged returns and other forecasting variables the model has several advantages it is parsimonious it does not require imposing parameter restrictions and it results in a positive definite estimated covariance matrix we apply the model to the covariance matrix of size sorted stock returns and find that two factors are sufficient to capture most of the dynamics

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

robustness of luenberger observers linear systems stabilized via non linear control abstract given a dynamical system whose state equations include time varying uncertain parameters it is often desirable to design a state feedback controller leading to uniform asymptotic stability of a given equilibrium point if however the controller operates on some estimate of the state instead of the true state itself it is of interest to know whether the desired stability will be preserved e g suppose that the measured output is processed by a luenberger observer this paper concentrates on the scenario above and in addition our analysis permits the controller to be non linear as a first step inequalities are developed which have implications on the system s robustness that is when the uncertain parameters satisfy these inequalities it becomes possible to separately design controller and observer this amounts to an extension of the classical separation theorem to the case when the controller is non linear it is also of interest to note that the approach given here guarantees stability for some non zero range of admissible parameter variations this is achieved by introducing a certain tuning parameter into the lyapunov function which is used to assure the stability of the combined plant observer controller system

bayesian inference for a covariance matrix a flexible class of prior distributions is proposed for the covariance matrix of a multivariate normal distribution yielding much more general hierarchical and empirical bayes smoothing and inference when compared with a conjugate analysis involving an inverted wishart distribution a likelihood approximation is obtained for the matrix logarithm of the covariance matrix via bellman s iterative solution to a volterra integral equation exact and approximate bayesian empirical and hierarchical bayesian estimation and finite sample inference techniques are developed some risk and asymptotic frequency properties are investigated a subset of the project talent american high school data is analyzed applications and extensions to multivariate analysis including a generalized linear model for covariance matrices are indicated

large sample properties of the matrix exponential spatial specification with an application to fdi this paper studies large sample properties of the matrix exponential spatial specification mess we find that the quasi maximum likelihood estimator qmle for the mess is consistent under heteroskedasticity a property not shared by the qmle of the sar model for the general model that has mess in both the dependent variable and disturbances labeled mess 1 1 the qmle can be consistent under unknown heteroskedasticity when the spatial weights matrices in the two mess processes are commutative we also consider the generalized method of moments estimator gmme in the homoskedastic case we derive a best gmme that is as efficient as the maximum likelihood estimator under normality and can be asymptotically more efficient than the qmle under non normality in the heteroskedastic case an optimal gmme can be more efficient than the qmle asymptotically the qml approach for the mess model has the computational advantage over that of a sar model the computational simplicity carries over to mess models with any finite order of spatial matrices no parameter range needs to be imposed in order for the model to be stable results of monte carlo experiments for finite sample properties of the estimators are reported finally the mess 1 1 is applied to belgium s outward fdi data and we observe that the dominant motivation of belgium s outward fdi lies in finding cheaper factor inputs

bayesian analysis of covariance matrices and dynamic models for longitudinal data summary parsimonious modelling of the within subject covariance structure while heeding its positive definiteness is of great importance in the analysis of longitudinal data using the cholesky decomposition and the ensuing unconstrained and statistically meaningful reparameterisation we provide a convenient and intuitive framework for developing conditionally conjugate prior distributions for covariance matrices and show their connections with generalised inverse wishart priors our priors offer many advantages with regard to elicitation positive definiteness computations using gibbs sampling shrinking covariances toward a particular structure with considerable flexibility and modelling covariances using covariates bayesian estimation methods are developed and the results are compared using two simulation studies these simulations suggest simpler and more suitable priors for the covariance structure of longitudinal data

anti windup design with guaranteed regions of stability for discrete time linear systems abstract the purpose of this paper is to study the determination of stability regions for discrete time linear systems with saturating controls through anti windup schemes considering that a linear dynamic output feedback has been designed to stabilize the linear discrete time system without saturation a method is proposed for designing an anti windup gain that maximizes an estimate of the basin of attraction of the closed loop system in the presence of saturation it is shown that the closed loop system obtained from the controller plus the anti windup gain can be locally modeled by a linear system with a deadzone nonlinearity then based on the use of a new sector condition and quadratic lyapunov functions stability conditions in an lmi form are stated these conditions are then considered in a convex optimization problem in order to compute an anti windup gain that maximizes an estimate of the basin of attraction of the closed loop system moreover considering asymptotically stable open loop systems it is shown that the conditions can be slightly modified in order to determine an anti windup gain that ensures global stability an extension of the proposed results to the case of dynamic anti windup synthesis is also presented in the paper

arma covariance structures with time heteroscedasticity for repeated measures experiments abstract rochon and helms 1989 presented a model for analyzing repeated measures experiments the general linear model was used to assess the influence of covariate information and arma time series models were put forward to characterize the covariance matrix among the repeated measures practical experience has suggested however that the arma assumption of constant variances and autocovariances over time is too restrictive for many applications for example observations may be relatively stable toward the beginning of the study but become more variable toward the end this article presents a modification to this structure which provides for heteroscedasticity over time maximum likelihood ml estimation procedures are considered and the estimators are found to enjoy optimal large sample properties a scoring algorithm is described for iterating to a solution of the ml equations the model is illustrated with data from a clinical trial investigating human erythropoietin for treating anemia in end

analysis of longitudinal data unbalanced over time summary the paper considers modelling estimating and diagnostically verifying the response process generating longitudinal data with emphasis on association between repeated measures from unbalanced longitudinal designs our model is based on separate specifications of the moments for the mean standard deviation and correlation with different components possibly sharing common parameters we propose a general class of correlation structures that comprise random effects measurement errors and a serially correlated process these three elements are combined via flexible time varying weights whereas the serial correlation can depend flexibly on the mean time and lag when the measurement schedule is independent of the response process our estimation procedure yields consistent and asymptotically normal estimates for the mean parameters even when the standard deviation and correlation are misspecified and for the standard deviation parameters even when the correlation is misspecified a generic diagnostic method is developed for verifying the models for the mean standard deviation and in particular the correlation which is applicable even when the data are severely unbalanced the methodology is illustrated by an analysis of data from a longitudinal study that was designed to characterize pulmonary growth in girls

estimating equations for parameters in means and covariances of multivariate discrete and continuous responses generalized estimating equations are introduced in an ad hoc fashion for the covariance matrix of a multivariate response these equations are to be solved jointly with score equations from a generalized linear model for mean parameters a class of quadratic exponential models is used to develop joint estimating equations for mean and covariance parameters in a more systematic fashion and proposals for the use of such equations are developed comments on the relative merits of the ad hoc and model based approaches to estimation are given and a regression illustration with a bivariate response is provided

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

maximum likelihood estimation for incomplete repeated measures experiments under an arma covariance structure a stochastic model is presented for the analysis of incomplete repeated measures experiments the general linear model is used to relate the response measures to other variables which are thought to account for inherent variation an autoregressive moving average arma time series representation is used to model disturbance terms maximum likelihood estimation procedures are considered and the properties of these estimators are derived it is concluded that while the assumptions underpinning the arma covariance models may be somewhat restrictive they provide a useful inferential vehicle particularly in the presence of missing values

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

a note on pole assignment in uncertain systems a new method for full rank state feedback pole assignment is introduced a particular advantage of this method is that no freedom in the design parameters is lost hence further design problems such as robust pole assignment in uncertain systems are alleviated an application of this feature is shown for a particular linear model of the f16 aircraft the connections between state feedback and several concepts in the literature such as incomplete input feedback incomplete state feedback output feedback and incomplete pole assignment are also given

bayesian nonparametric covariance regression capturing predictor dependent correlations amongst the elements of a multivariate response vector is fundamental to numerous applied domains including neuroscience epidemiology and finance although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors relatively little has been done in the multivariate case as a motivating example we consider the google flu trends data set which provides indirect measurements of influenza incidence at a large set of locations over time our predictor to accurately characterize temporally evolving influenza incidence across regions it is important to develop statistical methods for a time varying covariance matrix importantly the locations provide a redundant set of measurements and do not yield a sparse nor static spatial dependence structure we propose to reduce dimensionality and induce a flexible bayesian nonparametric covariance regression model by relating these location specific trajectories to a lower dimensional subspace through a latent factor model with predictor dependent factor loadings these loadings are in terms of a collection of basis functions that vary nonparametrically over the predictor space such low rank approximations are in contrast to sparse precision assumptions and are appropriate in a wide range of applications our formulation aims to address three challenges scaling to large p domains coping with missing values and allowing an irregular grid of observations the model is shown to be highly exible while leading to a computationally feasible implementation via gibbs sampling the ability to scale to large p domains and cope with missing values is fundamental in analyzing the google flu trends data

domain level covariance analysis for multilevel survey data with structured nonresponse health care quality surveys in the united states are administered to individual respondents i e hospital patients health plan members to evaluate the performance of health care organizations i e hospitals health plans which thus constitute estimation domains for better understanding and more parsimonious reporting of dimensions of quality we analyze relationships among quality measures at the domain level rather than specifying a full parametric model for the observed responses and the nonresponse patterns at the lower patient level we first fit generalized variance covariance functions that take into account nonresponse patterns in the survey responses then specify a likelihood function for the domain mean responses using these generalized variance covariance functions this allows us to model directly the relationships among domain means for different items because the response scales are bounded we assume that these means follow a truncated multivariate normal distribution we calcu

upwind scheme for acoustic disturbances generated by low speed flows computation of acoustic disturbances generated by unsteady low speed flows such as flows including vortices and shear layers can be obtained by a recently proposed two step method this method requires a hydrodynamic field solution and obtains the acoustic field from the perturbed inviscid compressible flow equations a numerical method for the solution of the equations governing the acoustic field is presented the primitive variable form of the governing equations is used for the numerical solution time integration is performed with a fourth order runge kutta method discretization of the primitive variables space derivatives is obtained with a high order upwind biased numerical scheme upwinding of these convective fluxes is performed according to the eigenvalue sign of the coefficient matrices nonreflecting boundary conditions are applied to properly convect outgoing waves away from the computational domain solutions are obtained for the acoustic field generated by a pair of corotating point vortices computed results are compared with the existing analytic solution for the sound field

a multivariate multilevel gaussian model with a mixed effects structure in the mean and covariance part a traditional gaussian hierarchical model assumes a nested multilevel structure for the mean and a constant variance at each level we propose a bayesian multivariate multilevel factor model that assumes a multilevel structure for both the mean and the covariance matrix that is in addition to a multilevel structure for the mean we also assume that the covariance matrix depends on covariates and random effects this allows to explore whether the covariance structure depends on the values of the higher levels and as such models heterogeneity in the variances and correlation structure of the multivariate outcome across the higher level values the approach is applied to the three dimensional vector of burnout measurements collected on nurses in a large european study to answer the research question whether the covariance matrix of the outcomes depends on recorded system level features in the organization of nursing care but also on not recorded factors that vary with countries hospitals and nursing units simulations illustrate the performance of our modeling approach

robust linear controllers using observers the possibility of determining a linear robust control law when the full state cannot be measured and observers are implemented to estimate the state is considered the focus is on systems where the uncertainty satisfies the matching condition the control law and the observer are designed using two riccati equations the first result establishes that if certain scalar parameters are chosen so that a matrix inequality is satisfied the closed loop system is stable for the uncertainty levels of interest it is then shown that if there are at least as many sensors as there are actuators and the transfer function of the nominal system or a squared down form of it does not have zeros in the closed right half plane the closed loop system can be stabilized by the technique regardless of the size of the uncertainty bounding set

least squares estimation of covariance matrices in balanced multivariate variance components models abstract the problem of estimating covariance matrices in balanced multivariate variance components models is discussed as with univariate models it is possible for the traditional estimators based on differences of the mean square matrices to produce estimates that are outside the parameter space in fact in many cases it is extremely likely that traditional estimates of the covariance matrices will not be nonnegative definite nnd in this article we develop an iterative estimation procedure satisfying a least squares criterion that is guaranteed to produce nnd estimates of the covariance matrices discuss the speed of convergence and provide an example to show how the estimates change

a riccati equation approach to the design of linear robust controllers abstract in this paper by the lyapunov stability criterion and the riccati equation we derive a new procedure for determining a linear control law to stabilize an uncertain system the main features of this approach are that no precompensator is needed the required feedback gains are small and the uncertain system can be exponentially stabilized with any prescribed exponential rate in addition the robust control law can be made linear quadratic optimal with respect to an index function for the nominal system two examples are given to illustrate the results

a matrix exponential spatial specification we introduce the matrix exponential as a way of modelling spatially dependent data the matrix exponential spatial specification mess simplifies the log likelihood allowing a closed form solution to the problem of maximum likelihood estimation and greatly simplifies the bayesian estimation of the model the mess can produce estimates and inferences similar to those from conventional spatial autoregressive models but has analytical computational and interpretive advantages we present maximum likelihood and bayesian approaches to the estimation of this spatial model specification along with methods of model comparisons over different explanatory variables and spatial specifications

the constrained lyapunov problem and its application to robust output feedback stabilization given a dynamical system whose description includes time varying uncertain parameters it is often desirable to design an output feedback controller leading to asymptotic stability of a given equilibrium point when designing such a controller one may consider static i e memoryless or dynamic compensation in this paper we show that solvability of various output feedback design problems is implied by existence of a solution to a certain constrained lyapunov problem clp the clp can be stated in purely algebraic terms once the clp is described we provide necessary and sufficient conditions for its solution to exist subsequently we consider application of the clp to a number of robust stabilization problems involving static output feedback and observer based feedback

exact predictive densities for linear models with arch disturbances abstract it is shown how exact predictive densities may be formed in the arch linear model by means of monte carlo integration with importance sampling several improvements in computational efficiency over earlier implementations of this procedure are developed including use of the exact likelihood function rather than an asymptotic approximation to construct the importance sampling distribution and antithetic acceleration of convergence a numerical approach to the formulation of posterior odds ratios and the combination of non nested models is also introduced these methods are applied to daily quotations of closing stock prices forecasts are formulated using linear models arch linear models and an integrated model constructed from the posterior probabilities of the respective models the use of the exact predictive density in a decision theoretic context is illustrated by deriving the optimal day to day portfolio adjustments of a trader with constant relative risk aversion

the matrix logarithmic covariance model abstract a flexible method is introduced to model the structure of a covariance matrix c and study the dependence of the covariances on explanatory variables by observing that for any real symmetric matrix a the matrix exponential transformation c exp a is a positive definite matrix because there is no constraint on the possible values of the upper triangular elements on a any possible structure of interest can be imposed on them the method presented here is not intended to replace the existing special models available for a covariance matrix but rather to provide a broad range of further structures that supplements existing methodology maximum likelihood estimation procedures are used to estimate the parameters and the large sample asymptotic properties are obtained a simulation study and two real life examples are given to illustrate the method introduced

reducing the sensitivity to parameter variations of a minimum order reduced order observer a quantitative upper hound is established which defines the extent to which a minimum order reduced order non adaptive observer may be rendered insensitive to parameter variations that upper bound depends on the number of measurements and the location of questionable parameters within the system matrices an integral squared error objective function is explicitly solved that objective function may be used to assess the sensitivity of the system to parameter errors a numerical example is presented for a continuous observer the results are extended to the discrete ease

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

marginal models for correlated binary responses with multiple classes and multiple levels of nesting a model for correlated binary data is presented marginal probabilities and odds ratios are allowed to have general regression structures that include multiple classes and multiple levels of nesting estimation is done through the generalized estimating equations approach of liang and zeger 1986 biometrika 73 13 22 they are contrasted with conditional models and recommendations for choosing between the two are given examples from genetic epidemiology are presented

calculation of the radiated sound field using an open kirchhoff surface means of improving the accuracy of kirchhoff surface integral evaluations for sound fields in cases where the surface may not be completely closed are investigated asymptotic analysis for large temporal wave number is used to analyze time harmonic integral forms applicability to the moderate temporal wave numbers of real problems is discussed stationary phase arguments are used to show geometrically where good results are expected from a kirchhoff integral on an open surface a similar asymptotic analysis is used to provide correction terms to account partially for the missing portion of the integral surface the present study is restricted to the case where the mean flow is parallel to the available portion of the surface the analysis is extended to time domain formulation of transient problems two and three dimensional numerical examples are given to demonstrate and evaluate the method it is found that the derived correction terms can reduce the error in an open surface calculation of the radiated sound field by more than an order of magnitude

numerical study of sound generation due to a spinning vortex pair a numerical approach for the calculation of an acoustic field is applied to the case of a spinning vortex pair to investigate the sound generation by quadrupole sources in unsteady vortical flows based on the unsteady hydrodynamic information from the known incompressible flowfield the perturbed compressible acoustic terms derived from the euler equations are calculated nonreflecting boundary conditions are developed to obtain highly stable solutions calculated results are compared with analytical solutions obtained by the method of matched asymptotic expansions the possibility of predicting the effect of convective mean flow is also tested it is concluded that the sound generated by the quadrupole sources of unsteady vortical flows without a sound generating body or surface can be calculated by using the source terms of hydrodynamic flow fluctuations

optimized compact finite difference schemes with maximum resolution direct numerical simulations and computational aeroacoustics require an accurate finite difference scheme that has a high order of truncation and high resolution characteristics in the evaluation of spatial derivatives compact finite difference schemes are optimized to obtain maximum resolution characteristics in space for various spatial truncation orders an analytic method with a systematic procedure to achieve maximum resolution characteristics is devised for multidiagonal schemes based on the idea of the minimization of dispersive phase errors in the wave number domain and these are applied to the analytic optimization of multidiagonal compact schemes actual performances of the optimized compact schemes with a variety of truncation orders are compared by means of numerical simulations of simple wave convections and in this way the most effective compact schemes are found for tridiagonal and pentadiagonal cases respectively from these comparisons the usefulness of an optimized high order tridiagonal compact scheme that is more efficient than a pentadiagonal scheme is discussed for the optimized high order spatial schemes the feasibility of using classical high order runge kutta time advancing methods is investigated

aeroacoustic computations using a high order shock capturing scheme for aeroacoustic computations in the supersonic regime it is necessary to use a numerical scheme that can represent shock waves without generating spurious numerical oscillations the centered schemes that are usually used with success in the subsonic case combined with a selective filtering will generally oscillate in the presence of discontinuities a new class of shock capturing schemes the one step monotonicity preserving schemes combine the high accuracy and the nonoscillating property it is thus a good candidate for supersonic aeroacoustic applications the good spectral properties of these schemes are illustrated in the scalar linear case results of aeroacoustic test problems for the euler and navier stokes equations are compared with a dispersion relation preserving scheme the application to a supersonic cavity flow which induces a complex pattern of moving shocks shows that the one step monotonicity preserving schemes capture the moving discontinuities without spurious oscillations and preserve a high accuracy at the same time

modeling the random effects covariance matrix for longitudinal data with covariates measurement error longitudinal data occur frequently in practice such as medical studies and life sciences generalized linear mixed models glmms are commonly used to analyze such data it is typically assumed that the random effects covariance matrix is constant among subjects in these models in many situations however the correlation structure may differ among subjects and ignoring this heterogeneity can lead to biases in model parameters estimate recently lee et al developed a heterogeneous random effects covariance matrix for glmms for error free covariates covariates measured with error also happen frequently in the longitudinal data set up eg blood pressure and cholesterol level ignoring this issue in the data may produce bias in model parameters estimate and lead to wrong conclusions in this paper we propose an approach to properly model the random effects covariance matrix based on covariates in the class of glmms where we also have covariates measured with error the resulting parameters from the decomposition of random effects covariance matrix have a sensible interpretation and can be easily modeled without the concern of positive definiteness of the resulting estimator the performance of the proposed approach is evaluated through simulation studies which show that the proposed method performs very well in terms of bias mean squared error and coverage rate an application of the proposed method is also provided using a longitudinal data from manitoba follow up study

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

design of observer based robust stabilizing controllers abstract this paper is concerned with the problem of designing stabilizing control laws for linear systems with time varying uncertainty since the entire state cannot be measured the controller must operate on some estimate of the state the approach used is to first obtain a linear robust controller based on the assumption that the complete state is available then an estimated state is generated via an observer and this estimate used in the implementation of the controller examples indicate that the use of an observer usually reduces the magnitude of the tolerable uncertainty the amount of this reduction depends on the choice made for the measured state variables

irregular n2sls and lasso estimation of the matrix exponential spatial specification model abstract in this paper we consider estimation of the matrix exponential spatial specification model with the durbin and endogenous regressors we find that the nonlinear two stage least squares n2sls estimator is in general consistent and asymptotically normal however when the durbin and endogenous regressors are irrelevant the gradient vector of the n2sls criterion function has a singular covariance matrix with probability approaching one w p a 1 some components of the n2sls estimator have slower rates of convergence and their asymptotic distributions are nonstandard the distance difference and gradient test statistics which have irregular asymptotic distributions are derived to test for the irrelevance of the durbin and endogenous regressors as an alternative estimation and model selection approach we propose the adaptive group lasso which penalizes the coefficients of the durbin and endogenous explanatory variables we show that the estimator has the oracle properties so the true model can be selected w p a 1 and the estimator always has the n rate of convergence and asymptotic normal distribution we propose to select the tuning parameter for the adaptive group lasso by minimizing an information criterion

modelling the random effects covariance matrix in longitudinal data a common class of models for longitudinal data are random effects mixed models in these models the random effects covariance matrix is typically assumed constant across subject however in many situations this matrix may differ by measured covariates in this paper we propose an approach to model the random effects covariance matrix by using a special cholesky decomposition of the matrix in particular we will allow the parameters that result from this decomposition to depend on subject specific covariates and also explore ways to parsimoniously model these parameters an advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix in addition the parameters resulting from this decomposition have a sensible interpretation we propose fully bayesian modelling for which a simple gibbs sampler can be implemented to sample from the posterior distribution of the parameters we illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects

observer based robust controller design for a linear system with time varying perturbations abstract in this paper an observer based robust controller design problem for the linear uncertain system is considered where the uncertain system is subject to the norm bounded and the structured time varying uncertainties using the riccati approach full order and reduced order observers are obtained to reconstruct the unmeasurable states so that the robust stability of the uncertain system can be guaranteed with the state feedback control law

a joint modelling approach for longitudinal studies in longitudinal studies it is of fundamental importance to understand the dynamics in the mean function variance function and correlations of the repeated or clustered measurements for modelling the covariance structure cholesky type decomposition based approaches have been demonstrated to be effective however parsimonious approaches for directly revealing the correlation structure between longitudinal measurements remain less well explored and existing joint modelling approaches may encounter difficulty in interpreting the covariation structure we propose a novel joint mean variance correlation modelling approach for longitudinal studies by applying hyperspherical co ordinates we obtain an unconstrained parameterization for the correlation matrix that automatically guarantees its positive definiteness and we develop a regression approach to model the correlation matrix of the longitudinal measurements by exploiting the parameterization the modelling framework proposed is parsimonious interpretable and flexible for analysing longitudinal data extensive data examples and simulations support the effectiveness of the approach proposed

modelling covariance structure in bivariate marginal models for longitudinal data summary it can be more challenging to efficiently model the covariance matrices for multivariate longitudinal data than for the univariate case due to the correlations arising between multiple responses the positive definiteness constraint and the high dimensionality are further obstacles in covariance modelling in this paper we develop a data based method by which the parametersinthecovariancematricesarereplacedbyunconstrainedandinterpretableparameterswith reduced dimensions the maximum likelihood estimators for the mean and covariance parameters are shown to be consistent and asymptotically normally distributed simulations and real data analysis show that the new approach performs very well even when modelling bivariate nonstationary dependence structures

a new class of stabilizing controllers for uncertain dynamical systems this paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems the vector of uncertain parameters q cdot is time varying and its values q t lie within a prespecified bounding set q in r p furthermore no statistical description of q cdot is assumed and the controller is shown to render the closed loop system practically stable in a so called guaranteed sense that is the desired stability properties are assured no matter what admissible uncertainty q cdot is realized within the perspective of previous research in this area this paper contains one salient feature the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time invariant in contrast in much of the previous literature see for example 1 2 7 and 9 a linear system is stabilized via nonlinear control another feature of this paper is the fact that the

estimation of covariance matrix of multivariate longitudinal data using modified choleksky and hypersphere decompositions linear models are typically used to analyze multivariate longitudinal data with these models estimating the covariance matrix is not easy because the covariance matrix should account for complex correlated structures the correlation between responses at each time point the correlation within separate responses over time and the cross correlation between different responses at different times in addition the estimated covariance matrix should satisfy the positive definiteness condition and it may be heteroscedastic however in practice the structure of the covariance matrix is assumed to be homoscedastic and highly parsimonious such as exchangeable or autoregressive with order one these assumptions are too strong and result in inefficient estimates of the effects of covariates several studies have been conducted to solve these restrictions using modified cholesky decomposition mcd and linear covariance models however modeling the correlation between responses at each time point is not easy because there is no natural ordering of the responses in this paper we use mcd and hypersphere decomposition to model the complex correlation structures for multivariate longitudinal data we observe that the estimated covariance matrix using the decompositions is positive definite and can be heteroscedastic and that it is also interpretable the proposed methods are illustrated using data from a nonalcoholic fatty liver disease study

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

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

a nonparametric prior for simultaneous covariance estimation in the modeling of longitudinal data from several groups appropriate handling of the dependence structure is of central importance standard methods include specifying a single covariance matrix for all groups or independently estimating the covariance matrix for each group without regard to the others but when these model assumptions are incorrect these techniques can lead to biased mean effects or loss of efficiency respectively thus it is desirable to develop methods to simultaneously estimate the covariance matrix for each group that will borrow strength across groups in a way that is ultimately informed by the data in addition for several groups with covariance matrices of even medium dimension it is difficult to manually select a single best parametric model among the huge number of possibilities given by incorporating structural zeros and or commonality of individual parameters across groups in this paper we develop a family of nonparametric priors using the matrix stick breaking process of dunson et al 2008 that seeks to accomplish this task by parameterizing the covariance matrices in terms of the parameters of their modified cholesky decomposition pourahmadi 1999 we establish some theoretic properties of these priors examine their effectiveness via a simulation study and illustrate the priors using data from a longitudinal clinical trial

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

intrinsic regression models for positive definite matrices with applications to diffusion tensor imaging the aim of this paper is to develop an intrinsic regression model for the analysis of positive definite matrices as responses in a riemannian manifold and their association with a set of covariates such as age and gender in a euclidean space the primary motivation and application of the proposed methodology is in medical imaging because the set of positive definite matrices do not form a vector space directly applying classical multivariate regression may be inadequate in establishing the relationship between positive definite matrices and covariates of interest such as age and gender in real applications our intrinsic regression model which is a semiparametric model uses a link function to map from the euclidean space of covariates to the riemannian manifold of positive definite matrices we develop an estimation procedure to calculate parameter estimates and establish their limiting distributions we develop score statistics to test linear hypotheses on unknown parameters and develop a test pr

covariance regression analysis abstractthis article introduces covariance regression analysis for a p dimensional response vector the proposed method explores the regression relationship between the p dimensional covariance matrix and auxiliary information we study three types of estimators maximum likelihood ordinary least squares and feasible generalized least squares estimators then we demonstrate that these regression estimators are consistent and asymptotically normal furthermore we obtain the high dimensional and large sample properties of the corresponding covariance matrix estimators simulation experiments are presented to demonstrate the performance of both regression and covariance matrix estimates an example is analyzed from the chinese stock market to illustrate the usefulness of the proposed covariance regression model supplementary materials for this article are available online

group comparison of eigenvalues and eigenvectors of diffusion tensors diffusion tensor imaging dti data differ from most medical images in that values at each voxel are not scalars but 3 3 symmetric positive definite matrices called diffusion tensors dts the anatomic characteristics of the tissue at each voxel are reflected by the dt eigenvalues and eigenvectors in this article we consider the problem of testing whether the means of two groups of dt images are equal at each voxel in terms of the dt s eigenvalues eigenvectors or both because eigendecompositions are highly nonlinear existing likelihood ratio statistics lrts for testing differences in eigenvalues or eigenvectors of means of gaussian symmetric matrices assume an orthogonally invariant covariance structure between the matrix entries while retaining the form of the lrts we derive new approximations to their true distributions when the covariance between the dt entries is arbitrary and possibly different between the two groups the approximate distributions are those of similar lrt statistics comput