rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

consistency and efficiency of regression coefficient estimates in location scale models summary the effect on estimation of regression coefficients in linear location scale models is investigated when the error distribution is misspecified it is shown that the maximum likelihood estimator under the incorrect model is still consistent its asymptotic efficiency relative to that of the maximum likelihood estimator based on the correct model is obtained and the estimation of asymptotic variances for the regression coefficient estimators is addressed

asymptotic behavior of robust estimators of regression and scale parameters with fixed carriers for the linear regression model y i mathbf x i mathbf beta varepsilon i with fixed mathbf x i s the asymptotic normality of hat mathbf beta hat sigma which minimizes the huber dutter loss function sum sigma rho y i mathbf x i mathbf beta sigma a n sigma is established under rather general conditions

chaotic principle an experimental test abstract the chaotic hypothesis discussed in gallavotti and cohen 1995 is tested experimentally in a simple conduction model besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which as the forcing strength grows the attractor ceases to be an anosov system and becomes an axiom a attractor a first text of new predictions is also attempted

a goodness of fit test for association in a bivariate survival model summary we propose a simple test of constant conditional hazard ratio in the clayton model 1978 by comparing the unweighted and weighted concordance estimators of the association parameter if the clayton model holds the difference of these two estimates converges to zero the proposed test is consistent against alternatives under which the two concordance estimators converge to different values we derive an explicit formula for the asymptotic variance and derive the asymptotic distribution of the test statistic under the clayton model then we extend the test statistic to incorporate censoring the proposed test is expected to perform well for a general class of alternatives with monotone conditional hazard ratio we examine the finite sample properties of the test statistic through simulations

global controllability for smooth nonlinear systems a geometric approach the paper consists of two parts in part i a global controllability theory is constructed local controllability criteria are integrated by means of the qualitative behavior of the dynamics involved leading to a global result the relation with global observability is discussed part ii is concerned with controllability by means of two vectorfields it is well known that each connected paracompact manifold of class c k 2 leqq k leqq infty or k omega carries a globally controllable set of two c k 1 vectorfields as an application of part i we construct control systems of the form dot x x uy defined on a compact manifold with the property that for x a morse smale vectorfield with no periodic orbits there exists a large class of vectorfields y such that the system is globally controllable by means of a bang bang two valued control it is stressed that the techniques applied imply the existence of a multitude of basically different globally controllable systems with two

lie brackets and local controllability a sufficient condition for scalar input systems we develop a general formalism based on exponential lie series which can be used to study control variations we apply the formalism to prove a result conjectured by h hermes that gives a sufficient condition for small time local controllability for single input systems

robust bayesian inference in elliptical regression models broadening the stochastic assumptions on the error terms of regression models was prompted by the analysis of linear multivariate t models in zellner 1976 we consider a possibly nonlinear regression model under any multivariate elliptical data density and examine bayesian posterior and predictive results the latter are shown to be robust with respect to the specific choice of a sampling density within this elliptical class in particular sufficient conditions for such model robustness are that we single out a precision factor 2 on which we can specify an improper prior density apart from theb posterior distribution of this nuisance parameter 2 the entire analysis will then be completely unaffected by departures from normality similar results hold in finite mixtures of such elliptical densities which can be used to average out specification uncertainty

on local controllability let x y be real analytic vector fields on a real analytic n dimensional manifold m consider a control system on m with dynamics described by 1 qquad dx dt x x t u t y x t quad x 0 p where an admissible control is lebesgue measurable with values u t leqq 1 the relationship between the map 2 qquad s 1 cdots s n to exp s 1 y circ cdots circ exp s n text ad n 1 x y circ exp tx p being one one on a neighborhood of 0 in mathbb r n for each 0 t varepsilon and other known necessary conditions for local controllability are studied in dimension n 2 many necessary conditions are equivalent and also sufficient for n geqq 3 the map 2 being locally one one implies many necessary conditions are satisfied but these need not be sufficient examples which illustrate what occurs geometrically are given

molecular dynamics and time reversibility we present a time symmetrical integer arithmetic algorithm for numerical molecular dynamics simulations of classical fluids this algorithm is used to illustrate through concrete examples that time asymmetric evolutions are typical for systems of many particles evolving according to reversible microscopic dynamics and to calculate the asymptotic behavior of the velocity autocorrelation function with an improved accuracy the equivalence between equilibrium time averages and microcanonical ensemble averages is checked via two new sampling methods for computing microcanonical averages of classical systems

billiards correlation functions we discuss various experiments on the time decay of velocity autocorrelation functions in billiards we perform new experiments and find results which are compatible with an exponential mixing hypothesis first put forward by friedman and martin fm they do not seem compatible with the stretched exponentials believed in spite of fm and more recently of chernov to describe the mixing the analysis leads to several byproducts we obtain information about the normal diffusive nature of the motion and we consider the probability distribution of the number of collisions in timetm astm finding a strong dependence on some geometric characteristics of the locus of the billiard obstacles

controllability in codimension one abstract local and global controlability of analytic affine control systems with an arbitrary number of controls are studied assuming strong accessibility of and codimension one of the lie algebra t generated by the input vector fields i e dim t p n 1 at every p m controls are assumed to have no a priori bound from the study of the set h where a necessary condition for local controllability at a point is verified and assuming some transversality relations an easy to verify geometric condition is proved h is a submanifold and is locally controllable at every point of h outside a codimension one submanifold a geometric sufficient condition for global controllability on simply connected manifolds is then obtained if every leaf of t intersects the manifold h and some transversality relations including those involved in the local condition are verified is globally controllable

local controllability of scalar input systems on 3 manifolds abstract local controllability of generic c k pairs of vector fields in a three dimensional connected manifold m is studied showing that in general a necessary condition is also sufficient on an open dense subset of the set of points where it is verified the results obtained are used to determine local controllability for scalar input affine control systems

conformally symplectic dynamics and symmetry of the lyapunov spectrum a generalization of the hamiltonian formalism is studied and the symmetry of the lyapunov spectrum established for the resulting systems the formalism is applied to the gausssian isokinetic dynamics of interacting particles with hard core collisions and other systems

local controllability of nonlinear systems abstract the local controllability of control systems with an arbitrary number of controls is considered first on an open set and then at a given point necessary conditions are derived concerning the lie algebra t generated by the input vector fields and applied to gradient systems the main results are a geometric sufficient condition for local controllability at a point and an equivalent condition based on the computation of lie brackets assuming t to be n 1 dimensional

temporal asymmetry of fluctuations in the nonequilibrium fpu model abstract the large deviation theory recently developed by bertini de sole gabrielli jona lasinio and landim is meant to extend the onsager machlup theory to nonequilibrium phenomena and predicts that the fluctuations of densities and currents in certain stochastic processes are not symmetric with respect to the time reversal operation in this paper several notions of fluctuations are introduced for deterministic systems and it is observed that temporally asymmetric not necessarily large fluctuations are ubiquitous even in the context of time reversal invariant dynamics of particle systems in nonequilibrium states to illustrate these ideas the nonequilibrium fpu chain devised by lepri livi and politi is studied in detail

n dimensional controllability with n 1 controls let m be a connected real analytic n dimensional manifold f g 1 g n 1 be complete real analytic vector fields on m which are linearly independent at some point of m and u 1 u n 1 be real valued controls consider the controllability of the system dot x t f x t sum min i 1 max n 1 u i t g i x t x 0 x 0 in m necessary and sufficient conditions are given so that this system is controllable on any simply connected domain d contained in m on which g 1 g n 1 are linearly independent these conditions depend on the computation of lie brackets at those points where f g 1 g n 1 are linearly dependent

geometric conditions for local controllability abstract small time local controllability of a c1 affine control system with a generic drift vector field and n 1 linearly independent input vector fields on an n dimensional connected c1 manifold m is studied showing that a necessary condition namely the drift vector field belonging to the convex hull of the control vector fields at the given point is also sufficient on an open dense subset h1 of the set of points where it is verified local controllability at the points in the interior of h 1 is also considered when the input vector fields generate an involutive distribution and a criterion based on the type of contract of h with the hyperplane spanned by the input vector fields is proved an example shows a situation where the sufficient condition for small time local controllability of h sussmann siam j control option 25 1987 158 194 cannot be applied but in which the method now presented distinguishes the possible cases

local controllability along a reference trajectory abstract local controllability along a reference trajectory of analytic and smooth affine single input control systems without any a priori bounds on the control is considered and a geometric proof of a version of the hermes conjecture is given

frank s family of bivariate distributions summary this paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent the proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the frechet bounds as well as the distribution corresponding to independent variables three nonparametric estimators of the association parameter are suggested and monte carlo experiments are used to compare their small sample behaviour to that of the maximum likelihood estimate

chaotic principle some applications to developed turbulence some models for developed turbulence are considered they are shown to obey a large fluctuations theorem and one of them also obeys a response reciprocity relation of onsager type this illustrates and extends ideas and techniques developed in earlier works mainly for nonequilibrium problems in statistical mechanics

modeling random effects for censored data by a multivariate normal regression model summary a normal distribution regression model with a frailty like factor to account for statistical dependence between the observed survival times is introduced this model as opposed to standard hazard based frailty models has survival times that conditional on the shared random effect have an accelerated failure time representation the dependence properties of this model are discussed and maximum likelihood estimation of the model s parameters is considered a number of examples are considered to illustrate the approach the estimated degree of dependence is comparable to other models but the present approach has the advantage that the interpretation of the random effect is simpler than in the frailty model

flexible maximum likelihood methods for bivariate proportional hazards models this article presents methodology for multivariate proportional hazards ph regression models the methods employ flexible piecewise constant or spline specifications for baseline hazard functions in either marginal or conditional ph models along with assumptions about the association among lifetimes because the models are parametric ordinary maximum likelihood can be applied it is able to deal easily with such data features as interval censoring or sequentially observed lifetimes unlike existing semiparametric methods a bivariate clayton model 1978 biometrika 65 141 151 is used to illustrate the approach taken because a parametric assumption about association is made efficiency and robustness comparisons are made between estimation based on the bivariate clayton model and working independence methods that specify only marginal distributions for each lifetime variable

local controllability in 3 manifolds small time local controllability of a two input ck affine control system on a 3 dimesional connected ck manifold m is studied showing that in general a necessary condition is also sufficient on an open dense subset of the set of points where it is verified an example shows a situation where the sufficient condition for small time local controllability of sussmann 8 cannot be applied but in which the method now presented distinguishes the possible cases

chaotic hypothesis onsager reciprocity and fluctuation dissipation theorem it is shown that the chaoticity hypothesis recently introduced in statistical mechanics which is analogous to ruelle s principle for turbulence implies the onsager reciprocity and the fluctuation dissipation theorem in various reversible models for coexisting transport phenomena

control systems which generate decomposable lie algebras let x y be real analytic vector fields on an n manifold m ad x y x y denote the lie product inductively ad k 1 x y x ad k x y and 1 ad v x y v 0 the attainable set at time t denoted download full size image t for the control system 1 x x x u t y x x 0 p u t 1 is contained in the integral manifold through p of the lie algebra l 1 generated by 1 l 1 is said to be decomposable at p if essentially when dim l 1 p n the solution of 1 can be written as exp tx exp f 1 t u v 1 exp f n t u v n p with v 1 v n l 1 this is true for example at any p if l 1 is nilpotent the f i t u are shown to satisfy a system on n of the form 2 x i u t g i t x 1 x i 1 x i 0 0 i 1 n where if l 1 is nilpotent each g i is a polynomial in x 1 x i 1 in this case reachability properties of 2 for controls being countably additive measures impluses reduce to the study of algebraic equations homogeneity allows these to be considered on projective space n giving local results by bezout s theorem similar results hold for controls in the unit ball of krener s results on approximating systems of the form 1 by systems which generate nilpotent lie algebras can then be used to remove the condition that l 1 be nilpotent the method applies to show that if m denotes the set of all products of k elements of 1 with k m and dim span m 1 p dim span m for all odd m then exp tx p int download full size image t for all t 0

bivariate location scale models for regression analysis with applications to lifetime data summary the literature on multivariate linear regression includes multivariate normal models models that are used in survival analysis and a variety of models that are used in other areas such as econometrics the paper considers the class of location scale models which includes a large proportion of the preceding models it is shown that for complete data the maximum likelihood estimators for regression coefficients in a linear location scale framework are consistent even when the joint distribution is misspecified in addition gains in efficiency arising from the use of a bivariate model as opposed to separate univariate models are studied a major area of application for multivariate regression models is to clustered parallel lifetime data so we also study the case of censored responses estimators of regression coefficients are no longer consistent under model misspecification but we give simulation results that show that the bias is small in many practical situations gains in efficiency from bivariate models are also examined in the censored data setting the methodology in the paper is illustrated by using lifetime data from the diabetic retinopathy study

on the definition of entropy production via examples we present a definition of entropy production rate for classes of deterministic and stochastic dynamics the point of departure is a gibbsian representation of the steady state path space measure for which the density is determined with respect to the time reversed process the gibbs formalism is used as a unifying algorithm capable of incorporating basic properties of entropy production in nonequilibrium systems our definition is motivated by recent work on the gallavotti cohen local fluctuation theorem and it is illustrated via a number of examples