on the method of tangent hyperbolas on banach spaces abstract as an application of the technique employed by the author in a series of papers 15 18 some results are established concerning convergence of the method of tangent hyperbolas for solving nonlinear equations in banach spaces as well as existence and uniqueness of solution the results are compared with those obtained by doring 5

semiparametric inference in a model for association in bivanate survival data summary clayton s 1978 model for association in bivariate survival data is both of intrinsic importance and an interesting example of a semiparametric estimation problem that is a problem where inference about a parameter is required in the presence of nuisance functions we derive the asymptotic variance of clayton s estimator obtaining a simple explicit formula for uncensored data and indicating the modification required when the survival times are subject to arbitrary random censorship some comparisons are made with results derived by oakes 1982 for other estimators within this model in the absence of censoring the exact null variance of the score statistic corresponding to clayton s estimator is derived and compared with that of the locally most powerful rank test given by cuzick 1982

nonparametric estimation of cause specific cross hazard ratio with bivariate competing risks data we propose an alternative representation of the cause specific cross hazard ratio for bivariate competing risks data the representation leads to a simple plug in estimator unlike an existing ad hoc procedure the large sample properties of the resulting inferences are established simulations and a real data example demonstrate that the proposed methodology may substantially reduce the computational burden of the existing procedure while maintaining similar efficiency properties

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

multiple positive solutions for a class of integral inclusions this paper deals with sufficient conditions for the existence of at least two positive solutions for a class of integral inclusions arising in the traffic theory to show our main results we apply a norm type expansion and compression fixed point theorem for multivalued map due to agarwal and o regan a note on the existence of multiple fixed points for multivalued maps with applications j differential equation 160 2000 389 403

oscillations of difference equations with non monotone retarded arguments consider the first order retarded difference equation x n p n x n 0 n n 0 where p n n 0 is a sequence of nonnegative real numbers and n n 0 is a sequence of integers such that n n 1 n 0 and lim n n under the assumption that the retarded argument is non monotone a new oscillation criterion involving lim inf is established an example illustrates the case when the result of the paper implies oscillation while previously known results fail

comparison theorems and oscillation criteria for difference equations abstract first we establish the equivalence of the oscillation of the delay difference equation x n p n x n k 0 and the second order difference equation 2 y n 1 2 k 1 k k k 1 p n k k k 1 k 1 y n 0 where pn is a sequence of nonnegative real numbers and k is a positive integer next we obtain some sharp conditions for oscillations and nonoscillations of the first equation

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

quantile association for bivariate survival data bivariate survival data arise frequently in familial association studies of chronic disease onset as well as in clinical trials and observational studies with multiple time to event endpoints the association between two event times is often scientifically important in this article we examine the association via a novel quantile association measure which describes the dynamic association as a function of the quantile levels the quantile association measure is free of marginal distributions allowing direct evaluation of the underlying association pattern at different locations of the event times we propose a nonparametric estimator for quantile association as well as a semiparametric estimator that is superior in smoothness and efficiency the proposed methods possess desirable asymptotic properties including uniform consistency and root n convergence they demonstrate satisfactory numerical performances under a range of dependence structures an application of our methods suggests interesting association patterns between time to myocardial infarction and time to stroke in an atherosclerosis study

inferences on the association parameter in copula models for bivariate survival data we investigate two stage parametric and two stage semi parametric estimation procedures for the association parameter in copula models for bivariate survival data where censoring in either or both components is allowed we derive asymptotic properties of the estimators and compare their performance by simulations both parametric and semi parametric estimators of the association parameter are efficient at independence and the parameter estimates in the margins have high efficiency and are robust to misspecification of dependency structures in addition we propose a consistent variance estimator for the semi parametric estimator of the association parameter we apply the proposed methods to an aids data set for illustration

time dependent cross ratio estimation for bivariate failure times in the analysis of bivariate correlated failure time data it is important to measure the strength of association among the correlated failure times one commonly used measure is the cross ratio motivated by cox s partial likelihood idea we propose a novel parametric cross ratio estimator that is a flexible continuous function of both components of the bivariate survival times we show that the proposed estimator is consistent and asymptotically normal its finite sample performance is examined using simulation studies and it is applied to the australian twin data

on assessing the strength of dependency between failure time variates summary the correlation p between cumulative hazard variates is considered as a measure of dependence between pairs of failure time variates such correlation is readily estimated in the absence of censorship but modelling assumptions are required for its estimation in the presence of independent right censorship a semiparametric class of bivariate failure time models in which a dependence parameter 0 is in one to one correspondence with the cumulative hazard variate correlation p is considered for this purpose a simple estimating function consisting of a weighted sum over the grid formed by the observed failure times of differences between nonparametric and model restricted estimates of covariance rates is proposed for estimation and corresponding asymptotic distribution theory is given this estimation procedure is shown to lack robustness under conditions of moderate to heavy censorship motivating consideration of dependency measures that can be defined on the support of the observed failure times two such measures the correlation between marginal martingales and a cumulative cross ratio statistic are discussed and corresponding nonparametric estimators are proposed

a newton type midpoint method with high efficiency index abstract in this paper we present a newton type two step method to approximate a solution of a nonlinear equation in banach spaces we establish a semilocal convergence theorem under newton kantorovich type conditions both the convergence order and the efficiency index of the developed method are found the iterative procedure presented here is a simple modification of the newton kantorovich method however with the same number of function and derivative evaluations at each iteration it is improved in two important aspects firstly the convergence order is increased from 2 for the newton kantorovich method to 1 2 2 414 for the new method secondly the efficiency index convergence order per function evaluation is improved from 2 1 414 to 1 2 1 2 1 553 we illustrate some of our results with a numerical example

a new semilocal convergence theorem for newton s method abstract a new semilocal convergence theorem for newton s method is established for solving a nonlinear equation f x 0 defined in banach spaces it is assumed that the operator f is twice frechet differentiable and f satisfies a lipschitz type condition results on uniqueness of solution and error estimates are also given finally these results are compared with those that use kantorovich conditions

estimation of time dependent association for bivariate failure times in the presence of a competing risk this article targets the estimation of a time dependent association measure for bivariate failure times the conditional cause specific hazards ratio ccshr which is a generalization of the conditional hazards ratio chr to accommodate competing risks data we model the ccshr as a parametric regression function of time and event causes and leave all other aspects of the joint distribution of the failure times unspecified we develop a pseudo likelihood estimation procedure for model fitting and inference and establish the asymptotic properties of the estimators we assess the finite sample properties of the proposed estimators against the estimators obtained from a moment based estimating equation approach data from the cache county study on dementia are used to illustrate the proposed methodology

nonparametric estimation of bivariate failure time associations in the presence of a competing risk most research on the study of associations among paired failure times has either assumed time invariance or been based on complex measures or estimators little has accommodated competing risks this paper targets the conditional cause specific hazard ratio henceforth called the cause specific cross ratio a recent modification of the conditional hazard ratio designed to accommodate competing risks data estimation is accomplished by an intuitive non parametric method that localizes kendall s tau time variance is accommodated through a partitioning of space into bins between which the strength of association may differ inferential procedures are developed small sample performance is evaluated and the methods are applied to the investigation of familial association in dementia onset

oscillation of a quasilinear impulsive delay parabolic equation with two different boundary conditions in this paper we discuss the oscillation for a class of quasilinear impulsive delay parabolic equations with two different boundary conditions and obtain several oscillation criteria

fixed points of multivalued operators in ordered metric spaces with applications abstract the purpose of this paper is to present some new hybrid fixed point theorems involving multivalued operators which satisfy weakly generalized contractive conditions in an ordered complete metric space an example of the existence of solutions for a perturbed impulsive hyperbolic differential inclusion with variable times is given to illustrate the usability of our results

the positive solutions of nonautonomous hyperlogistic delay difference equations consider the nonautonomous hyperlogistic delay difference equation xn pnxn 1 xnkn r n 0 1 2 where pn is a sequence of positive real numbers kn a sequence of nonnegative integers such that n kn is nondecreasing and r a ratio of two odd integers our main results given sufficient conditions that guarantee every solution to be positive the conditions under which for all n 1 either xn 1 or 0 xn 1 are given respectively for the asymptotic behavior we give sufficient conditions that guarantee every positive solution to converge to the equilibrium x 1 of the model or to oscillate about 1 the results improve and generalize some recent results established by chen and yu 1 and zhou and zhang 2 some remarks and examples illustrate our theorems the methods used here are different from those in 3

a two step steffensen s method under modified convergence conditions a simplification of a third order iterative method is proposed the main advantage of this method is that it does not need to evaluate neither any frechet derivative nor any bilinear operator a semilocal convergence theorem in banach spaces under modified kantorovich conditions is analyzed a local convergence analysis is also performed finally some numerical results are presented

covariance and survivor function estimation using censored multivariate failure time data summary the covariance between counting process martingales is used to characterize the dependence between two failure time variates a representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function a closely related representation expresses the bivariate survivor function in terms of marginal survivor functions and a conditional covariance function leading to a new nonparametric survivor function estimator generalizations to higher dimensional failure time variates are also given simulation evaluations of the survivor function estimator are presented and generalizations to regression problems are outlined

nondensely defined evolution impulsive differential inclusions with nonlocal conditions in this paper we shall establish sufficient conditions for the existence of integral solutions for some nondensely defined evolution impulsive differential inclusions in banach spaces with nonlocal conditions

a note on the kantorovich theorem for newton iteration abstract in this paper a new theorem for the newton method convergence is obtained its condition is different from that of the kantorovich theorem and therefore it has theoretical and practical value

semicycles of solutions of nonlinear difference equations with several delays abstract in this paper we study the semicycles of oscillatory solutions of nonlinear difference equation with several delays where pi n is a real sequence with pi n 0 for all large n l mi kij are positive integers ij i 1 2 l j 1 2 mi are nonnegative real numbers with mij 1 ij 1 i 1 2 l upper bound of numbers of terms of semicycles are determined

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

oscillations of delay difference equations in a critical state consider the first order delay difference equation xn i 1m pi n xn ki 0 n 0 1 2 in the case where lim infn pi n pi 0 ki 0 i 1 2 a necessary and sufficient condition for the oscillation of all solutions of the above equation is established in the critical state that the corresponding limiting equation xn i 1m pixn ki 0 n 0 1 2 admits a nonoscillatory solution it is to be pointed out that there is no result in this critical state for a delay difference equation with more than one delay argument

an estimate of numbers of terms of semicycles of delay difference equations in this paper we study the semicycles of oscillatory solutions of the delay difference equation yn 1 yn pnyn k 0 where pn is a sequence of nonnegative real numbers and k is a positive integer upper bound of numbers of terms of semicycles are determined in the case when our results improve and complement known results in literature

global bounds and asymptotics for a system of reaction diffusion equations on etudie le probleme aux valeurs limites non lineaire u t a u u v dans r v t c u d v u v dans r avec les conditions u v 0 sur r et u 0 x u 0 x v 0 x v 0 x dans on etablit l existence de solutions globales fortes et on etudie leur comportement quand t

on the convergence of modified newton methods for solving equations containing a non differentiable term we provide a semilocal convergence analysis for certain modified newton methods for solving equations containing a non differentiable term the sufficient convergence conditions of the corresponding newton methods are often taken as the sufficient conditions for the modified newton methods that is why the latter methods are not usually treated separately from the former however here we show that weaker conditions as well as a finer error analysis than before can be obtained for the convergence of modified newton methods numerical examples are also provided

oscillations of difference equations with several delays abstract consider the first order delay difference equation where lim infn pi n pi 0 ki 0 i 1 2 sufficient conditions for the oscillation of all solutions of the above equation are established in the case when the corresponding limiting equation admits nonoscillatory solutions oscillation criteria for the nonlinear difference equation are also derived as applications

permanence oscillation and attractivity of the discrete hematopoiesis model with variable coefficients abstract in this paper we consider the nonlinear delay difference equation with periodic coefficients p n 1 p n n p n n 1 p n m and demonstrate that solutions are permanent the existence of a positive periodic solution is proven and sufficient conditions for the attractivity of this solution are obtained oscillation and nonoscillation about the positive periodic solution is considered

existence theory for perturbed impulsive hyperbolic differential inclusions with variable times in this paper the existence of solutions for a perturbed impulsive hyperbolic differential inclusion with variable times is proved under the mixed generalized lipschitz and caratheodory s conditions

modelling multivariate failure time associations in the presence of a competing risk there has been much research on analysing multivariate failure times but little that has accommodated failures that arise in the presence of a competing failure process this paper studies the problem of describing associations among times to such failures it proposes a modified conditional hazard ratio measure of association that is tailored to competing risks data develops frailty models and a nonparametric method for describing the proposed measure and contrasts estimation by proposed methods with the standard of treating competing risks as independently censoring failure times due to targeted causes the methods are investigated on simulated and real data

comparison principles for impulsive hyperbolic equations of first order strong and weak comparison principles for impulsive hyperbolic equations of first order are proved uniqueness criterion is obtained

nonlinear impulse evolution systems and applications to population models abstract we apply results on the existence uniqueness and stability of solutions obtained previously for the abstract impulse evolution system to the study of the mathematical model of population subject to abrupt changes of important biological parameters caused by harvesting diseases immigration etc

a cell population model described by impulsive pdes existence and numerical approximation this paper considers a cell population model described by impulsive pdes existence and numerical approximation of solutions are investigated by showing that the related operator a x ddx on c0 generates a strongly conitunous semigroups under general assumption on a x we prove the existence of the solution of the nonlinear problem with impulses and given approximation of the solution of the homogenuous equation

strong ergodic properties of a first order partial differential equation on etudie l equation differentielle d ordre 1 u t c x u x f x u pour t x 0 0 1 avec la condition initiale u 0 x v x pour x 0 1 on demontre l existence d une mesure invariante exacte ayant certaines proprietes supplementaires

on first order impulsive partial differential inequalities abstract this paper deals with the cauchy problem for nonlinear impulsive partial differential equations of first order theorems on impulsive differential inequalities are obtained comparison results implying uniqueness criteria are proved

the semicycles of solutions of delay difference equations in this paper we study the semicycles of oscillatory solutions of the delay difference equation yn 1 yn pnyn k 0 where pn is is a sequence of nonnegative real numbers and k is a positive integer upper bound of numbers of terms of semicycles are determined