statistical inference procedures for bivariate archimedean copulas abstract a bivariate distribution function h x y with marginals f x and g y is said to be generated by an archimedean copula if it can be expressed in the form h x y 1 f x g y for some convex decreasing function defined on 0 1 in such a way that 1 0 many well known systems of bivariate distributions belong to this class including those of gumbel ali mikhail haq thelot clayton frank and hougaard frailty models also fall under that general prescription this article examines the problem of selecting an archimedean copula providing a suitable representation of the dependence structure between two variates x and y in the light of a random sample x 1 y 1 x n y n the key to the estimation procedure is a one dimensional empirical distribution function that can be constructed whether the uniform representation of x and y is archimedean or not and independently of their marginals this semiparametric estimator based on a decomposition of kendall s tau statistic

adaptation of bivariate frailty models for prediction with application to biological markers as prognostic indicators serial biological markers are often used in medicine as prognostic indicators for example elevated tumour antigen tests presage tumour recurrence rapid decrease in the cd4 cell counts of hiv individuals indicate high risk for developing aids methods for evaluating the usefulness of markers should address how the prediction of future risk is revised in a way that assists the making of decisions at the time such an indicator is observed proportional hazards modelling with time varying covariates a common approach seems unnatural for this purpose because its orientation is explanatory it addresses the question is the individual suffering a failure more likely to have had the marker and allows use of all information prior to the failure rather than the more relevant predictive question does the appearance of the marker alter the individual s subsequent risk enough to warrant intervention today frailty models do address this question but available methods for their analysis make censoring assumptions which are inappropriate in the predictive setting we adapt frailty models to relevant censoring processes and propose a predictively oriented test statistic and a related estimation procedure based on summing concurrent martingales each representing a landmark analysis

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

a two sample comparison for multiple ordered event data summary a longitudinal study is conducted to compare the process of a particular disease between two groups the process of the disease is monitored according to which of several ordered events occur in the paper the sojourn time between two successive events is considered as the outcome of interest the group effects on the sojourn times of the multiple events are parameterized by scale changes in a semiparametric accelerated failure time model where the dependence structure among the multivariate sojourn times is unspecified suppose that the sojourn times are subject to dependent censoring and the censoring times are observed for all subjects a log rank type estimating approach by rescaling the sojourn times and the dependent censoring times into the same distribution is constructed to estimate the group effects and the corresponding estimators are consistent and asymptotically normal without the dependent censoring the independent censoring times in general are not available for the uncensored data in order to complete the censoring information pseudo censoring times are generated from the corresponding nonparametrically estimated survival function in each group and we can still obtained unbiased estimating functions for the group effects a real application and a simulation study are conducted to illustrate the proposed methods

a resampling method based on pivotal estimating functions summary suppose that under a semiparametric model setting one is interested in drawing inferences about a finite dimensi onal parameter vector based on an estimating function generally a consistent point estimator j for 0 the true value for j can be easily obtained by finding a root of the corresponding estimating equation to estimate the variance of ft however may involve complicated and subjective nonparametric functional estimates in this paper a general and simple resampling method for inferences about js0 based on pivotal estimating functions is proposed the new procedure is illustrated with the quantile and rank regression models for both cases our proposal can be easily and efficiently implemented with existing statistical software

brief paper controllability of boolean control networks via the perron frobenius theory boolean control networks bcns are recently attracting considerable interest as computational models for genetic and cellular networks addressing control theoretic problems in bcns may lead to a better understanding of the intrinsic control in biological systems as well as to developing suitable protocols for manipulating biological systems using exogenous inputs we introduce two definitions for controllability of a bcn and show that a necessary and sufficient condition for each form of controllability is that a certain nonnegative matrix is irreducible or primitive respectively our analysis is based on a result that may be of independent interest namely a simple algebraic formula for the number of different control sequences that steer a bcn between given initial and final states in a given number of time steps while avoiding a set of forbidden states

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

testing the assumption of independence of truncation time and failure time summary for data subject to random censorship it is well known that the assumption of independence between censoring time and failure time cannot be tested nonparametrically for data subject to random truncation however it is possible to test independence of truncation time and failure time a statistic generalizing kendall s tau is proposed for testing the independence assumption and asymptotic properties under the null hypothesis are derived a conditional permutation test is also derived for small data sets generalization to allow right censoring and an application to truncated linear regression are also briefly discussed

stability of discrete time switching systems with constrained switching sequences we introduce a novel framework for the stability analysis of discrete time linear switching systems with switching sequences constrained by an automaton the key element of the framework is the algebraic concept of multinorm which associates a different norm per node of the automaton and allows to exactly characterize stability building upon this tool we develop the first arbitrarily accurate approximation schemes for estimating the constrained joint spectral radius that is the exponential growth rate of a switching system with constrained switching sequences more precisely given a relative accuracy r 0 the algorithms compute an estimate of within the range 1 r these algorithms amount to solve a well defined convex optimization program with known time complexity and whose size depends on the desired relative accuracy r 0

the boundedness of all products of a pair of matrices is undecidable we show that the boundedness of the set of all products of a given pair sigma of rational matrices is undecidable furthermore we show that the joint or generalized spectral radius rho sigma is not computable because testing whether rho sigma less than or equal to1 is an undecidable problem as a consequence the robust stability of linear systems under time varying perturbations is undecidable and the same is true for the stability of a simple class of hybrid systems we also discuss some connections with the so called finiteness conjecture our results are based on a simple reduction from the emptiness problem for probabilistic finite automata which is known to be undecidable c 2000 elsevier science b v all rights reserved

approximation of the constrained joint spectral radius via algebraic lifting this paper studies the linear constrained switching system which is a discrete time switched linear system whose switching sequences are constrained by a deterministic finite automaton the stability of a constrained switching system is characterized by its constrained joint spectral radius that is known to be difficult to compute or approximate using the semi tensor product of matrices the matrix form expression of a constrained switching system is shown to be equivalent to that of a lifted arbitrary switching system then the constrained joint generalized spectral radius of a constrained switching system is proved to be equal to the joint generalized spectral radius of its lifted arbitrary switching system which can be approximated by off the shelf algorithms

stability analysis of switched linear systems defined by regular languages in this work we study the stability of an autonomous discrete time linear switched system whose switching sequences are generated by a muller automaton this system arises in various engineering problems such as distributed communication and automotive engine control the asymptotic stability of this system referred to as regular asymptotic stability ras generalizes two well known definitions of stability of autonomous discrete time linear switched systems namely absolute asymptotic stability aas and shuffle asymptotic stability sas we also extend these stability definitions to robust versions we show that absolute asymptotic stability robust absolute asymptotic stability and robust shuffle asymptotic stability are equivalent to exponential stability in addition by using the kronecker product we prove that a robust regular asymptotic stability problem is equivalent to the conjunction of several robust absolute asymptotic stability problems

sets of matrices all infinite products of which converge an infinite product iit lmi of matrices converges on the right if limi m mi exists a set z ai i l of n x n matrices is called an rcp set rightconvergent product set if all infinite products with each element drawn from z converge such sets of matrices arise in constructing self similar objects like von koch s snowflake curve in various interpolation schemes in constructing wavelets of compact support and in studying nonhomogeneous markov chains this paper gives necessary conditions and also some sufficient conditions for a set x to be an rcp set these are conditions on the eigenvalues and left eigenspaces of matrices in 2 and finite products of these matrices necessary and sufficient conditions are given for a finite set z to be an rcp set having a limit function m d rit lad where d d d which is a continuous function on the space of all sequences d with the sequence topology finite rcp sets of column stochastic matrices are completely characterized some results are given on the problem of algorithmically deciding if a given set x is an rcp set

semiparametric inferences for association with semi competing risks data in many biomedical studies it is of interest to assess dependence between bivariate failure time data we focus here on a special type of such data referred to as semi competing risks data in this article we develop methods for making inferences regarding dependence of semi competing risks data across strata of a discrete covariate z a class of rank statistics for testing constancy of association across strata are proposed its asymptotic properties are also derived we develop a novel resampling based technique for calculating the variances of the proposed test statistics in addition we develop methods for combining test statistics for assessing marginal effects of z on the dependent censoring variable as well as its effects on association the finite sample properties of the proposed methodology are assessed using simulation studies and they are applied to data from a leukaemia transplantation study copyright 2005 john wiley sons ltd

matrix approach to model matching of asynchronous sequential machines in this note we propose a matrix based approach for asynchronous sequential machines using semi tensor product of matrices we convert an asynchronous machine into a discrete time bilinear system and study its dynamics by investigating its structure matrices we give simple algorithms for cycle detection and reachability analysis and moreover provide a control design method for the model matching of two input state machines

model selection and semiparametric inference for bivariate failure time data abstract we propose model selection procedures for bivariate survival models for censored data generated by the archimedean copula family in route to constructing the selection methodology we develop estimates of some time dependent association measures including estimates of the local and global kendall s tau local odds ratio and other measures defined throughout the literature we propose a goodness of fit based model selection methodology as well as a graphical approach we show that the proposed methods have desirable asymptotic properties and perform well in finite samples

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

a linear representation of dynamics of boolean networks a new matrix product called semi tensor product of matrices is reviewed using it a matrix expression of logic is proposed where a logical variable is expressed as a vector a logical function is expressed as a multiple linear mapping under this framework a boolean network equation is converted into an equivalent algebraic form as a conventional discrete time linear system analyzing the transition matrix of the linear system formulas are obtained to show a the number of fixed points b the numbers of cycles of different lengths c transient period for all points to enter the set of attractors and d basin of each attractor the corresponding algorithms are developed and used to some examples

computing the joint spectral radius this paper presents algorithms for finding an arbitrarily small interval that contains the joint spectral radius of a finite set of matrices it also presents a numerical criterion for verifying in certain cases that the joint spectral radius is the maximum of the spectral radii of the given matrices error bounds are derived for the case where calculations are done with finite precision and the matrices are not known exactly the algorithms are implemented and applied to estimate holder exponents of the orthonormal wavelets n constructed by daubechies for 3 n 8

boosted string representation and its application to video surveillance this paper presents a new behavior analysis system for analyzing human movements via a boosted string representation first of all we propose a triangulation based method to transform each action sequence into a set of symbols then an action sequence can be interpreted and analyzed using this string representation to analyze action sequences with this string representation three practical problems should be tackled usually an action sequence has different temporal scaling changes different initial states and symbol converting errors traditional methods like hidden markov models and finite state machines have limited abilities to deal with the above problems since many unknown states should be constructed and initialized to tackle the problems a novel string hypothesis generator is then proposed for generating a bank of string features from which different invariant features can be learned for classifying behaviors more accurately to learn the invariant features the adaboost algorithm is used and modified to train a strong classifier from the set of string hypotheses so that multiple human action events can be well classified in addition a forward classification scheme is proposed to classify all input action sequences more accurately even though they have various scaling changes and coding errors experimental results prove that the proposed method is a robust accurate and powerful tool for human movement analysis

approximation of the joint spectral radius using sum of squares we provide an asymptotically tight computationally efficient approximation of the joint spectral radius of a set of matrices using sum of squares sos programming the approach is based on a search for an sos polynomial that proves simultaneous contractibility of a finite set of matrices we provide a bound on the quality of the approximation that unifies several earlier results and is independent of the number of matrices additionally we present a comparison between our approximation scheme and earlier techniques including the use of common quadratic lyapunov functions and a method based on matrix liftings theoretical results and numerical investigations show that our approach yields tighter approximations

joint spectral radius and path complete graph lyapunov functions we introduce the framework of path complete graph lyapunov functions for approximation of the joint spectral radius the approach is based on the analysis of the underlying switched system via inequalities imposed among multiple lyapunov functions associated to a labeled directed graph inspired by concepts in automata theory and symbolic dynamics we define a class of graphs called path complete graphs and show that any such graph gives rise to a method for proving stability of the switched system this enables us to derive several asymptotically tight hierarchies of semidefinite programming relaxations that unify and generalize many existing techniques such as common quadratic common sum of squares path dependent quadratic and maximum minimum of quadratics lyapunov functions we compare the quality of approximation obtained by certain classes of path complete graphs including a family of dual graphs and all path complete graphs with two nodes on an alphabet of two matrices we derive approximation guarantees for several families of path complete graphs such as the de bruijn graphs this provides worst case performance bounds for path dependent quadratic lyapunov functions and a constructive converse lyapunov theorem for maximum minimum of quadratics lyapunov functions

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