decay rate dependent conditions for exponential stability of stochastic neutral systems with markovian jumping parameters abstract this note studies the problem of decay rate dependent exponential stability for neutral stochastic delay systems with markovian jumping parameters first by introducing an operator d x t i as well as a novel lyapunov krasovskii functional sufficient conditions for exponential stability of system with a decay rate are obtained second the results are extended to the robust exponential estimates for uncertain neutral stochastic delay systems with markovian jumping parameters finally numerical examples are provided to show the effectiveness of the proposed results

regression models for longitudinal binary responses with informative drop outs this paper reviews both likelihood based and non likelihood generalized estimating equations regression models for longitudinal binary responses when there are drop outs throughout it is assumed that the regression parameters for the marginal expectations of the binary responses are of primary scientific interest the association or time dependence between the responses is largely regarded as a nuisance characteristic of the data the performance of the methods is compared in terms of asymptotic bias under mis specification of the association between the responses and the missing data mechanism or drop out process

the generalized estimating equation approach when data are not missing completely at random abstract we propose two methods for handling missing data in generalized estimating equation gee analyses mean imputation and multiple imputation each provides valid gee estimates when data are missing at random missing outcomes are imputed sequentially starting from the outcome nearest in time to the observed outcome the estimators from the two kinds of imputation are compared with the weighting method of robins et al we show that multiple imputation with an infinite number of replications is asymptotically equivalent to mean imputation the methods are applied to a stroke study in which neurological outcomes are measured over time after stroke but some outcomes are missing due to death or loss to follow up

estimation and comparison of changes in the presence of information right censoring by modeling the censoring process abstract in estimating and comparing the rates of change of a continuous variable between two groups the unweighted averages of individual simple least squares estimates from each group are often used under a linear random effects model when all individuals have completed observations at identical time points these statistics are maximum likelihood estimates for the expected rates of change however with censored of missing data these estimates are no longer efficient when compared to generalized least squares estimates when in addition the right censoring process is dependent upon the individual rates of change i e informative right censoring the generalized least squares estimates will be biased likelihood ratio test for informativeness of the censoring process and maximum likelihood estimates for the expected rates of change and the parameters of the right censoring process are developed under a linear random effect models with a probit model for the right censoring process in realistic situations we illustrate that the bias in estimating group rate of change and the reduction of power in comparing group difference could be substantial when strong dependency of the right censoring process on individual rates of change is ignored author

quadratic stability and stabilization of uncertain linear discrete time systems with state delay abstract this paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete time systems with state delay the system under consideration involves state time delay and time varying norm bounded parameter uncertainties appearing in all the matrices of the state space model necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities respectively a robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities two examples are presented to demonstrate the effectiveness of the proposed approach

spherical harmonic analysis on affine buildings let be a locally finite regular affine building with root system r there is a commutative algebra spanned by averaging operators a p acting on the space of all functions f v p where v p is in most cases the set of all special vertices of and p is a set of dominant coweights of r this algebra is studied in 6 and 7 for a n buildings and the general case is treated in 15 in this paper we show that all algebra homomorphisms h may be expressed in terms of the macdonald spherical functions we also provide a second formula for these homomorphisms in terms of an integral over the boundary of we may regard as a subalgebra of the c algebra of bounded linear operators on l2 v p and we write for the closure of in this algebra we study the gelfand map where m2 and we compute m2 and the plancherel measure of we also compute the l2 operator norms of the operators a p in terms of the macdonald spherical functions

multiple imputation in mixture models for nonignorable nonresponse with follow ups abstract one approach to inference for means or linear regression parameters when the outcome is subject to nonignorable nonresponse is mixture modeling mixture models assume separate parameters for respondents and nonrespondents implementation by multiple imputation consists of repeatedly filling in missing values for nonrespondents estimating parameters using the filled in data and then adjusting for variability between imputations we evaluated the performance of this scheme using simulated data with a 25 sample of nonrespondents followed up we conclude that it provides a generally satisfactory and robust approach to inference for means and regression parameters in this case although a greater number of imputations may be required for good performance compared to the number required for estimation when nonresponse is ignorable

regression analysis with missing covariate data using estimating equations in regression analysis missing covariate data has been among the most common problems frequently practitioners adopt the so called complete case analysis i e performing the analysis on only a complete dataset after excluding records with missing covariates performing a complete case analysis is convenient with existing statistical packages but it may be inefficient since the observed outcomes and covariates on those records with missing covariates are not used it can even give misleading statistical inference if missing is not completely at random this paper introduces a joint estimating equation jee for regression analysis in the presence of missing observations on one covariate which may be thought of as a method in a general framework for the missing covariate data problem proposed by robins rotnitzky and zhao 1994 journal of the american statistical association 89 846 866 a generalization of jee to more than one such covariate is discussed the jee is generally applicable to estimating regression coefficients from a regression model including linear and logistic regression provided that the missing covariate data is either missing completely at random or missing at random in addition to mild regularity conditions estimates of regression coefficients from the jee are consistent and have an asymptotic normal distribution simulation results show that the asymptotic distribution of estimated coefficients performs well in finite samples also shown through the simulation study is that the validity of jee estimates depends on the correct specification of the probability function that characterizes the missing mechanism suggesting a need for further research on how to robustify the estimation from making this nuisance assumption finally the jee is illustrated with an application from a case control study of diet and thyroid cancer

on an estimate of the decay rate for stable linear delay systems in this paper it is shown that for a certain class of stable linear delay systems we can obtain an estimate of the decay rate of the solution by a simple computation

robust exponential stability of uncertain systems with time varying delays focuses on the problem of robust exponential stability of a class of uncertain systems described by functional differential equations with time varying delays the uncertainties are assumed to be continuous time varying nonlinear and norm bounded sufficient conditions for robust exponential stability are given for both single and multiple delays cases

adjusting for nonignorable drop out using semiparametric nonresponse models abstract consider a study whose design calls for the study subjects to be followed from enrollment time t 0 to time t t at which point a primary endpoint of interest y is to be measured the design of the study also calls for measurements on a vector v t of covariates to be made at one or more times t during the interval 0 t we are interested in making inferences about the marginal mean 0 of y when some subjects drop out of the study at random times q prior to the common fixed end of follow up time t the purpose of this article is to show how to make inferences about 0 when the continuous drop out time q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables in particular we consider two models for the conditional hazard of drop out given v t y where v t denotes the history of the process v t through time t t 0 t in the first model we assume that q t v t y exp 0 y where 0 is a scalar paramet

regression analysis for categorical variables with outcome subject to nonignorable nonresponse abstract we develop a log linear model for categorical response subject to nonignorable nonresponse the paper differs from fay 1986 in its focus on estimation and hypothesis testing in a regression setting as opposed to imputation in a multivariate setting we present several new results concerning the existence of solutions on the boundary of the parameter space and the construction of confidence intervals for estimates we illustrate the method by estimating the proportion of voters preferring truman in a 1948 preelection poll mosteller hyman mccarthy marks and truman 1949 results may depend strongly on the model assumed for nonresponse goodness of fit tests are available for comparing alternative models

solution estimates for linear differential equations with delay abstract in this paper we give explicit exponential estimates x t m e t t 0 where t t0 m 0 for solutions of a linear scalar delay differential equation x t k 1 m b k t x h k t f t t t 0 x t t t t 0 we consider two different cases when 0 corresponding to exponential stability and the case of in the first case together with the exponential estimate we also obtain an exponential stability test in the second case we get estimation for solution growth here both the coefficients and the delays are measurable not necessarily continuous

new exponential estimates for time delay systems this note considers the problem of exponential stability for time delay systems in terms of linear matrix inequalities a new sufficient condition for exponential stability is obtained based on this an improved upper bound of the decay rate can be easily calculated when time varying norm bounded parameter uncertainties appear a new sufficient condition for robust exponential stability of uncertain time delay systems is also provided the reduced conservatism of the proposed conditions is illustrated via two numerical examples

multiple imputation methods for the missing covariates in generalized estimating equation this paper discusses the missing covariates problem in the generalized estimating equation gee model estimates by various multiple imputation techniques mi are examined and compared to the sample average imputation method sa through simulations and an example the simulation results show that under the correct model specification the mi estimators have negligible bias and have fairly similar efficiencies as the sa estimator a practical advantage of the mi estimates is that the standard errors can be more easily computed than the sa estimates

exponential estimates for retarded time delay systems an lmi approach exponential estimates and sufficient conditions for the exponential stability of linear time delay systems are given the proof make use of lyapunov krasovskii functionals and the conditions are expressed in terms of linear matrix inequalities

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

inference from nonrandomly missing categorical data an example from a genetic study on turner s syndrome abstract the process leading to partial classification with categorical data is sometimes nonrandom a particular model accounting for incomplete data which allows the probability of uncertain classification to depend on category identity is utilized for an analysis of data obtained from a genetic study on turner s syndrome estimates of population proportions are obtained from maximum likelihood a method for handling nonrandomly missing data arrayed in contingency tables is discussed sensitivity analyses incorporating parameters related to the missing data mechanism are recommended for estimation and testing

semiparametric regression for repeated outcomes with nonignorable nonresponse abstract we consider inference about the parameter indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values that is nonresponse is nonignorable we propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal can for estimating when the response probabilities can be parametrically modeled and a can estimator exists the proposed estimators do not require full specification of a parametric likelihood and their computation does not require numerical integration our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse we show that our class essentially consists of all can estimators of we also show that the asymptotic variance of the optimal estimator in our

analysis of semi parametric regression models with non ignorable non response in this article we consider the problem of making inferences about the parameter 0 indexing the conditional mean of an outcome given a vector of regressors when a subset of the variables outcome or covariates are missing for some study subjects and the probability of non response depends upon both observed and unobserved data values that is non response is non ignorable we propose a new class of inverse probability of censoring weighted estimators that are consistent and asymptotically normal can for estimating 0 when the non response probabilities can be parametrically modelled and a can estimator exists the proposed estimators do not require full specification of the likelihood and their computation does not require numerical integration we show that the asymptotic variance of the optimal estimator in our class attains the semi parametric variance bound for the model in some models no can estimator of 0 exists we provide a general algorithm for determining when can estimators of 0 exist our results follow after specializing a general representation described in the article for the efficient score and the influence function of regular asymptotically linear estimators in an arbitrary semi parametric model with non ignorable non response in which the probability of observing complete data is bounded away from zero and the non response probabilities can be parametrically modelled 1997 by john wiley sons ltd

bivariate binary data analysis with nonignorably missing outcomes one of the objectives in the northern manhattan stroke study is to investigate the impact of stroke subtype on the functional status 2 years after the first ischemic stroke a challenge in this analysis is that the functional status at 2 years after stroke is not completely observed in this paper we propose a method to handle nonignorably missing binary functional status when the baseline value and the covariates are completely observed the proposed method consists of fitting four separate binary regression models for the baseline outcome the outcome 2 years after the stroke the product of the previous two and finally the missingness indicator we then conduct a sensitivity analysis by varying the assumptions about the third and the fourth binary regression models our method belongs to an imputation paradigm and can be an alternative to the weighting method of rotnitzky and robins 1997 statistics in medicine 16 81 102 a jackknife variance estimate is proposed for the variance of the resulting estimate the proposed analysis can be implemented using statistical software such as sas

delay dependent robust h sub spl infin and l sub 2 l sub spl infin filtering for a class of uncertain nonlinear time delay systems this note presents delay dependent robust h sub spl infin and l sub 2 l sub spl infin filter designs for a class of nonlinear systems with multiple time varying delays in the state and parameter uncertainties residing in a polytope the nonlinearities are assumed to satisfy global lipschitz conditions attention is focused on the design of robust full order and reduced order filters guaranteeing a prescribed noise attenuation level in an h sub spl infin or l sub 2 l sub spl infin sense the admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms

on computing the maximal delay intervals for stability of linear delay systems this note is concerned with stability properties of linear time invariant delay systems the authors consider delay systems of both retarded and neutral types expressed in state space forms the author s main goal is to provide a computation oriented method for computing the maximal delay intervals over which the systems under consideration maintain stability the author s results show that this can be accomplished by computing the generalized eigenvalues of certain frequency dependent matrices based on these results the author also states a necessary and sufficient condition concerning stability independent of delay for each of the retarded and neutral systems the author s results can be readily implemented and appear suitable for analyzing systems with high dimensions and many delay units

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

memoryless h controller design for switched non linear systems with mixed time varying delays this article deals with the h control problem for a class of switched non linear systems with mixed time varying delays the novel features here are that the system in consideration is non linear perturbation with discrete and distributed delays the time varying delay is also involved in the observation output and the controllers to be designed satisfy some exponential stability constraints on the closed loop poles by using lyapunov razumikhin functional approach new sufficient conditions for the h control with exponential stability constraint are derived in terms of the solution of riccati type equations the approach allows for simultaneous computation of the two bounds that characterise the stability rate of the solution

robust stabilization of uncertain t s fuzzy time delay systems with exponential estimates this paper deals with the problem of robust stabilization for uncertain takagi sugeno t s fuzzy systems with constant time delays the purpose is to design a state feedback fuzzy controller such that the closed loop system is robustly exponentially stable with a prescribed decay rate sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities lmis by using feasible solutions of these lmis desired fuzzy controllers are designed and their corresponding exponential estimates are given in addition the main results of this paper are explicitly dependent on the decay rate this enables one to design fuzzy controllers by freely selecting decay rates according to different practical conditions two numerical examples are provided finally to demonstrate the effectiveness of the proposed design methods

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays this paper is concerned with exponential estimates and stabilization for a class of uncertain singular systems with discrete and distributed delays a sufficient condition which does not only guarantee the exponential stability and admissibility but also gives the estimates of decay rate and decay coefficient is established in terms of the linear matrix inequality lmi technique and a new lyapunov krasovskii functional the estimating procedure is implemented by solving a set of lmis which can be checked easily by effective algorithms under the proposed condition the algebraic subsystems possess the same decay rate as the differential ones moreover a state feedback stabilizing controller which makes the closed loop system exponentially stable and admissible with a prescribed lower bound of the decay rate is designed numerical examples are provided to illustrate the effectiveness of the theoretical results

exponential stability of time delay systems via new weighted integral inequalities in this paper new weighted integral inequalities wiis are first derived based on jensen s integral inequalities in single and double forms it is theoretically shown that the newly derived inequalities in this paper encompass both the jensen inequality and its most recent improvement based on wirtinger s integral inequality the potential capability of wiis is demonstrated through applications to exponential stability analysis of some classes of time delay systems in the framework of linear matrix inequalities lmis the effectiveness and least conservativeness of the derived stability conditions using wiis are shown by various numerical examples

asymptotic and exponential stability of uncertain system with interval delay abstract this paper considers the problem of asymptotic and exponential stability analysis of the continuous system with interval time varying delay and uncertainties by constructing a new lyapunov krasovskii functional several delay range dependent conditions are derived in terms of the linear matrix inequalities lmis two novel integral equalities are employed to overcome the disadvantages of the methods in existing references the merits of the proposed criteria lie in the exponential stability being a free value and the less conservativeness finally some numerical examples are included to illustrate the effectiveness and the improvement of the proposed method

effect of dropouts in a longitudinal study an application of a repeated ordinal model an analysis is presented of a longitudinal study of fluvoxamine an antidepressant drug with ordinal responses regressed on a combination of discrete and continuous covariates and with a substantial proportion of dropouts classical methods such as weighted least squares sas procedure catmod and logistic regression are not suitable for the analysis of such data instead we illustrate how a recently introduced model can be used to solve most of the problems posed the method is likelihood based and is an extension of the bivariate dale model to an arbitrary number of outcomes the method is suitable for several types of designs commonly employed in clinical trials

a delay dependent approach to robust h sub spl infin filtering for uncertain discrete time state delayed systems a delay dependent approach to robust h sub spl infin filtering is proposed for linear discrete time uncertain systems with multiple delays in the state the uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed h sub spl infin noise attenuation level the proposed filter design methodology incorporates some recently appeared results such as moon s new version of the upper bound for the inner product of two vectors and de oliveira s idea of parameter dependent stability which greatly reduce the overdesign introduced in the derivation process in addition to the full order filtering problem the challenging reduced order case is also addressed by using different linearization procedures both full and reduced order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies

h spl infin output feedback controller design for linear systems with time varying delayed state this paper considers the h spl infin controller design problem for linear systems with time varying delays in states the authors obtain sufficient conditions for the existence of h spl infin controllers in terms of three linear matrix inequalities lmis these sufficient conditions are dependent on the maximum value of the time derivative of time varying delay furthermore they briefly explain how to construct such controllers from the positive definite solutions of their lmis and give an example

the analysis of longitudinal ordinal data with nonrandom drop out a model is proposed for longitudinal ordinal data with nonrandom drop out which combines the multivariate dale model for longitudinal ordinal data with a logistic regression model for drop out since response and drop out are modelled as conditionally independent given complete data the resulting likelihood can be maximised relatively simply using the em algorithm which with acceleration is acceptably fast and with appropriate additions can produce estimates of precision the approach is illustrated with an example such modelling of nonrandom drop out requires caution because the interpretation of the fitted models depends on assumptions that are unexaminable in a fundamental sense and the conclusions cannot be regarded as necessarily robust the main role of such modelling may be as a component of a sensitivity analysis

comments on on an estimate of the delay rate for stable linear delay systems it is shown that an estimate of the decay rate of a class of stable linear delay systems can be obtained without solving the transcendental equation and is in addition less restrictive than that given by mori et al 1982

analysis of longitudinal binary data from multiphase sampling the efficient use of surrogate or auxiliary information has been investigated within both model based and design based approaches to data analysis particularly in the context of missing data here we consider the use of such data in epidemiological studies of disease incidence in which surrogate measures of disease status are available for all subjects at two time points but definitive diagnoses are available only in stratified subsamples we briefly review methods for the analysis of two phase studies of disease prevalence at a single time point and we discuss the extension of four of these methods to the analysis of incidence studies their performance is compared with special reference to a study of the incidence of senile dementia

jackknife estimators of variance for parameter estimates from estimating equations with applications to clustered survival data an estimate of a parameter vector beta is often obtained by setting a score vector equal to zero and solving for beta estimating equations of this type include maximum likelihood quasi likelihood mccullagh 1983 annals of statistics 11 59 67 and generalized estimating equations liang and zeger 1986 biometrika 73 13 22 white 1982 econometrica 50 1 26 proposed a variance estimator for beta that is robust to model misspecification we show that a one step jackknife estimator of variance is asymptotically equivalent to the variance estimator proposed by white the one step variance estimator may be preferred when the appropriate computer packages are not available to compute white s estimator directly this jackknife estimator is very useful in our example with clustered survival data

a mean score method for missing and auxiliary covariate data in regression models summary we consider regression analysis when incomplete or auxiliary covariate data are available for all study subjects and in addition for a subset called the validation sample true covariate data of interest have been ascertained the term auxiliary data refers to data not in the regression model but thought to be informative about the true missing covariate data of interest we discuss a method which is nonparametric with respect to the association between available and missing data allows missingness to depend on available response and covariate values and is applicable to both cohort and case control study designs the method previously proposed by flanders greenland 1991 and by zhao lipsitz 1992 is generalised and asymptotic theory is derived our expression for the asymptotic variance of the estimator provides intuition regarding performance of the method optimal sampling strategies for the validation set are also suggested by the asymptotic results