a semiparametric approach for the two sample comparison of survival times with long term survivors summary in the two sample comparison of survival times with long term survivors the overall difference between the two distributions reflects differences occurring in early follow up for susceptible subjects and in long term follow up for nonsusceptible subjects in this setting we propose statistics for testing i no overall ii no short term and iii no long term difference between the two distributions to be compared the statistics are derived as follows a semiparametric model is defined that characterizes a short term effect and a long term effect by approximating this model about no difference in early survival a time dependent proportional hazards model is obtained the statistics are obtained from this working model the asymptotic distributions of the statistics for testing no overall or no short term effects are ascertained while that of the statistic for testing no long term effect is valid only when the short term effect is small simulation studies investigate the power properties of the proposed tests for different configurations the results show the interesting behavior of the proposed tests for situations where a short term effect is expected an example investigating the impact of progesterone receptors status on local tumor relapse for patients with early breast cancer illustrates the use of the proposed tests

non linear observer design by transformation into a generalized observer canonical form an observer design method for a certain class of non linear single output systems is introduced the characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non linear system is approximated by a linear one the present paper deals with the derivation of a transformation of the considered non linear system into a generalized observer canonical form gocf which enables a systematic observer design similar to the linear one based on the well known linear observer canonical form to assign conditions for its existence the transformation into the gocf is carried out in two steps via a generalized observability canonical form gobcf in contrast to previous forms used for linear systems the two non linear canonical forms presented here also depend on the time derivatives of the input variables this means that the resulting observer has to be supplied not only with the input and output variables of the given system but also with deri

stochastic stability of jump linear systems in this note some testable conditions for mean square i e second moment stability for discrete time jump linear systems with time homogenous and time inhomogenous finite state markov chain form processes are presented

the asymptotic properties of nonparametric tests for comparing survival distributions the asymptotic distribution under alternative hypotheses is derived for a class of statistics used to test the equality of two survival distributions in the presence of arbitrary and possibly unequal right censoring the test statistics include equivalents to the log rank statistic the modified wilcoxon statistic and the class of rank invariant test procedures introduced by peto peto when there are equal censoring distributions and the hazard functions are proportional the sample size formula for the f test used to compare exponential samples is shown to be valid for the log rank test in certain situations the power of the log rank test falls as the amount of censoring decreases

three classes of censored data rank tests strengths and weaknesses under censoring summary nonparametric tests are useful when definite parametric alternatives are not available the behaviour under censoring of extensions of the tests is used to delineate three distinct classes of censored data rank tests asymptotically efficient approximately distribution free and approximately unbiased section 2 gives qualitative comparisons 3 gives some representative numerical comparisons the pitman efficiencies approximated by lee desu gehan 1975 from simulations with 50 observations in each group are shown to agree with asymptotic calculations 1 weighted log rank tests it is assumed that two samples of randomly censored observations are available that is that the true lifetimes yij have cumulative distribution functions f y i oj for j 1 n i i 1 2 that the censoring times cij have cumulative distribution functions h y i of and that the observable quantities are xij min yij c and dij xij yij where a denotes the indicator function of the set a it is assumed that 01 0 that f t 1 0 is continuous in 0 and that the null hypothesis is 61 02 0 the true value of 02 will be denoted by 0 and the functions f t i 0 and h t i 0 will be abbreviated to f and h survival distributions will be denoted by a bar so that f t 1 f t the hazard rates of f and f t 10 will be denoted by a and ao respectively the test statistics studied are functions of di t the number of deaths observed before time t in the ith sample ri t the number at risk at time t in the ith sample and aj an estimator of the cumulative hazard function for the ith sample these functions are defined formally by n i n i

stability of discrete linear inclusion let m ai be a set of linear operators on rn the discrete linear inclusion dli m is the set of possible trajectories xi i 0 such that xn ainain 1 ai1x0 where x0 rn and aij m we study several notions of stability for dli m including absolute asymptotic stability aas which is that all products ain ai1 0 as n we mainly study the case that m is a finite set we give criteria for the various forms of stability two new approaches are taken one relates the question of aas of dli m to formal language theory and finite automata while the second connects the aas property to the structure of a lie algebra associated to the elements of m more generally the discrete linear inclusion dli m makes sense for m contained in a banach algebra b we prove some results for aas in this case and give counterexamples showing that some results valid for finite sets of operators on rn are not true for finite sets m in a general banach algebras b

on the relationship between the sample path and moment lyapunov exponents for jump linear systems in this paper we study the relationship between the sample and moment lyapunov exponents for jump linear systems using a large deviation theorem a modified version of arnold s formula for connecting sample path and moment lyapunov exponents for continuous time linear stochastic systems is extended to discrete time jump linear systems sample path stability properties of linear stochastic systems are determined by the top lyapunov exponent and relating sample and moment lyapunov exponents may be useful for developing computationally efficient methods for determining the almost sure sample path stability of linear stochastic systems

sobolev norms based state estimation and input recovery for a class of nonlinear systems design and experimental results in this paper we address the problem of state estimation and input recovery for a class of nonlinear systems in the presence of disturbances in both the state and output equations indeed one of the main difficulties that arise when input recovery is considered is how to cope with the problem of disturbance s derivative for the filter design our contribution lies in the use of sobolev norms to develop a simple and useful observer we provide first the state filtering and input recovery equations after based on the lyapunov stability theory and some robustness criteria new sufficient synthesis conditions are given in terms of linear matrix inequalities lmis to show performances of the proposed method we considered the problem of simultaneous synchronization and decryption in chaotic communication systems with some experimental results

a formula connecting sample and moment stability of linear stochastic systems given the linear stochastic system dot x a xi t x x in mathbb r d xi t some nice diffusion sample and moment stability of x equiv 0 are studied via the sample lyapunov exponent lambda and the lyapunov exponent of the pth mean g p of a solution generalizing a result of molchanov for the undamped linear oscillator it is shown that g p is a smooth convex function of p in mathbb r with g 0 0 and g 0 lambda for trace a 0 a second zero of g at p d is detected this allows one to draw simple but quite complete conclusions about the relation between sample and moment stability

h observer design for uncertain one sided lipschitz nonlinear systems with time varying delay abstract the h observer design for uncertain one sided lipschitz nonlinear systems with time varying delay is investigated in this paper by considering the quadratic inner bounded requirement and the one sided lipschitz condition concurrently and employing a class of relaxed integral inequalities the h observer for nominal lipschitz systems is designed firstly then the results are extended to the one sided lipschitz systems with norm bounded uncertainties finally the proposed results are demonstrated via two simulation examples

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

extremal and barabanov semi norms of a semigroup generated by a bounded family of matrices abstract let s s i i i be an arbitrary family of complex n by n matrices where 1 n let s denote the joint spectral radius of s defined as s lim sup l sup i 1 i l i l s i 1 s i l 1 l which is independent of the norm used here a semi norm on c n is called extremal of s if it satisfies x 0 and x s i s x x x 1 x n c n and i i in this paper using an elementary analytical approach we show that if s is bounded in c n n then there always exists for s an extremal semi norm on c n if additionally s is compact in c n n this extremal semi norm has the barabanov type property i e to any x c n one can find an infinite sequence i n i with x s i 1 s i k s k x for each k 1 as a common starting point this directly implies the fundamental results barabanov s norm theorem berger wang s formula and elsner s reduction theorem

observers for lipschitz nonlinear systems this paper presents some fundamental insights into observer design for the class of lipschitz nonlinear systems the stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix the correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented these conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix the eigenvalues have to be located sufficiently far out into the left half plane and the eigenvectors also have to be sufficiently well conditioned for ensuring asymptotic stability based on these results a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability

a gel fand type spectral radius formula and stability of linear constrained switching systems abstract using ergodic theory in this paper we present a gel fand type spectral radius formula which states that the joint spectral radius is equal to the generalized spectral radius for a matrix multiplicative semigroup s restricted to a subset that need not carry the algebraic structure of s this generalizes the berger wang formula using it as a tool we study the absolute exponential stability of a linear switched system driven by a compact subshift of the one sided markov shift associated to s

a new bayesian model for survival data with a surviving fraction abstract we consider bayesian methods for right censored survival data for populations with a surviving cure fraction we propose a model that is quite different from the standard mixture model for cure rates we provide a natural motivation and interpretation of the model and derive several novel properties of it first we show that the model has a proportional hazards structure with the covariates depending naturally on the cure rate second we derive several properties of the hazard function for the proposed model and establish mathematical relationships with the mixture model for cure rates prior elicitation is discussed in detail and classes of noninformative and informative prior distributions are proposed several theoretical properties of the proposed priors and resulting posteriors are derived and comparisons are made to the standard mixture model a real dataset from a melanoma clinical trial is discussed in detail

nonparametric estimation and testing in a cure model nonparametric generalized maximum likelihood product limit point estimators and confidence intervals are given for a cure model with random censorship one two and k sample likelihood ratio tests for inference on the cure rates are developed in the two sample case its power is compared to the power of several alternatives including the log rank and gray and tsiatis 1989 biometrics 45 899 904 tests implications for the use of the likelihood ratio test in a clinical trial designed to compare cure rates are discussed

continuous discrete time observer design for lipschitz systems with sampled measurements this technical note concerns observer design for lipschitz nonlinear systems with sampled output using reachability analysis an upper approximation of the attainable set is given when this approximation is formulated in terms of a convex combination of linear mappings a sufficient condition is given in terms of linear matrix inequalities lmis which can be solved employing an lmis solver this novel approach seems to be an efficient tool to solve the problem of observer synthesis for a class of lipschitz systems of small dimensions

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

effective sample size for tests of censored survival data summary when survival experience of two groups is compared in the presence of arbitrary right censoring the effective sample size for determining the power of the test used is usually taken to be the number of uncensored observations this convention is examined through a monte carlo study empirical powers of the generalized savage test and generalized wilcoxon test with uncensored data are compared to those with censored data containing approximately the same number of uncensored observations large sample relative efficiencies are calculated for a lehmann family of alternatives it is shown that depending on the underlying distribution and censoring mechanism censored observations can add appreciably to the power of either test

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

technical communique a characterization of the generalized spectral radius with kronecker powers based on turan s power sum theory we extend a recent result obtained by blondel and nesterov blondel v d nesterov y 2005 computationally efficient approximations of the joint spectral radius siam journal on matrix analysis and applications 27 256 272 by deriving a new characterization of the generalized spectral radius in terms of kronecker powers

cure rate models power of the logrank and generalized wilcoxon tests this paper reports the results of simulations that compare the power of the logrank and generalized wilcoxon tests in situations where the cure rate model is appropriate

brief paper periodically switched stability induces exponential stability of discrete time linear switched systems in the sense of markovian probabilities the conjecture that periodically switched stability implies absolute asymptotic stability of random infinite products of a finite set of square matrices has recently been disproved under the guise of the finiteness conjecture in this paper we show that this conjecture holds in terms of markovian probabilities more specifically let s k c n x n 1 k k be arbitrarily given k matrices and s k k j j 1 1 k j k for each j 1 where n k 2 then we study the exponential stability of the following discrete time switched dynamics s x j s k j s k 1x 0 j 1 and x 0 c n where k j j 1 s k can be an arbitrary switching sequence for a probability row vector p p 1 p k r k and an irreducible markov transition matrix p r k x k with pp p we denote by m p p the markovian probability on s k corresponding to p p by using symbolic dynamics and ergodic theoretic approaches we show that if s possesses the periodically switched stability then i it is exponentially stable m p p almost surely ii the set of stable switching sequences k j j 1 s k has the same hausdorff dimension as s k thus the periodically switched stability of a discrete time linear switched dynamics implies that the system is exponentially stable for almost all switching sequences

when do several linear operators share an invariant cone abstract we establish a criterion for a finite family of matrices to possess a common invariant cone the criterion reduces the problem of existence of an invariant cone to equality of two special numbers that depend on the family in spite of theoretical simplicity the practical use of the criterion may be difficult we show that the problem of existence of a common invariant cone for four matrices with integral entries is algorithmically undecidable corollaries of the criterion which give sufficient and necessary conditions are derived finally we introduce a co directional number of several matrices we prove that this parameter is close to zero iff there is a small perturbation of matrices after which they get an invariant cone an algorithm for its computation is presented

a monte carlo study of some two sample rank tests with censored data abstract the powers of several nonparametric tests for the two sample problem with censored data are compared by simulation the tests studied include gehan s efron s and peto s and prentice s generalized wilcoxon tests along with the logrank test the test with the greatest power changes with the sample sizes censoring mechanism and distribution of the random variables the test that performed the best overall was the peto prentice generalized wilcoxon statistic with an asymptotic variance estimate

h synthesis of unknown input observers for non linear lipschitz systems the problem of unknown input observer design for non linear lipschitz systems is considered a new dynamic framework which is a generalization of previously used linear unknown input observers is introduced the additional degrees of freedom offered by this dynamic framework are used to deal with the lipschitz non linearity the necessary and sufficient condition that ensures asymptotic convergence of the new observer is presented and the equivalence between this condition and an h optimal control problem which satisfies the standard regularity assumptions in the h optimization theory is shown based on these results a design procedure that is solvable using commercially available software is presented a simulation example is given to illustrate the proposed design

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

observer design for systems with multivariable monotone nonlinearities globally convergent observers are designed for a class of systems with multivariable nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a state dependent multivariable nonlinearity we first extend an earlier design automatica 37 12 2001 1923 to multivariable nonlinearities satisfying an analog of the scalar nondecreasing property next we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system this relaxed design renders the feasibility conditions less restrictive and widens the applicability of the observer as illustrated with examples finally output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters

nonlinear state observation using h sub spl infin filtering riccati design the authors propose an observer for continuous time nonlinear systems the observer gain is computed by a riccati differential equation similar to the extended kalman filter they prove that under certain conditions the proposed observer is an exponential observer by choosing an appropriate lyapunov function furthermore the authors explore some important relations of the proposed observer to robust control theory and h sub spl infin filtering to examine the practical usefulness of the proposed observer they applied it to an induction motor for the estimation of the rotor flux and the angular velocity

a note on observer design for one sided lipschitz nonlinear systems in this note observer design of a class of nonlinear systems is considered based on the one sided lipschitz condition sufficient conditions for the existence of observers of the class of nonlinear systems are presented a design method of the observer that is dependent on the solution of the linear matrix inequality is then presented furthermore a gain matrix of the observer is given the method given in this note makes the applicable class larger than that given in the literature it should be noticed that the proposed method is applicable not only to the monotone nonlinearities and lipschitz nonlinearities but also to the one sided lipschitz nonlinearities which are neither monotone nonlinearities nor usual lipschitz nonlinearities finally we use the proposed method to design observers for three simulative examples and the effect of each state trajectory tracking is very satisfactory

generalized joint spectral radius and stability of switching systems abstract this paper extends the notion of generalized joint spectral radius with exponents originally defined for a finite set of matrices to probability distributions we show that under a certain invariance condition the radius is calculated as the spectral radius of a matrix that can be easily computed extending the classical counterpart using this result we investigate the mean stability of switching systems in particular we establish the equivalence of mean square stability simultaneous contractibility in square mean and the existence of a quadratic lyapunov function also the stabilization of positive switching systems is studied numerical examples are given to illustrate the results

the berger wang formula for the markovian joint spectral radius abstract the berger wang formula establishes equality between the joint and generalized spectral radii of a set of matrices for matrix products whose multipliers are applied not arbitrarily but in accordance with some markovian law there are also known analogs of the joint and generalized spectral radii however the known proofs of the berger wang formula hardly can be directly applied in the case of markovian products of matrices since they essentially rely on the arbitrariness of appearance of different matrices in the related matrix products nevertheless as has been shown by x dai 1 the berger wang formula is valid for the case of markovian analogs of the joint and the generalized spectral radii too although the proof in this case heavily exploits the more involved techniques of multiplicative ergodic theory in the paper we propose a matrix theory construction allowing to deduce the markovian analog of the berger wang formula from the classical berger wang formula

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

group sequential designs for cure rate models with early stopping in favour of the null hypothesis ewell and ibrahim derived the large sample distribution of the logrank statistic under general local alternatives their asymptotic results enable us to extend several group sequential designs which allow for early stopping in favour of the null hypothesis to the setting in which the cure rate model is appropriate in particular we derive stopping rules for the cure rate model using conditional power predictive power and repeated confidence intervals methods we illustrate the methods proposed using a hypothetical phase iii clinical trial which is typical for melanoma studies

almost sure stability of discrete time switched linear systems a topological point of view in this paper we study the stability of discrete time switched linear systems via symbolic topology formulation and the multiplicative ergodic theorem a sufficient and necessary condition for mu a almost sure stability is derived where mu a is the parry measure of the topological markov chain with a prescribed transition 0 1 matrix a the obtained mu a almost sure stability is invariant under small perturbations of the system the topological description of stable processes of switched linear systems in terms of hausdorff dimension is given and it is shown that our approach captures the maximal set of stable processes for linear switched systems the obtained results cover the stochastic markov jump linear systems where the measure is the natural markov measure defined by the transition probability matrix two examples are provided to illustrate the theoretical outcomes of the paper

observer synthesis under time varying sampling for lipschitz nonlinear systems in this work the problem of observation of continuous time nonlinear lipschitz systems under time varying discrete measurements is considered this class of systems naturally occurs when continuous processes are observed through digital sensors and information is sent via a network to a computer for state estimation since the network introduces variations in the sampling time the observer must be designed so that it takes them into account here impulsive observers which make instantaneous correction when information is received are investigated moreover we consider time varying observer gains adapting to the varying sampling interval in order to deal with both continuous time and discrete time dynamics a new hybrid model is used to state the problem and establish the convergence of the proposed observer first generic conditions are provided using a hybrid lyapunov function then a restriction of the generic lyapunov function is used to establish tractable conditions that allows the analysis and synthesis of an impulsive gain

pointwise stability of discrete time stationary matrix valued markovian processes in this technical note we study the pointwise stability of a discrete time matrix valued and stationary markovian jump linear system when the system is restricted to a linear subspace we show that it is pointwise convergent if and only if it is pointwise exponentially convergent under the framework of probability and symbolic dynamics

the generalized spectral radius theorem an analytic geometric proof abstract let be a bounded set of complex matrices m a 1 a m a i the generalized spectral radius theorem states that where and are defined as follows lim sup m 1 m where m sup a a m with a the spectral radius lim sup m 1 m where m sup a a m with any matrix norm we give an elementary proof based on analytic and geometric tools which is in some ways simpler than the first proof by berger and wang

a note on observers for lipschitz nonlinear systems this note deals with the design of reduced order observers for lipschitz nonlinear systems it shows that the conditions under which a full order observer exists also guarantee the existence of a reduced order observer a design method of the reduced order observer that is dependent on the solution of the riccati equation is then presented and an example is given to illustrate effects of the design method

observability through delayed measurements a new approach to state observers design an original approach for the construction of state observers for dynamic systems is presented in this article new notions of observability delay observability and delay drift observability useful for the development of the observer equations and for the convergence proof are introduced and compared with other standard observability concepts in particular it is shown that delay drift observability is an extension of the well known drift observability property the construction of the proposed observer is straightforward and does not require any coordinate transformation of the system into a canonical form which is a common feature of many other approaches a numerical example is reported where a system that is not drift observable is considered in this case the proposed observer is easily constructed and performs well

observer with linear error dynamics for nonlinear multi output systems based upon nonlinear state coordinate transformations and a condensed dual brunovsk form for multi output systems a method for designing nonlinear state observers with linear error dynamics is presented necessary and sufficient conditions are provided for identifying the class of nonlinear systems for which state observers with linear error dynamics can be obtained

observability and observers for nonlinear systems this paper deals with observability and observers for general nonlinear systems in the non control affine case we characterize systems that are observable independently of the inputs an exponential observer for these systems is also exhibited

observers for a class of lipschitz systems with extension to h performance analysis abstract in this paper observer design for a class of lipschitz nonlinear dynamical systems is investigated one of the main contributions lies in the use of the differential mean value theorem dmvt which allows transforming the nonlinear error dynamics into a linear parameter varying lpv system this has the advantage of introducing a general lipschitz like condition on the jacobian matrix for differentiable systems to ensure asymptotic convergence in both continuous and discrete time systems such sufficient conditions expressed in terms of linear matrix inequalities lmis are established an extension to h filtering design is obtained also for systems with nonlinear outputs a comparison with respect to the observer method of gauthier et al a simple observer for nonlinear systems applications to bioreactors ieee trans automat control 37 6 1992 875 880 is presented to show that the proposed approach avoids high gain for a class of triangular globally lipschitz systems in the last section academic examples are given to show the performances and some limits of the proposed approach the last example is introduced with the goal to illustrate good performances on robustness to measurement errors by avoiding high gain

survivorship analysis when cure is a possibility a monte carlo study parametric survivorship analyses of clinical trials commonly involves the assumption of a hazard function constant with time when the empirical curve obviously levels off one can modify the hazard function model by use of a gompertz or weibull distribution with hazard decreasing over time some cancer treatments are thought to cure some patients within a short time of initiation then instead of all patients having the same hazard decreasing over time a biologically more appropriate model assumes that an unknown proportion 1 pi have constant high risk whereas the remaining proportion pi have essentially no risk this paper discusses the maximum likelihood estimation of pi and the power curves of the likelihood ratio test monte carlo studies provide results for a variety of simulated trials empirical data illustrate the methods

a comparison of tests of the difference in the proportion of patients who are cured we compared by simulation the likelihood ratio wald and score tests based on a mixture model similar to that proposed by farewell 1982 biometrics 38 1041 1046 and a simple nonparametric test based on the plateau value of the product limit estimate for testing the difference in cured proportions between two groups the parametric tests obtained their asymptotic properties even in small samples provided that one could assume equal failure rates in the two groups otherwise good agreement with predictions required that essentially all potential failures had been observed the comparative properties of the parametric tests depended on whether the population survival functions crossed with the power of the wald test as good as or better than the others in the common situation when the survival functions do not cross however its size was sometimes less than nominal the score test was often not defined and is therefore of limited value the product limit test often performed as well as the parametric tests and despite being biased in some circumstances may be a useful alternative to these especially in small samples when some potential failures have not been observed

stochastic stability of jump discrete time linear systems with markov chain in a general borel space necessary and sufficient conditions for stochastic stability ss of discrete time linear systems subject to markov jumps in the parameters are considered assuming that the markov chain takes values in a general borel space s it is shown that ss is equivalent to the spectrum radius of a bounded linear operator in a banach space being less than 1 or to the existence of a solution of a lyapunov type equation these results generalize several previous results in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

a strong tracking extended kalman observer for nonlinear discrete time systems the authors show how the extended kalman filter used as an observer for nonlinear discrete time systems or extended kalman observer eko becomes a useful state estimator when the arbitrary matrices namely r sub k and q sub k are adequately chosen as a first step we use the linearization technique given by boutayed et al 1997 which consists of introducing unknown diagonal matrices to take the approximation errors into account it is shown that the decreasing lyapunov function condition leads to a linear matrix inequality lmi problem which points out the connection between a good convergence behavior of the eko and the instrumental matrices r sub k and q sub k in order to satisfy the obtained lmi a particular design of q sub k is given high performances of the proposed technique are shown through numerical examples under the worst conditions

on exponential almost sure stability of random jump systems this paper is concerned with a class of random jump systems represented by transition operators which includes switched linear systems with strictly stationary switching signals in infinite modes space as its special case a series of necessary and sufficient conditions are established for almost sure stability of this class of random jump systems under different scenarios the stability criteria obtained are further extended to markov jump linear systems with infinite states and hence a unified approach to describing the almost sure stability of mjlss is addressed under this context all the results in the work are developed for both the continuous and discrete time systems

observer design for stochastic nonlinear systems via contraction based incremental stability this paper presents a new design approach to nonlinear observers for ito stochastic nonlinear systems with guaranteed stability a stochastic contraction lemma is presented which is used to analyze incremental stability of the observer a bound on the mean squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of the contraction rate and maximum noise intensity the observer design is based on a non unique state dependent coefficient sdc form which parametrizes the nonlinearity in an extended linear form the observer gain synthesis algorithm called linear matrix inequality state dependent algebraic riccati equation lmi sdare is presented the lmi sdare uses a convex combination of multiple sdc parametrizations an optimization problem with state dependent linear matrix inequality sdlmi constraints is formulated to select the coefficients of the convex combination for maximizing the convergence rate and robustness against disturbances two variations of lmi sdare algorithm are also proposed one of them named convex state dependent riccati equation csdre uses a chosen convex combination of multiple sdc matrices and the other named fixed sdare uses constant sdc matrices that are pre computed by using conservative bounds of the system states while using constant coefficients of the convex combination pre computed by a convex lmi optimization problem a connection between contraction analysis and l 2 gain of the nonlinear system is established in the presence of noise and disturbances results of simulation show superiority of the lmi sdare algorithm to the extended kalman filter ekf and state dependent differential riccati equation sddre filter

maximum likelihood methods for cure rate models with missing covariates we propose maximum likelihood methods for parameter estimation for a novel class of semiparametric survival models with a cure fraction in which the covariates are allowed to be missing we allow the covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one dimensional conditional distributions we propose a novel em algorithm for maximum likelihood estimation and derive standard errors by using louis s formula louis 1982 journal of the royal statistical society series b 44 226 233 computational techniques using the monte carlo em algorithm are discussed and implemented a real data set involving a melanoma cancer clinical trial is examined in detail to demonstrate the methodology

bounded semigroups of matrices in this note are proved two conjectures of daubechies and lagarias the first asserts that if z is a bounded set of matrices such that all left infinite products converge then 8 generates a bounded semigroup the second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices one definition involves the conventional spectral radius and one involves the operator norm

asymptotic stability and generalized gelfand spectral radius formula let be a set of n n complex matrices for m 1 2 let m be the set of all products of matrices in of length m denote by the multiplicative semigroup generated by is said to be asymptotically stable in the sense of dynamical systems if there is 0 1 such that there are bounded neighborhoods u v cn of the origin for which av mu for all a m m 1 2 for a bounded set of n n complex matrices it is shown that the following conditions are mutually equivalent i is asymptotically stable ii g9 lim supm supa m a 1 m 1 iii lim supm supa m a 1 m 1 where a stands for the spectral radius of a and iv there exists a positive number such that a 1 for all a this fact answers an open question raised by brayton and tong the generalized gelfand spectral radius formula that is g9 conjectured by daubechies and lagarias and proved by berger and wang using advanced tools from ring theory and then by elsner using analytic geometric tools follows immediately form the above asymptotic stability theorem

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example