good filtrations and strong f regularity of the ring of u p invariants abstract let k be an algebraically closed field of positive characteristic g a reductive group over k and v a finite dimensional g module let p be a parabolic subgroup of g and u p its unipotent radical we prove that if s sym v has a good filtration then s u p is strongly f regular

estimation efficiency with omitted covariates in generalized linear models abstract although omitting covariates associated with the response in generalized linear models can yield seriously biased estimates of the effects of the included covariates in certain settings there is no bias this article considers the effect of omitted covariates on the efficiency of the estimated effects of the included covariates in these cases i consider the case where the omitted covariate is independent of the included covariates as in studies with randomized treatment assignment as well as the case where the omitted covariate is correlated with the included but not a confounder i present expressions to show that omitting covariates associated with the response and independent of the included covariate can result in serious efficiency losses for estimates of the effects of the included covariates i also present expressions to show that omitting nonconfounding covariates can lead to efficiency gains these expressions also quantify the magnitude of estimation efficiency with omitted covaria

asynchronous l 2 l filtering for discrete time stochastic markov jump systems with randomly occurred sensor nonlinearities this paper is concerned with the problem of asynchronous l 2 l filtering for discrete time stochastic markov jump systems with sensor nonlinearity the sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the bernoulli distribution a sufficient condition is first given such that the resultant filtering error system which is a kind of nonhomogeneous markov jump system is stochastically stable with a guaranteed l 2 l performance index then the existence criterion of the desired asynchronous filter with piecewise homogeneous markov chain is proposed in terms of a set of linear matrix inequalities a numerical example is given to show the effectiveness and potential of the developed theoretical results

inconsistent treatment estimates from mis specified logistic regression analyses of randomized trials when the difference between treatments in a clinical trial is estimated by a difference in means then it is well known that randomization ensures unbiassed estimation even if no account is taken of important baseline covariates however when the treatment effect is assessed by other summaries for example by an odds ratio if the outcome is binary then bias can arise if some covariates are omitted regardless of the use of randomization for treatment allocation or the size of the trial we present accurate closed form approximations for this asymptotic bias when important normally distributed covariates are omitted from a logistic regression we compare this approximation with ones in the literature and derive more convenient forms for some of these existing results the expressions give insight into the form of the bias which simulations show is usable for distributions other than the normal the key result applies even when there are additional binary covariates in the model

h sub 2 near optimal model reduction this note considers the problem of finding a stable reduced order model for a given stable model so that its h sub 2 model reduction cost differs by less than a prescribed error from the optimal cost which may or may not be achievable it is shown that this new version of the long standing h sub 2 optimal model reduction problem can be reduced to a well posed smooth constrained minimization problem whose global solution is guaranteed to exist in addition a globally convergent algorithm in the form of an ordinary differential equation is derived

testing model fit in longitudinal data analysis against alternatives with omitted covariates several types of common model misspecifications can be re formulated as problems of omitted covariates these include situations with unmeasured confounders measurement errors in observed covariates and informative censoring longitudinal data present special opportunities for detecting omitted covariates that are related to the observed ones differently across time than across individuals this situation arises with period and cohort effects as well as with usual formulations of classical measurement error in observed covariates in this article we focus on testing for the existence of omitted covariates in longitudinal data analysis when models are fit by generalized estimation equations when omitted covariates are present specification of the correct link function conditionally on only observed covariates under the alternative usually involves complicated numerical integration we propose a quasi score test statistic that avoids the need to fit such alternative models the statistic is asymptotically chi square distributed under the null hypothesis of no omitted covariates with degrees of freedom determined by the assumed alternative structure we study the significance level and the power of the quasi score test in linear and logistic regression models the test is then applied to an analysis of excessive daytime sleepiness

a note on fitting a marginal model to mixed effects log linear regression data via gee marginal generalized linear models for correlated data are often fit by generalized estimating equations liang k y and zeger s l 1986 biometrika 73 13 22 which requires the marginal expectation to be correctly specified while the covariance structure is allowed to be misspecified this note is concerned with the correct specification of the marginal mean for data from a mixed log linear regression model and the relationship between the true subject specific parameters and the true marginal parameters

uber bewertungen welche unter einer reduktiven gruppe invariant sind letg be a reductive group defined over an algebraically closed fieldk and letx be ag variety in this paper we studyg invariant valuationsv of the fieldk of rational functions onx these objects are fundamental for the theory of equivariant completions ofx letb be a borel subgroup andu the unipotent radical ofb it is proved thatv is uniquely determined by its restriction toku then we study the set of invariant valuations having some fixed restrictionv0 tokb ifv0 is geometric i e induced by a prime divisor then this set is a polyhedron in some vector space in characteristic zero we prove that this polyhedron is a simplicial cone and in fact the fundamental domain of finite reflection groupwx thus the classification of invariant valuations is almost reduced to the classification of valuations ofkb

convergent algorithms for frequency weighted l 2 model reduction abstract this paper is concerned with computing an l 2 optimal reduced order model for a given stable multivariable linear system in the presence of input and output frequency weightings by parametrizing a class of reduced order models in terms of an orthogonal projection and using manifold techniques as tools both continuous and iterative algorithms are derived and their convergence properties are established as an application we show that an l 2 optimal reduced order filter in the closed loop sense can be computed using these algorithms

the impact of covariate adjustment at randomization and analysis for binary outcomes understanding differences between superiority and noninferiority trials the question of when to adjust for important prognostic covariates often arises in the design of clinical trials and there remain various opinions on whether to adjust during both randomization and analysis at randomization alone or at analysis alone furthermore little is known about the impact of covariate adjustment in the context of noninferiority ni designs the current simulation based research explores this issue in the ni setting as compared with the typical superiority setting by assessing the differential impact on power type i error and bias in the treatment estimate as well as its standard error in the context of logistic regression under both simple and covariate adjusted permuted block randomization algorithms in both the superiority and ni settings failure to adjust for covariates that influence outcome in the analysis phase regardless of prior adjustment at randomization results in treatment estimates that are biased toward zero with standard errors that are deflated however as no treatment difference is approached under the null hypothesis in superiority and under the alternative in ni this results in decreased power and nominal or conservative deflated type i error in the context of superiority but inflated power and type i error under ni results from the simulation study suggest that regardless of the use of the covariate in randomization it is appropriate to adjust for important prognostic covariates in analysis as this yields nearly unbiased estimates of treatment as well as nominal type i error

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

matching conditional and marginal shapes in binary random intercept models using a bridge distribution function summary random effects logistic regression models are often used to model clustered binary response data regression parameters in these models have a conditional subject specific interpretation in that they quantify regression effects for each cluster very often the logistic functional shape conditional on the random effects does not carry over to the marginal scale thus parameters in these models usually do not have an explicit marginal population averaged interpretation we study a bridge distribution function for the random effect in the random intercept logistic regression model under this distributional assumption the marginal functional shape is still of logistic form and thus regression parameters have an explicit marginal interpretation the main advantage of this approach is that likelihood inference can be obtained for either marginal or conditional regression inference within a single model framework the generality of the results and some properties of the bridge distribution functions are discussed an example is used for illustration

reduction and reconstruction for symmetric ordinary differential equations we discuss the reduction and reconstruction problem for ordinary differential equations that admit a linear symmetry group the goal is to prove that modulo reduction there remain only linear differential equations and to construct these explicitly extending previous work on one parameter groups we show this for certain unipotent and solvable groups and for all semisimple groups some applications to relative equilibria are given

a geometric approach to assess bias due to omitted covariates in generalized linear models summary misspecifying generalized linear models by omitting covariates associated with the response can result in seriously biased estimates of the effects of the included covariates for certain models such bias can occur even when the omitted covariate is independent of the included covariates as in studies with randomized treatment assignment this paper presents a geometric approach to assess the direction of the bias resulting from omitted covariates and develop intuition about the effects of omitted covariates we show that the direction of the bias depends simply on geometric properties of the link function we present an expression for the magnitude of the bias and the results of simulations which corroborate these findings we also consider an extension of the methods to assess the effects of omitted covariates which are correlated with those included generalized linear models are frequently used in situations where the model has been incompletely specified due to the omission of important covariates for example in observational studies important covariates may be omitted from the regression model due to either an incorrect conceptual understanding of the phenomenon under study or an inability to collect data on all the relevant factors related to the outcome under study in experimental studies involving randomization covariates may also be omitted in the latter situation one may feel that model misspecification due to omitted covariates should not alter estimates of treatment effect since the omitted covariates are independent of treatment assignment although this is true for the linear regression model the classic example of collapsing 2 x 2 tables shows that incorrectly specifying logistic regression models by omitting covariates associated with the binary response can result in seriously attenuated estimates of the regression coefficients even when the omitted covariate is independent of the included covariates suppose that y is a binary outcome x and z are binary covariates and that the true model for the probability of response is given by

optimal time weighted h 2 model reduction for markovian jump systems this article addresses the optimal time weighted h 2 model reduction problem for markovian jump linear systems that is for a given mean square stable markovian jump system our aim is to find a mean square stable jump system of lower order such that the time weighted h 2 norm of the corresponding error system is minimised the time weighted h 2 norm of the system is first defined and then a computational method is constructed the computation requires the solution of two sets of recursive lyapunov type linear matrix equations associated with the markovian jump system to solve the optimal time weighted h 2 model reduction problem we propose a gradient flow method for its solution a necessary condition for minimality is derived and a computational procedure is provided to obtain the minimising reduced order model the necessary condition generalises the standard result for systems when markov jumps and the time weighting term do not appear finally two numerical examples are given to demonstrate the

reduced order models with delay the paper considers the problem of h 2 optimal approximation of a high order system by a low order system with delay an algorithm to solve this problem is presented it consists of optimization with respect to the delay only where the rational part of the model and the quadratic cost are given by a solution of an equivalent order reduction problem without delay it is shown by means of an example that introduction of delay into the model leads in certain cases to considerable improvement in the approximation the results are extended to multiple input multiple output systems and also to frequency weighted order reduction

robust h_ infty fuzzy control approach for a class of markovian jump nonlinear systems this paper addresses the problem of stabilizing a class of nonlinear systems subject to markovian jump parameters using a robust stochastic fuzzy controller with hinfin performance the class of jump nonlinear systems considered is described by a fuzzy model composed of two levels a crisp level which represents the jumps and a fuzzy level which represents the system nonlinearities considering the approximation error between the fuzzy model and the jump nonlinear system as norm bounded uncertainties we develop a systematic technique based on a coupled lyapunov function to obtain a robust stochastic fuzzy controller which guarantees the l2 gain of the closed loop system in respect to external inputs to be equal to or less than a prescribed value a simulation example on an industrial power plant operating in a cogeneration scheme is presented to illustrate the effectiveness of the proposed stabilizing controller in reducing oscillations as well as maintaining a desired operation condition in the presence of fluctuations in the local load

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

the optimal projection equations for model reduction and the relationships among the methods of wilson skelton and moore first order necessary conditions for quadratically optimal reduced order modeling of linear time invariant systems are derived in the form of a pair of modified lyapunov equations coupled by an oblique projection which determines the optimal reduced order model this form of the necessary conditions considerably simplifies previous results of wilson 1 and clearly demonstrates the quadratic extremality and nonoptimality of the balancing method of moore 2 the possible existence of multiple solutions of the optimal projection equations is demonstrated and a relaxation type algorithm is proposed for computing these local extrema a component cost analysis of the model error criterion similar to the approach of skelton 3 is utilized at each iteration to direct the algorithm to the global minimum

an approximate approach to h sup 2 optimal model reduction deals with the problem of computing an h sub 2 optimal reduced order model for a given stable multivariable linear system by way of orthogonal projection the problem is formulated as that of minimizing the h sub 2 model reduction cost over the stiefel manifold so that the stability constraint on reduced order models is automatically satisfied and thus totally avoided in the new problem formulation the closed form expression for the gradient of the cost over the manifold is derived from which a gradient flow results as an ordinary differential equation ode a number of nice properties about such a flow are established furthermore two explicit iterative convergent algorithms are developed from the flow one has a constant step size and the other has a varying step size and is much more efficient both of them inherit the properties that the iterates remain on the manifold starting from any orthogonal initial point and that the model reduction cost is decreasing to minima along the iterates a procedure for closing the gap between the original and modified problem is proposed in the symmetric case the two problems are shown to be equivalent numerical examples are presented to illustrate the effectiveness of the proposed algorithms as well as convergence

a note on the bias due to omitted confounders in observational studies some confounders may be unknown and therefore omitted from the analysis while others are adjusted for approximations to the functions defining the relationship between the parameters in the full and reduced models are proposed leading to asymptotic bias estimates numerical calculations for logistic and poisson regression models show good agreement between asymptotic and simulation bias a data set containing the relationship between low birth weight and smoking hosmer lemeshow 1989 is used as an illustration

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

a general approach to evaluating the bias of 2 stage instrumental variable estimators unmeasured confounding is a common concern when researchers attempt to estimate a treatment effect using observational data or randomized studies with nonperfect compliance to address this concern instrumental variable methods such as 2 stage predictor substitution 2sps and 2 stage residual inclusion 2sri have been widely adopted in many clinical studies of binary and survival outcomes 2sri has been accepted as the method of choice over 2sps but a compelling theoretical rationale has not been postulated we evaluate the bias and consistency in estimating the conditional treatment effect for both 2sps and 2sri when the outcome is binary count or time to event we demonstrate analytically that the bias in 2sps and 2sri estimators can be reframed to mirror the problem of omitted variables in nonlinear models and that there is a direct relationship with the collapsibility of effect measures in contrast to conclusions made by previous studies terza et al 2008 we demonstrate that the consistency of 2sri estimators only holds under the following conditions 1 when the null hypothesis is true 2 when the outcome model is collapsible or 3 when estimating the nonnull causal effect from cox or logistic regression models the strong and unrealistic assumption that the effect of the unmeasured covariates on the treatment is proportional to their effect on the outcome needs to hold we propose a novel dissimilarity metric to provide an intuitive explanation of the bias of 2sri estimators in noncollapsible models and demonstrate that with increasing dissimilarity between the effects of the unmeasured covariates on the treatment versus outcome the bias of 2sri increases in magnitude

closure of the class of binary generalized linear models in some non standard settings summary this paper considers fitting generalized linear models to binary data in non standard settings such as case control samples studies with misclassified responses and misspecified models we develop simple methods for fitting models to case control data and show that a closure property holds for generalized linear models in the non standard settings i e if the responses follow a generalized linear model in the population of interest then so will the observed response in the non standard setting but with a modified link function these results imply that we can analyse data and study problems in the non standard settings by using classical generalized linear model methods such as the iteratively reweighted least squares algorithm example data illustrate the results

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

a cohomological characterization of parabolic subgroups of reductive algebraic groups let g be an algebraic group defined over an algebraically closed field k and rat g the category of rational g modules for any closed subgroup h of g and any rational h module v let v ig denote the rational g module induced from i the induction functor ig rat h rat g is left exact and we denote its derived functors by l j for n o 1 2 of course these derived functors are 0 for n 2 1 whenever 1 g is exact and by a result of cline parshall and scott 3 this happens precisely when g h is an afftne variety so the case of an afftne quotient is characterized by the vanishing of the higher derived functors in a like vein in this paper we will attempt to find a property of these functors which characterizes the case of a projective quotient since by definition g h is projective iff h p is a parabolic subgroup of g we are in effect looking for a cohomological characterization of parabolic subgroups of g the property of the functors l j we consider is a certain finiteness condition explained below the author was originally led to consider this question in 14 where induction from certain nonparabolic subgroups is studied and is shown to have this finiteness property it is well known that for every rational h module v there is an induced bundle l on g h with rank equal to dim i such that l j v identifies naturally with the sheaf cohomology group h g h l see 4 for details thus we may apply standard results from algebraic geometry to obtain some basic facts for example lg g 0 for n dim g h and serre s theorem gives the easy half of the result of cline parshall and scott men

effect of omitted confounders on the analysis of correlated binary data summary marginal analysis using the generalized estimating equation approach is widely applied to correlated observations as occur in studies with clusters and in longitudinal follow up of individuals in this article we investigate the effect of confounding in such models we assume that a risk factor x and a confounder z are related by a generalized linear model to the outcome y which can be binary or ordinal in order to investigate confounding arising from the omission of z a joint structure for x and z must be specified modeling normally distributed x z as sums of between and within individual or cluster components allows us to incorporate different degrees of betweenand within individual correlation such a structure includes as special cases cohort and period effects in longitudinal settings and random intercept models the latter situation corresponds to allowing z to vary only on the between individual or cluster level and to be uncorrelated with x and leads to attenuation of the coefficient of x in marginal models with the logit and probit links more complex situations occur when z is allowed to also vary on the within individual or cluster level and when z is correlated with x we examine the model specification and the expected bias when fitting a marginal model in the presence of the omitted confounder z we derive general formulas and interpret the parameters and results in an ongoing cohort study testing for omitted covariates is also discussed

h model reduction of markovian jump linear systems abstract in this paper the h model reduction problem for linear systems that possess randomly jumping parameters is studied the development includes both the continuous and discrete cases it is shown that the reduced order models exist if a set of matrix inequalities is feasible an effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the model reduction solutions using the numerical solutions of the matrix inequalities the reduced order models can be obtained an example is given to illustrate the proposed model reduction method

jump linear quadratic regulator with controlled jump rates deals with the class of continuous time linear systems with markovian jumps we assume that jump rates are controlled our purpose is to study the jump linear quadratic jlq regulator of the class of systems the structure of the optimal controller is established for a one dimensional 1 d system an algorithm for solving the corresponding set of coupled riccati equations of this optimal control problem is provided two numerical examples are given to show the usefulness of our results

a note on comparing the estimates of models for cluster correlated or longitudinal data with binary or ordinal outcomes when using linear models for cluster correlated or longitudinal data a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps new predictors might be added to the model or a more complex covariance structure might be specified for the observations when fitting models for binary or ordered categorical outcomes however comparisons between such models are impeded by the implicit rescaling of the model estimates that takes place with the inclusion of new predictors and or random effects this paper presents an approach for putting the estimates on a common scale to facilitate relative comparisons between models fit to binary or ordinal outcomes the approach is developed for both population average and unit specific models

analysis and synthesis of markov jump linear systems with time varying delays and partially known transition probabilities in this note the stability analysis and stabilization problems for a class of discrete time markov jump linear systems with partially known transition probabilities and time varying delays are investigated the time delay is considered to be time varying and has a lower and upper bounds the transition probabilities of the mode jumps are considered to be partially known which relax the traditional assumption in markov jump systems that all of them must be completely known a priori following the recent study on the class of systems a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality lmi formulation and the design of the stabilizing controller is further given a numerical example is used to illustrate the developed theory

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

brief continuous time state feedback h2 control of markovian jump linear systems via convex analysis continuous time h 2 control problem for the class of linear systems with markovian jumps mjls using convex analysis is considered in this paper the definition of the h 2 norm for continuous time mjls is presented and related to the appropriate observability and controllability gramians a convex programming formulation for the h 2 control problem of mjls is developed that enables us to tackle the optimization problem of mjls under the assumption that the transition rate matrix p p i j for the markov chain may not be exactly known but belongs to an appropriate convex set an equivalence between the convex formulation when p is exactly known and the usual dynamic programming approach of quadratic optimal control of mjls is established it is shown that there exists a solution for the convex programming problem if and only if there exists the mean square stabilizing solution for a set of coupled algebraic riccati equations these results are compared with other related works in the current literature

ℋ model reduction for linear parameter varying systems with distributed delay this paper is concerned with the model reduction for linear parameter varying lpv systems with both discrete and distributed delays for a given stable system our attention is focused on the construction of reduced order models which approximate the original system well in an norm sense first a sufficient condition is proposed for the asymptotic stability with an performance of the error system by using the parameter dependent lyapunov functional method then the decoupling technique is applied such that there does not exist any product term between the lyapunov matrices and the system matrices in the parametrised linear matrix inequality plmi constraints thus a new sufficient condition is obtained based on the new condition two different approaches are developed to solve the model reduction problem one is the convex linearisation approach and the other is the projection approach finally a numerical example is provided to demonstrate the effectiveness of the proposed design method

classification of four dimensional estimation algebras of central importance in nonlinear filtering theory is the classification of finite dimensional estimation algebras through which we can construct recursive filters we classify all t dimensional estimation algebras t spl les 4 for arbitrary state space dimension

on h2 model reduction of bilinear systems the h 2 model reduction problem for continuous time bilinear systems is studied in this paper by defining the h 2 norm of bilinear systems in terms of the state space matrices the h 2 model reduction error is computed via the reachability or observability gramian necessary conditions for the reduced order bilinear models to be h 2 optimal are given the gradient flow approach is used to obtain the solution of the h 2 model reduction problem the formulation allows certain properties of the original models to be preserved in the reduced order models the model reduction procedure developed can also be applied to finite dimensional linear time invariant systems a numerical example is employed to illustrate the effectiveness of the proposed method

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

fault detection for discrete time markov jump linear systems with partially known transition probabilities in this article the fault detection fd problem for a class of discrete time markov jump linear system mjls with partially known transition probabilities is investigated the proposed systems are more general which relax the traditional assumption in markov jump systems that all the transition probabilities must be completely known a residual generator is constructed and the corresponding fd is formulated as an h filtering problem by which the error between residual and fault are minimised in the h sense the linear matrix inequality based sufficient conditions for the existence of fd filter are derived a numerical example on a multiplier accelerator model economic system is given to illustrate the potential of the developed theoretical results

a gradient flow approach to decentralized output feedback optimal control this paper visits the quadratic optimal control problem of decentralised control systems via static output feedback a gradient flow approach is introduced as a tool to compute the optimal output feedback gain several nice properties are revealed concerning the convergence of the gain matrix along the trajectory of an ordinary differential equation obtained from the gradient of objective cost i e the objective cost is decreasing along this trajectory if the equilibrium points are isolated the convergence can be guaranteed a simulation example is given to illustrate the effectiveness of this approach

algebraic hamiltonian actions in this paper we deal with a hamiltonian action of a reductive algebraic group g on an irreducible normal affine poisson variety x we study the quotient morphism mu g x g x g rightarrow mathfrak g g of the moment map mu g x x rightarrow mathfrak g we prove that for a wide class of hamiltonian actions including for example actions on generically symplectic varieties all fibers of the morphism g x g have the same dimension we also study the stein factorization of g x g namely let c g x denote the spectrum of the integral closure of mu g x mathbb k mathfrak g g in mathbb k x g we investigate the structure of the mathfrak g g scheme c g x our results partially generalize those obtained by f knop for the actions on cotangent bundles and symplectic vector spaces

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

bias and efficiency loss due to misclassified responses in binary regression summary methods that ignore errors in binary responses yield biased estimators of the associations of covariates with response this paper derives general expressions for the magnitude of the bias due to errors in the response and shows that unless both the sensitivity and specificity are very high ignoring errors in the responses will yield highly biased covariate effect estimators when the true error free response follows a generalised linear model and misclassification probabilities are known and independent of covariate values responses observed with error also follow such a model with a modified link function we describe a simple method to obtain consistent estimators of covariate effects and associated errors in this case and derive an expression for the asymptotic relative efficiency of covariate effect estimators from the correct likelihood for the responses with errors with respect to estimates based on the true error free responses this expression shows that errors in the response can lead to substantial losses of information about covariate effects data from a study on infection with human papilloma virus among women and simulation studies motivate this work and illustrate the findings

brief a gradient flow approach to on line robust pole assignment for synthesizing output feedback control systems pole assignment is a basic design method for synthesis of feedback control systems in this paper a gradient flow approach is presented for robust pole assignment in synthesizing output feedback control systems the proposed approach is shown to be capable of synthesizing linear output feedback control systems via on line robust pole assignment convergence of the gradient flow can be guaranteed moreover with appropriate design parameters the gradient flow converges exponentially to an optimal solution to the robust pole assignment problem and the closed loop control system based on the gradient flow is globally exponentially stable these desired properties make it possible to apply the proposed approach to slowly time varying linear control systems simulation results are shown to demonstrate the effectiveness and advantages of the proposed approach