comments on a necessary and sufficient condition for the stability of nonnegative interval discrete systems absrac in the above note the authors gave necessary and sufficient conditions for the schur stability of nonnegative interval matrices we comment that these conditions may be more conveniently stated in terms of characterizations of m matrices and are easy consequences of some well known facts in nonnegative matrix theory the m matrix characterization further reveals that the conditions in the note fall into a special case of a known result for the general interval matrices in a recent note shafai et al gave necessary and sufficient conditions for the schur stability of nonnegative interval matrices specifically they considered the set of matrices

parameter identification of multi input single output systems based on fir models and least squares principle by means of auxiliary models finite impulse response fir models this paper develops an identification algorithm for multi input single output stochastic systems the basic idea is to estimate the fir model parameters of each fictitious subsystem submodel with the fir model orders increasing and to use auxiliary models to predict estimate the outputs of the submodels and further to use the pade approximation method to produce the parameter estimates of submodels some simulation results are given

root locus approach to the stability analysis of interval matrices a new approach called the root locus approach is developed for the stability analysis of perturbed matrices the basic idea of this approach is to ensure that the root loci of a continuously perturbed matrix remain in the open left half complex s plane based on this approach new techniques are presented to analyse the stability of interval matrices examples are given to demonstrate the merit of the proposed theorems

a note on residual life summary two further characterizations are given of a family of survival distributions introduced by hall wellner 1984 the second result involves a new family of semiparametric models requiring proportional mean residual life theorem 1 let s x be an absolutely continuous survivor function with s o 1 and suppose that the residual life distribution s y x of s x satisfies 4 for some nonnegative function 0 x then 0 x is linear and s x satisfies 3 proof equation 4 gives 0 x s x 0 x y s x s y we may deduce successively i that s x 0 implies 0 x 0 ii s 0 0 implies s x 0 implies x q s x supposing that s x y0 x 0 we may apply q to 4 to obtain

performance analysis of multi innovation gradient type identification methods it is well known that the stochastic gradient sg identification algorithm has poor convergence rate in order to improve the convergence rate we extend the sg algorithm from the viewpoint of innovation modification and present multi innovation gradient type identification algorithms including a multi innovation stochastic gradient misg algorithm and a multi innovation forgetting gradient mifg algorithm because the multi innovation gradient type algorithms use not only the current data but also the past data at each iteration parameter estimation accuracy can be improved finally the performance analysis and simulation results show that the proposed misg and mifg algorithms have faster convergence rates and better tracking performance than their corresponding sg algorithms

an effective semiparametric estimation approach for the sufficient dimension reduction model abstractin the exploratory data analysis the sufficient dimension reduction model has been widely used to characterize the conditional distribution of interest different from the existing approaches our main achievement is to simultaneously estimate two essential elements basis and structural dimension of the central subspace and the bandwidth of a kernel distribution estimator through a single estimation criterion with an appropriate order of kernel function the proposed estimation procedure can be effectively carried out by starting with a dimension of zero until the first local minimum is reached meanwhile the optimal bandwidth selector is ensured to be a valid tuning parameter for the central subspace estimator an important advantage of this estimation technique is its flexibility to allow a response to be discrete and some of covariates to be discrete or categorical providing that a certain continuity condition holds under very mild assumptions we further derive the uniform consistency of

on the robustness of linear continuous time dynamic systems in this note for a given linear continuous time dynamic system dot x ax bu we determine sufficient conditions for the existence of a constant feedback matrix k such that the closed loop system matrix a bk admits a diagonal positive solution of the lyapunov equation an algorithm for the determination of such k matrix is given and some examples are solved

covariate bias induced by length biased sampling of failure times although many authors have proposed different approaches to the analysis of length biased survival data a number of issues have not been fully addressed the most important among these issues is perhaps that regarding inclusion of covariates into the analysis of length biased lifetime data collected through cross sectional sampling of a population one aspect of this problem which appears to have been neglected in the literature concerns the effect of length bias on the sampling distribution of the covariates in most regression analyses it is conventional to condition on the observed covariate values however certain covariate values could be preferentially selected into the sample being linked to the long term survivors who themselves are favored by the sampling mechanism this observation raises two questions 1 does the conditional analysis of covariates lead to biased estimators of regression coefficients and 2 does inference through the joint l likelihood of covariates and failure times

survival analysis without survival data connecting length biased and case control data we show that relative mean survival parameters of a semiparametric log linear model can be estimated using covariate data from an incident sample and a prevalent sample even when there is no prospective follow up to collect any survival data estimation is based on an induced semiparametric density ratio model for covariates from the two samples and it shares the same structure as for a logistic regression model for case control data likelihood inference coincides with well established methods for case control data we show two further related results first estimation of interaction parameters in a survival model can be performed using covariate information only from a prevalent sample analogous to a case only analysis furthermore propensity score and conditional exposure effect parameters on survival can be estimated using only covariate data collected from incident and prevalent samples

lmi characterization of structural and robust stability abstract this paper introduces several stability conditions for a given class of matrices expressed in terms of linear matrix inequalities lmi being thus simply and efficiently computable diagonal and simultaneous stability both characterized by polytopes of matrices are addressed using this approach a method particularly attractive to test a given matrix for d stability is proposed lyapunov parameter dependent functions are built in order to reduce conservativeness of the stability conditions the key idea is to relate hurwitz stability with a positive realness condition

another sufficient condition for the stability of interval matrices a sufficient condition for the stability of interval matrices is presented which is based on the condition given by yedavalli 1985 b examples are given which illustrate the improvement of the proposed condition over that given by yedavalli 1986

the residual based interactive stochastic gradient algorithms for controlled moving average models this paper derives a residual based interactive stochastic gradient isg parameter estimation algorithm for controlled moving average cma models and studied the performance of the residual based isg algorithm under weaker conditions on statistical properties of the noise compared with the residual based extended stochastic gradient algorithm for identifying cma models the proposed isg algorithm can give highly accurate parameter estimates by the simulation example

performance analysis of the am sg parameter estimation for multivariable systems the auxiliary model based stochastic gradient am sg parameter estimation method is an important identification one this paper analyzes the performances of the am sg estimation algorithm for multiple input single output systems i e multivariable systems under the strong persistent excitation condition the analysis and simulation results indicate that the parameter estimation errors converge to zero

parameter estimation of dual rate stochastic systems by using an output error method in this note a new gradient based recursive algorithm for estimating parameters of dual rate sampled data systems is presented the basic idea is by using an output error method to identify the single rate models and the unknown noise free outputs true outputs directly from dual rate input output data further convergence properties of the proposed algorithm in parameter and output estimation are analyzed and the result is illustrated and tested with an experimental water level system

sufficient conditions on stability of interval matrices connections and new results the stability properties of interval matrices are discussed sufficient conditions are given for these properties based upon gershgorin s theorem and its extension and they are shown to improve previous results the derivation helps clarify relations between certain previously available results and shows they can be derived using gershgorin s theorem furthermore the problem of determining the stability of interval matrices is related to that of characterizing certain nonsingular m matrices

matrix wa atw and its applications for matrix a with off diagonal elements not necessarily of the same sign conditions are obtained for the existence of a positive definite diagonal matrix w such that matrix wa atw is positive definite and the applications of the latter to the determination of the stability of interval matrices are considered

on the asymptote of the optimal routing policy for two service stations it has been previously proved that the optimal routing control of a two station markovian network with linear cost is described by a monotone switching curve with the discounted cost objective function it is proven in this paper that the optimal switching curve has a finite asymptotic limit when c sub 1 not c sub 2 where c sub i is the unit inventory cost at station i whereas for the case with c sub 1 c sub 2 as well as the case with the long run average objective function the switching curve does not have a finite asymptote

a rank statistics approach to the consistency of a general bootstrap a general notion of a bootstrapped mean constructed by exchangeably weighting sample points is introduced consistency of this generalized bootstrapped mean which includes proposals of efron and rubin among others is proved by classical linear rank statistics theory the consistency of generalized bootstrapped empirical and quantile processes is also established

on the determination of a diagonal solution of the lyapunov equation in this note for a given matrix a the solution of the lyapanov equation a p pa q 0 considering p diagonal or both p and q diagonal matrices is investigated for this purpose a simple algorithm based on nonlinear programming is presented

the limiting distribution of the maximum rank correlation estimator han s maximum rank correlation mrc estimator is shown to be 4 consistent and asymptotically normal the proof rests on a general method for determining the asymptotic distribution of a maximization estimator a simple u statistic decomposition and a uniform bound for degenerate u processes a consistent estimator of the asymptotic covariance matrix is provided along with a result giving the explicit form of this matrix for any model within the scope of the mrc estimator the latter result is applied to the binary choice model and it is found that the mrc estimator does not achieve the semiparametric efficiency bound

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

a numerical method for the stability analysis of quasi polynomial vector fields this paper shows the sufficient conditions for the existence of a lyapunov function in the class of quasi polynomial dynamical systems we focus on the cases where the system s parameters are numerically specified a numerical algorithm to analyze this problem is presented which involves the resolution of a linear matrix inequality lmi this lmi is collapsed to a linear programming problem from the numerical viewpoint this computational method is very useful to search for sufficient conditions for the stability of non linear systems of odes the results of this paper greatly enlarge the scope of applications of a method previously presented by the authors

robustness analysis of matrices with highly structured uncertainties lyapunov s method is used to analyze the robustness of system matrices with structured uncertainties in particular the 2 norm matrix measure is used to give less conservative stability results

non parametric analysis of a generalized regression model the maximum rank correlation estimator the paper considers estimation of a model yi d f x i 0 ui where the composite transformation d f is only specified that d r r is non degenerate monotonic and f r2 r is strictly monotonic in each of its variables the paper thus generalizes standard data analysis which assumes that the functional form of d f is known and additive the estimator which it proposes is the maximum rank correlation estimator which is non parametric in the functional form of d f and non parametric in the distribution of the error terms ui the estimator is shown to be strongly consistent for the parameters 0 up to a scale coefficient

stability of a polytope of matrices counterexamples while there have been significant breakthroughs for the stability of a polytope of polynomials since v l kharitonov s 1978 seminal result on interval polynomials for a polytope of matrices the stability problem is considered far from completely resolved counterexamples are provided for three conjectures that are directly motivated by the results in the polynomial case these counterexamples illustrate the fundamental differences between polynomial stability and matrix stability problems and indicate that some obvious lines of attack on the matrix polytope stability problem will fail

nonparametric estimation from cross sectional survival data abstract in many follow up studies survival data are often observed according to a cross sectional sampling scheme data of this type are subject to left truncation in addition to the usual right censoring a number of characteristics and properties of the product limit estimate for left truncated and right censored data have been explored and found to be similar to those of the kaplan meier estimate under the stationarity assumption however it is believed that an alternative estimate has much better efficiency in this article the conditional maximum likelihood estimate mle property of the product limit estimate is visited the non parametric mle of the truncation distribution is derived use of this estimate includes testing the stationarity assumption estimating the proportion of truncated data and other applications in prevalent cohort studies the analysis of the estimation is based on a working data approach the asymptotic properties of the proposed estimates are developed through nonpar

stability analysis of dynamic interval systems abstract the stability analysis of interval matrices with certain stability margins is considered by means of similarity transformation and gershgorin s theorem new criteria are developed and illustrated by examples we also demonstrate a counter example to a recent result by argoun 1986

sufficient conditions for stability of interval matrices extremely simple sufficient conditions are presented for the stability of interval matrices these complement the necessary and sufficient conditions developed by bialas 1983 which become unwieldy for large matrices 4 4 and above

robustness analysis of interval matrices based on kharitonov s theorem this paper deals with the robustness analysis problem of interval matrices expansion of det a b is used to get characteristic polynomials of two corresponding systems kharitonov s theorem is applied to test hurwitz properties of the two polynomials a new sufficient condition for all eigenvalues of the interval matrix to lie in a damping cone on complex plan is derived illustrative examples are given

matrix theoretic conditions for the realizability of sliding manifolds systems of the type s ksgn s s rm where sgn is the vector sign function usually determine the realizability of sliding modes in control systems with high frequency gain k a new condition on k is established for the global stability of this system using a nonsmooth liapunov function this condition is used to establish necessary and sufficient stability conditions for second order systems

on structural properties of the lyapunov matrix equation for optimal diagonal solutions we revisit the classical problem of finding a positive diagonal solution p to the lyapunov equation at p pa 0 that minimizes the lyapunov exponent the maximum eigenvalue of at p pa for a isin rnxn with the aim of identifying structural properties of the lyapunov matrix equation at the optimum using eigenvalue sensitivity notions together with optimization machinery we are able to obtain an explicit characterization of the minimum lyapunov exponent that provides such structural insight

hierarchical least squares identification methods for multivariable systems for multivariable discrete time systems described by transfer matrices we develop a hierarchical least squares iterative hlsi algorithm and a hierarchical least squares hls algorithm based on a hierarchical identification principle we show that the parameter estimation error given by the hlsi algorithm converges to zero for the deterministic cases and that the parameter estimates by the hls algorithm consistently converge to the true parameters for the stochastic cases the algorithms proposed have significant computational advantage over existing identification algorithms finally we test the proposed algorithms on an example and show their effectiveness

convergence analysis of estimation algorithms for dual rate stochastic systems identification is to estimate the unknown parameters of systems by using the measured input output data u t y t most existing identification approaches assume that the input output u t y t is available at each sampling instant t this paper focuses on a class of dual rate sampled data systems in which all inputs u t are available but only scarce outputs y qt are available q 1 being an integer we derive a mathematical model for such dual rate systems by using a polynomial transformation technique and present new algorithms for parameter identification and intersample output estimation using directly the dual rate input output data u t y qt and study in detail convergence properties of the algorithms in the stochastic framework by using the stochastic process theory and stochastic martingale theory we show that 1 the parameter estimation error consistently converges to zero under the persistent excitation condition 2 the intersample output estimation error is uniformly bounded finally we illustrate and test the proposed algorithms with example systems including an experimental water level system

on the existence of positive diagonal p such that pa a t p l 0 given a real square matrix a we address the question does there exist a positive diagonal matrix p such that pa a t p is negative definite we present an algorithm which when applied to a gives a definite yes or no answer to this question if the answer is yes the algorithm will provide one such p

a necessary and sufficient condition for the stability of interval matrices consider the linear dynamical system described by the equation xdot t ax t where a is a constant real matrix with dimensions n n and the elements of matrix a are not known precisely we know only the upper and lower bounds of the intervals in which the elements of matrix a are confined in this paper there is proved a necessary and sufficient condition for the stability of solutions of eqn 1 with incomplete information about the elements of matrix a

comments on sufficient condition for the asymptotic stability of interval matrices abstract recently jiang 1987 has shown that a set of interval matrices is stable if the symmetric part of the vertex matrices are stable this result of jiang 1987 is shown to be only applicable to matrices with all the diagonal elements negative

robust interval stability persistence and partial stability on lotka volterra systems with time delay abstract lotka volterra ecological systems with discrete time delays are studied where the information about the biological vital parameters such as the rates of birth death and interaction between species is incomplete but their upper and lower bounds are known by using stability theory of the interval dynamical systems and constructing suitable liapunov functionals robust stability partial robust stability and robust persistence of those lotka volterra systems are investigated and sufficient conditions are obtained respectively

combined parameter and output estimation of dual rate systems using an auxiliary model for a dual rate sampled data system an auxiliary model based identification algorithm for combined parameter and output estimation is proposed the basic idea is to use an auxiliary model to estimate the unknown noise free output true output of the system and directly to identify the parameters of the underlying fast single rate model from the dual rate input output data it is shown that the parameter estimation error consistently converges to zero under generalized or weak persistent excitation conditions and unbounded noise variance and that the output estimates uniformly converge to the true outputs an example is included

proportional mean residual life model for right censored length biased data summary to study disease association with risk factors in epidemiologic studies cross sectional sampling is often more focused and less costly for recruiting study subjects who have already experienced initiating events for time to event outcome however such a sampling strategy may be length biased coupled with censoring analysis of length biased data can be quite challenging due to induced informative censoring in which the survival time and censoring time are correlated through a common backward recurrence time we propose to use the proportional mean residual life model of oakes dasu biometrika 77 409 10 1990 for analysis of censored length biased survival data several nonstandard data structures including censoring of onset time and cross sectional data without follow up can also be handled by the proposed methodology

hierarchical gradient based identification of multivariable discrete time systems in this paper we use a hierarchical identification principle to study identification problems for multivariable discrete time systems we propose a hierarchical gradient iterative algorithm and a hierarchical stochastic gradient algorithm and prove that the parameter estimation errors given by the algorithms converge to zero for any initial values under persistent excitation the proposed algorithms can be applied to identification of systems involving non stationary signals and have significant computational advantage over existing identification algorithms finally we test the proposed algorithms by simulation and show their effectiveness

performance analysis of estimation algorithms of nonstationary arma processes the correlation analysis based methods are not suitable for identifying parameters of nonstationary autoregressive ar moving average ma and arma systems by using estimation residuals in place of unmeasurable noise terms in information vector or matrix we develop a least squares based and gradient based algorithms and establish the consistency of the proposed algorithms without assuming noise stationarity ergodicity or existence of higher order moments furthermore we derive the conditions for convergence of the parameter estimation the simulation results validate the convergence theorems proposed

identification of mimo systems using radial basis function networks with hybrid learning algorithm when a radial basis function network rbfn is used for identification of a nonlinear multi input multi output mimo system the number of hidden layer nodes the initial parameters of the kernel and the initial weights of the network must be determined first for this purpose a systematic way that integrates the support vector regression svr and the least squares regression lsr is proposed to construct the initial structure of the rbfn the first step of the proposed method is to determine the number of hidden layer nodes and the initial parameters of the kernel by the svr method then the weights of the rbfn are determined by solving a simple minimization problem based on the concept of lsr after initialization an annealing robust learning algorithm arla is then applied to train the rbfn with the proposed initialization approach one can find that the designed rbfn has few hidden layer nodes while maintaining good performance to show the feasibility and superiority of the annealing robust radial basis function networks arrbfns for identification of mimo systems several illustrative examples are included

stability of interval matrix polynomial in continuous and discrete cases abstract sufficient conditions of asymptotic stability of interval matrix polynomial of both continuous and discrete cases are given these conditions are presented in terms of the positive definiteness of either an ln ln or l l hermitian and interval matrix therefore the computation of the determinant interval polynomial is avoided

scaling a canonical design problem for networks motivated by decentralized control and numerical methods applications we explore the scaling problem that is we consider the design of a diagonal matrix k so as to i place the eigenvalues of the product kg in the olhp and ii optimize a scalar performance measure c kg of interest for a square topology matrix g we first illustrate our methodology for scaling design which combines optimization machinery with graph algebra notions for a class of topology matrices and a specific performance measure in particular for symmetric positive definite topologies and for a dominant eigenvalue ratio performance measure we find that the optimally scaled system kg has a special structure the right eigenvectors associated with the largest and smallest eigenvalues have corresponding entries of identical magnitude and hence differ only in sign pattern using this structure we develop both explicit and algorithmic methods for computing the optimal scaling and cost after illustrating our methodology with this

positive definite constrained least squares estimation of matrices abstract this paper presents a method for positive definite constrained least squares estimation of matrices the approach is to transform the problem into an equivalent convex quadratic program with infinitely many linear constraints and solve the latter by generating and solving a sequence of ordinary convex quadratic programs

necessary and sufficient conditions for stability of a class of interval matrices in this paper some necessary and sufficient conditions for stability complete instability and composite stability type of a class of interval matrices are given

convergence of hls estimation algorithms for multivariable arx like systems a hierarchical least squares hls algorithm is derived in details for identifying mimo arx like systems based on the hierarchical identification principle it is shown that the parameter estimation errors by the hls algorithm consistently converge to zero for bounded noise variances by using the stochastic martingale theory a numerical example is given

general single index survival regression models for incident and prevalent covariate data and prevalent data without follow up this article mainly focuses on analyzing covariate data from incident and prevalent cohort studies and a prevalent sample with only baseline covariates of interest and truncation times our major task in both research streams is to identify the effects of covariates on a failure time through very general single index survival regression models without observing survival outcomes with a strict increase of the survival function in the linear predictor the ratio of incident and prevalent covariate densities is shown to be a non degenerate and monotonic function of the linear predictor under covariate independent truncation without such a structural assumption the conditional density of a truncation time in a prevalent cohort is ensured to be a non degenerate function of the linear predictor in light of these features some innovative approaches which are based on the maximum rank correlation estimation or the pseudo least integrated squares estimation are developed to estimate the coefficients of covariates up to a scale factor existing theoretical results are further used to establish the n consistency and asymptotic normality of the proposed estimators moreover extensive simulations are conducted to assess and compare the finite sample performance of various estimators to illustrate the methodological ideas we also analyze data from the worcester heart attack study and the national comorbidity survey replication

identification of hammerstein nonlinear armax systems two identification algorithms an iterative least squares and a recursive least squares are developed for hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by armax carma models the basic idea is to replace unmeasurable noise terms in the information vectors by their estimates and to compute the noise estimates based on the obtained parameter estimates convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition the simulation results validate the algorithms proposed

survival analysis of backward recurrence times abstract many surveys include questions that attempt to measure the time of the most recent occurrence of some event for example last visit to a physician although it is tempting to apply survival failure time methods to such data the conditions under which such applications are appropriate have not been apparent in this article it is shown that standard methods may be applied when the data arise from certain well known stochastic processes special procedures may be necessary if the models include duration dependence however the methods are illustrated by the estimation of regression models for data on residential mobility