survival analysis using a scale change random effects model abstract frailty models are effective in broadening the class of survival models and inducing dependence in multivariate survival distributions in proportional hazards the random effect multiplies the hazard function the scale change model incorporates unobserved heterogeneity through a random effect that enters the baseline hazard function to change the time scale we interpret this random effect as frailty or other unobserved risks that create heterogeneity in the population this model produces a wide range of shapes for univariate survival and hazard functions we extend this model to multivariate survival data by assuming that members of a group share a common random effect this structure induces association among the survival times in a group and provides alternative association structures to the proportional hazards frailty model we present parametric and semiparametric estimation techniques and illustrate these methods with an example

non uniform specification and large deviations for weak gibbs measures we establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak gibbs measures under some mild assumptions we obtain upper and lower bounds for the measure of deviation sets of some non uniformly expanding maps including quadratic maps and robust multidimensional non uniformly expanding local diffeomorphisms for that purpose a measure theoretical weak form of specification is introduced and proved to hold for the robust classes of multidimensional non uniformly expanding local diffeomorphisms and viana maps

on the cox model with time varying regression coefficients in the analysis of censored failure time observations the standard cox proportional hazards model assumes that the regression coefficients are time invariant often these parameters vary over time and the temporal covariate effects on the failure time are of great interest in this article following previous work of cai and sun we propose a simple estimation procedure for the cox model with time varying coefficients based on a kernel weighted partial likelihood approach we construct pointwise and simultaneous confidence intervals for the regression parameters over a properly chosen time interval via a simple resampling technique we derive a prediction method for future patients survival with any specific set of covariates building on the estimates for the time varying coefficients we also consider the mixed case and present an estimation procedure for time independent parameters in the model furthermore we show how to use an integrated function of the estimate for a specific regression coeffic

estimating treatment effects with treatment switching via semicompeting risks models an application to a colorectal cancer study treatment switching is a frequent occurrence in clinical trials where during the course of the trial patients who fail on the control treatment may change to the experimental treatment analysing the data without accounting for switching yields highly biased and inefficient estimates of the treatment effect in this paper we propose a novel class of semiparametric semicompeting risks transition survival models to accommodate treatment switches theoretical properties of the proposed model are examined and an efficient expectation maximization algorithm is derived for obtaining the maximum likelihood estimates simulation studies are conducted to demonstrate the superiority of the model compared with the intent to treat analysis and other methods proposed in the literature the proposed method is applied to data from a colorectal cancer clinical trial

partially linear hazard regression with varying coefficients for multivariate survival data summary the paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data a profile pseudo partial likelihood estimation method is proposed the estimation of the parameters of the linear part is accomplished via maximization of the profile pseudo partial likelihood whereas the varying coefficient functions are considered as nuisance parameters that are profiled out of the likelihood it is shown that the estimators of the parameters are root n consistent and the estimators of the non parametric coefficient func tions achieve optimal convergence rates asymptotic normality is obtained for the estimators of the finite parameters and varying coefficient functions consistent estimators of the asymptotic variances are derived and empirically tested which facilitate inference for the model we prove that the varying coefficient functions can be estimated as well as if the parametric components were known and the failure times within each subject were independent simulations are con ducted to demonstrate the performance of the estimators proposed a real data set is analysed to illustrate the methodology proposed

the aalen additive gamma frailty hazards model in this paper we consider clustered right censored time to event data such data can be analysed either using a marginal model if one is interested in population effects or using so called frailty models if one is interested in covariate effects on the individual level and in estimation of correlation the cox frailty model has been studied extensively in the last decade or so and estimation techniques and large sample results are now available it is however difficult to deal with time changing covariate effects when using the cox model an appealing alternative model is the aalen additive hazards model in which it is easy to work with time dynamics in this paper we describe an innovative approach to estimation in the aalen additive gamma frailty hazards model we give the large sample properties of the estimators and investigate their small sample properties by monte carlo simulation a real example is provided for illustration copyright 2011 oxford university press

efficient estimation and inferences for varying coefficient models abstract this article deals with statistical inferences based on the varying coefficient models proposed by hastie and tibshirani local polynomial regression techniques are used to estimate coefficient functions and the asymptotic normality of the resulting estimators is established the standard error formulas for estimated coefficients are derived and are empirically tested a goodness of fit test technique based on a nonparametric maximum likelihood ratio type of test is also proposed to detect whether certain coefficient functions in a varying coefficient model are constant or whether any covariates are statistically significant in the model the null distribution of the test is estimated by a conditional bootstrap method our estimation techniques involve solving hundreds of local likelihood equations to reduce the computational burden a one step newton raphson estimator is proposed and implemented the resulting one step procedure is shown to save computational cost on an order of tens with no

on contact anosov flows exponential decay of correlations for co 4 contact anosov flows is established this implies in particular exponential decay of correlations for all smooth geodesic flows in strictly negative curvature

zero entropy dynamical systems with the gluing orbit property abstract under the assumption of the gluing orbit property equivalent conditions to having zero topological entropy are investigated in particular we show that a dynamical system has the gluing orbit property and zero topological entropy if and only if it is minimal and equicontinuous

non uniform hyperbolicity and universal bounds for s unimodal maps an s unimodal map f is said to satisfy the collet eckmann condition if the lower lyapunov exponent at the critical value is positive if the infimum of the lyapunov exponent over all periodic points is positive then f is said to have a uniform hyperbolic structure we prove that an s unimodal map satisfies the collet eckmann condition if and only if it has a uniform hyperbolic structure the equivalence of several non uniform hyperbolicity conditions follows one consequence is that some renormalization of an s unimodal map has an absolutely continuous invariant probability measure with exponential decay of correlations if and only if the collet eckmann condition is satisfied the proof uses new universal bounds that hold for any s unimodal map without periodic attractors

multifractal analysis of hyperbolic flows we establish the multifractal analysis of hyperbolic flows and of suspension flows over subshifts of finite type a non trivial consequence of our results is that for every holder continuous function non cohomologous to a constant the set of points without birkhoff average has full topological entropy

topological features of flows with the reparametrized gluing orbit property abstract the notions of shadowing specification and gluing orbit property differ substantially for discrete and continuous time dynamical systems in the present paper we continue the study of the topological and ergodic properties of continuous flows with the reparametrized periodic and nonperiodic gluing orbit properties initiated in 3 we prove these flows satisfy a weak mixing condition with respect to balls and if the flow is komuro expansive the topological entropy is a lower bound for the exponential growth rate of periodic orbits moreover we show that periodic measures are dense in the set of all invariant probability measures and that ergodic measures are generic furthermore we prove that irrational rotations and some minimal flows on tori and circle extensions over expanding maps satisfy gluing orbit properties thus emphasizing the difference of this property with respect the notion of specification

semiparametric estimation of random effects using the cox model based on the em algorithm consider a survival experiment where individuals within a certain subset of the population share a common unobservable random frailty such a frailty could be an unobservable genetic or early environmental effect if individuals were in sibling groups or an environmental effect if individuals were grouped by households suppose that if the frailty omega is known the cox proportional hazards model for the observable covariates is valid with the consequence of the random effect being a multiplicative factor on the hazard rate assuming tht the random frailties follow a gamma distribution estimates of the fixed and random effects are obtained by using an em algorithm based on a profile likelihood construction the method developed is applied to the framingham heart study to examine the risks of smoking and cholesterol levels adjusting for potential random effects

from rates of mixing to recurrence times via large deviations abstract a classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties for example the existence of invariant measures with stochastic like behaviour such as large deviations or decay of correlations such geometric structures are generally highly non trivial and thus a natural question is the extent to which this approach can be applied in this paper we show that in many cases stochastic like behaviour itself implies that the system has certain non trivial geometric properties which are therefore necessary as well as sufficient conditions for the occurrence of the statistical properties under consideration as a by product of our techniques we also obtain some new results on large deviations for certain classes of systems which include viana maps and multidimensional piecewise expanding maps

nonparametric survival analysis with time dependent covariate effects a penalized partial likelihood approach techniques are developed for nonparametric analysis of data under a cox regression like model permitting time dependent covariate effects determined by a regression function beta 0 t estimators resulting from maximization of an appropriate penalized partial likelihood are shown to exist and a computational approach is outlined weak uniform consistency with a rate of convergence and pointwise asymptotic normality of the estimators are established under regularity conditions a consistent estimator of a common baseline hazard function is presented and used to construct a consistent estimator of the asymptotic variance of the estimator of the regression function extensions to multiple covariates general relative risk functions and time dependent covariates are discussed

stability of mixing and rapid mixing for hyperbolic flows we obtain general results on the stability of mixing and rapid mixing superpolynomial decay of correlations for hyperbolic flows amongst c r axiom a flows r 2 we show that there is a c 2 open c r dense set of flows for which each nontrivial hyperbolic basic set is rapid mixing this is the first general result on the stability of rapid mixing or even mixing for axiom a

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

large deviations for countable to one markov systems in this paper we study large deviation properties for countable to one markov systems associated to weak gibbs measures for non holder potentials furthermore we establish multifractal large deviation laws for countable to one piecewise conformal markov systems which are derived systems constructed over hyperbolic regions for certain nonhyperbolic systems exhibiting intermittency we apply our results to higher dimensional number theoretical transformations

large deviations for nonuniformly hyperbolic systems we obtain large deviation estimates for a large class of nonuniformly hyperbolic systems namely those modelled by young towers with summable decay of correlations in the case of exponential decay of correlations we obtain exponential large deviation estimates given by a rate function in the case of polynomial decay of correlations we obtain polynomial large deviation estimates and exhibit examples where these estimates are essentially optimal in contrast with many treatments of large deviations our methods do not rely on thermodynamic formalism hence for holder observables we are able to obtain exponential estimates in situations where the space of equilibrium measures is not known to be a singleton as well as polynomial estimates in situations where there is not a unique equilibrium measure

spectral theory zeta functions and the distribution of periodic points for collet eckmann maps we study unimodal interval mapst with negative schwarzian derivative satisfying the collet eckmann condition dtn tc k cn for some constantsk 0 and c 1 c is the critical point oft we prove exponential mixing properties of the unique invariant probability density oft describe the long term behaviour of typical in the sense of lebesgue measure trajectories by central limit and large deviations theorems for partial sum processes of the form s n sigma i 0 n 1 f t i x and study the distribution of typical periodic orbits also in the sense of a central limit theorem and a large deviations theorem

some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates abstract recurrent event time data are common in medical research examples include infections in aids patients and seizures in epilepsy patients in this context as well as in the more usual context of a single failure time variable time dependent covariates are frequently of interest we suggest some rate functions that might be displayed when analyzing recurrent failure time data or when the effect of a categorical time dependent covariate is of interest estimators of these functions are provided along with two sample test statistics a new approach to regression modeling of these data is suggested and contrasted with existing methods our methods do not require that an explicit model be formulated for the probabilistic association between failure times within an individual this is in line with the currently popular generalized estimating equation approach to longitudinal data if the nature of such associations is known or is of particular interest then alternative methods may be appropriate

vector fields with topological stability in this paper we give a characterization of the structurally stable vector fields by making use of the notion of topological stability more precisely it is proved that the c1 interior of the set of all topologically stable c1 vector fields coincides with the set of all vector fields satisfying axiom a and the strong transversality condition

variable selection for cox s proportional hazards model and frailty model a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in fan and li 2001a it has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance such a property is called an oracle property the proposed procedures were illustrated in the context of linear regression robust linear regression and generalized linear models in this paper the nonconcave penalized likelihood approach is extended further to the cox proportional hazards model and the cox proportional hazards frailty model two commonly used semi parametric models in survival analysis as a result new variable selection procedures for these two commonly used models are proposed it is demonstrated how the rates of convergence depend on the regularization parameter in the penalty function further with a proper choice of the regularization parameter and the penalty function the proposed estimators possess an oracle property standard error formulae are derived and their accuracies are empirically tested simulation studies show that the proposed procedures are more stable in prediction and more effective in computation than the best subset variable selection and they reduce model complexity as effectively as the best subset variable selection compared with the lasso which is the penalized likelihood method with the l 1 penalty proposed by tibshirani the newly proposed approaches have better theoretic properties and finite sample performance

on iterations of 1 ax 2 on 1 1 on etudie des iterations de f x a 1 ax u 2 1 x 1 ou a est un parametre dans l intervalle 0 2 on etablit la non existence de cycles attractifs on definit une partition on donne une estimation uniforme de la a derivee

on simon s two stage design for single arm phase iia cancer clinical trials under beta binomial distribution simon control clin trials 1989 10 1 10 s two stage design has been broadly applied to single arm phase iia cancer clinical trials in order to minimize either the expected or the maximum sample size under the null hypothesis of drug inefficacy i e when the pre specified amount of improvement in response rate rr is not expected to be observed this paper studies a realistic scenario where the standard and experimental treatment rrs follow two continuous distributions e g beta distribution rather than two single values the binomial probabilities in simon s control clin trials 1989 10 1 10 design are replaced by prior predictive beta binomial probabilities that are the ratios of two beta functions and domain restricted rrs involve incomplete beta functions to induce the null hypothesis acceptance probability we illustrate that beta binomial mixture model based two stage design retains certain desirable properties for hypothesis testing purpose however numerical results show that such designs may not exist under certain hypothesis and error rate type i and ii setups within maximal sample size approximately 130 furthermore we give theoretical conditions for asymptotic two stage design non existence sample size goes to infinity in order to improve the efficiency of design search and to avoid needless searching

asymptotic theory for the frailty model the frailty model is a generalization of cox s proportional hazards model which includes a random effect nielsen gill andersen and sorensen 1992 proposed an em algorithm to estimate the cumulative baseline hazard and the variance of the random effect here the asymptotic distribution of the estimators is given along with a consistent estimator of the asymptotic variance

the gluing orbit property uniform hyperbolicity and large deviations principles for semiflows abstract we introduce a gluing orbit property weaker than specification for both continuous maps and flows we prove that flows with the c 1 robust gluing orbit property are uniformly hyperbolic and that every uniformly hyperbolic flow satisfies the gluing orbit property we also prove a level 1 large deviations principle and a level 2 large deviations lower bound for semiflows with the gluing orbit property as a consequence we establish a level 1 large deviations principle for hyperbolic flows and every continuous observable and also a level 2 large deviations lower bound finally since many non uniformly hyperbolic flows can be modeled as suspension flows we also provide criteria for such flows to satisfy uniform and non uniform versions of the gluing orbit property

nonsingular star flows satisfy axiom a and the no cycle condition we give an affirmative answer to a problem of liao and mane which asks whether for a nonsingular flow to loose the stability it must go through a critical element bifurcation more precisely a vector field s on a compact boundaryless manifold is called a star system if s has a c 1 neighborhood mathcal u in the set of c 1 vector fields such that every singularity and every periodic orbit of every x in mathcal u is hyperbolic we prove that any nonsingular star flow satisfies axiom a and the no cycle condition

consistency in a proportional hazards model incorporating a random effect supported in part by the north atlantic treaty organization under a grant awarded in 1990 conducted at the mathematical institute of the university of utrecht the netherlands

semiparametric transformation models with random effects for recurrent events in this article we study a class of semiparametric transformation models with random effects for the intensity function of the counting process these models provide considerable flexibility in formulating the effects of possibly time dependent covariates on the developments of recurrent events while accounting for the dependence of the recurrent event times within the same subject we show that the nonparametric maximum likelihood estimators npmles for the parameters of these models are consistent and asymptotically normal the limiting covariance matrices for the estimators of the regression parameters achieve the semiparametric efficiency bounds and can be consistently estimated the limiting covariance function for the estimator of any smooth functional of the cumulative intensity function also can be consistently estimated we develop a simple and stable em algorithm to compute the npmles as well as the variance and covariance estimators simulation studies demonstrate that the proposed methods per

the specification property for flows from the robust and generic viewpoint abstract we prove that if x has the weak specification property robustly where is an isolated set then is a hyperbolic topologically mixing set and as a consequence if x is a vector field that has the weak specification property robustly on a closed manifold m then the flow x t is a topologically mixing anosov flow also we prove that there exists a residual subset r x 1 m so that if x r and x has the weak specification property then x t is an anosov flow

differentiability of thermodynamical quantities in non uniformly expanding dynamics abstract in this paper we study the ergodic theory of a robust non uniformly expanding maps where no markov assumption is required we prove that the topological pressure is differentiable as a function of the dynamics and analytic with respect to the potential moreover we not only prove the continuity of the equilibrium states and their metric entropy as well as the differentiability of the maximal entropy measure and extremal lyapunov exponents with respect to the dynamics we also prove a local large deviations principle and central limit theorem and show that the rate function mean and variance vary continuously with respect to observables potentials and dynamics finally we show that the correlation function associated to the maximal entropy measure is differentiable with respect to the dynamics and it is c 1 convergent to zero in addition precise formulas for the derivatives of thermodynamical quantities are given

estimating equations for hazard ratio parameters based on correlated failure time data summary weighted partial likelihood estimating equations are proposed for the estimation of marginal hazard ratio parameters based on correlated failure time data asymptotic distribution theory is derived for the solution to such equations using martingale convergence results and inverse function theory simulation studies and theoretical efficiency calculations indicate that the inclusion of weights in the estimating equation produces important efficiency gains only if the dependencies among the failure times are strong

a bayesian predictive two stage design for phase ii clinical trials in this paper we propose a bayesian two stage design for phase ii clinical trials which represents a predictive version of the single threshold design std recently introduced by tan and machin the std two stage sample sizes are determined specifying a minimum threshold for the posterior probability that the true response rate exceeds a pre specified target value and assuming that the observed response rate is slightly higher than the target unlike the std we do not refer to a fixed experimental outcome but take into account the uncertainty about future data in both stages the design aims to control the probability of getting a large posterior probability that the true response rate exceeds the target value such a probability is expressed in terms of prior predictive distributions of the data the performance of the design is based on the distinction between analysis and design priors recently introduced in the literature the properties of the method are studied when all the design parameters vary

equivalence of gibbs and equilibrium states for homeomorphisms satisfying expansiveness and specification letm be a compact metrizable space f m m a homeomorphism satisfying expansiveness and specification anda m a function such that left sum limits k 0 n 1 a f k x a f k y right mathbin lower 3ex hbox buildrel over smash scriptstyle vphantom x k varepsilon infty whenevern 1 andx y are e n close i e d fkx fky 0 under these conditions bowen has shown that there is a uniqueequilibrium state fora assuming thatk 0 when 0 we show that is also the uniquegibbs state fora we further definequasi gibbs states and show that is the uniquef invariant quasi gibbs state fora

specification on the interval we study the consequences of discontinuities on the specification property for interval maps after giving a necessary and sufficient condition for a piecewise monotonic piecewise continuous map to have this property we show that for a large and natural class of families of such maps including the 3 transformations the set of parameters for which the specification property holds though dense has zero lebesgue measure thus regarding the specification property the general case is at the opposite of the continuous case solved by a m blokh russian math surveys 38 1983 133 134 for which we give a proof

hazard models with varying coefficients for multivariate failure time data statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis a local pseudo partial likelihood procedure is proposed for estimating the unknown coefficient functions a weighted average estimator is also proposed in an attempt to improve the efficiency of the estimator the consistency and asymptotic normality of the proposed estimators are established and standard error formulas for the estimated coefficients are derived and empirically tested to reduce the computational burden of the maximum local pseudo partial likelihood estimator a simple and useful one step estimator is proposed statistical properties of the one step estimator are established and simulation studies are conducted to compare the performance of the one step estimator to that of the maximum local pseudo partial likelihood estimator the results show that the one step estimator can save computational cost without compromising performance both asymptotically and empirically and that an optimal weighted average estimator is more efficient than the maximum local pseudo partial likelihood estimator a data set from the busselton population health surveys is analyzed to illustrate our proposed methodology

large deviations for non uniformly expanding maps we obtain large deviation bounds for non uniformly expanding maps with non flat singularities or criticalities and for partially hyperbolic non uniformly expanding attracting sets that is given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map showing that the lebesgue measure of the set of points whose time averages stay away from the space average tends to zero exponentially fast with the number of iterates involved as easy by products we deduce escape rates from subsets of the basins of physical measures for these types of maps the rates of decay are naturally related to the metric entropy and pressure function of the system with respect to a family of equilibrium states

denseness of intermediate pressures for systems with the climenhaga thompson structures abstract we show that systems with the structure introduced by climenhaga and thompson have dense intermediate pressures and dense intermediate entropies of ergodic measures the result applies to the mane diffeomorphisms

estimating time varying effects for overdispersed recurrent events data with treatment switching in the analysis of multivariate event times frailty models assuming time independent regression coefficients are often considered mainly due to their mathematical convenience in practice regression coefficients are often time dependent and the temporal effects are of clinical interest motivated by a phase iii clinical trial in multiple sclerosis we develop a semiparametric frailty modelling approach to estimate time varying effects for overdispersed recurrent events data with treatment switching the proposed model incorporates the treatment switching time in the time varying coefficients theoretical properties of the proposed model are established and an efficient expectation maximization algorithm is derived to obtain the maximum likelihood estimates simulation studies evaluate the numerical performance of the proposed model under various temporal treatment effect curves the ideas in this paper can also be used for time varying coefficient frailty models without treatment switching as well as for alternative models when the proportional hazard assumption is violated a multiple sclerosis dataset is analysed to illustrate our methodology

asymptotic theory for the correlated gamma frailty model the frailty model is a generalization of cox s proportional hazard model where a shared unobserved quantity in the intensity induces a positive correlation among the survival times murphy showed consistency and asymptotic normality of the nonparametric maximum likelihood estimator npmle for the shared gamma frailty model without covariates in this paper we extend this result to the correlated gamma frailty model and we allow for covariates we discuss the definition of the nonparametric likelihood function in terms of a classical proof of consistency for the maximum likelihood estimator which goes back to wald our proof of the consistency for the npmle is essentially the same as the classical proof for the maximum likelihood estimator a new central limit theorem for processes of bounded variation is given furthermore we prove that a consistent estimator for the asymptotic variance of the npmle is given by the inverse of a discrete observed information matrix

on the periodic orbits shadowing and strong transitivity of continuous flows abstract we prove that chaotic flows i e flows that satisfy the shadowing property and have a dense subset of periodic orbits satisfy a reparametrized gluing orbit property similar to the one introduced in bomfim and varandas 2015 in particular these are strongly transitive in balls of uniform radius we also prove that the shadowing property for a flow and a generic time t map and having a dense subset of periodic orbits hold for a c 0 baire generic subset of lipschitz vector fields that generate continuous flows similar results also hold for c 0 generic homeomorphisms and in particular we deduce that chain recurrent classes of c 0 generic homeomorphisms have the gluing orbit property

optimal three stage designs for phase ii cancer clinical trials the objective of a phase ii cancer clinical trial is to screen a treatment that can produce a similar or better response rate compared to the current treatment results this screening is usually carried out in two stages as proposed by simon for ineffective treatment the trial should terminate at the first stage ensign et al extended two stage optimal designs to three stages however they restricted the rejection region in the first stage to be zero response and the sample size to at least 5 this paper extends simon s two stage to a three stage design without these restrictions and provides tables for both optimal and minimax designs one can use the three stage design to reduce the expected sample size when the treatment is not promising a priori and when the accrual rate is slow the average reduction in size from a two stage to three stage design is 10 per cent

thermodynamic formalism for countable to one markov systems for countable to one transitive markov systems we establish thermodynamic formalism for non holder potentials in nonhyperbolic situations we present a new method for the construction of conformal measures that satisfy the weak gibbs property for potentials of weak bounded variation and show the existence of equilibrium states equivalent to the weak gibbs measures we see that certain periodic orbits cause a phase transition non gibbsianness and force the decay of correlations to be slow we apply our results to higher dimensional maps with indifferent periodic points

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

marginal regression models for multivariate failure time data abstract in this article we propose a general cox type regression model to formulate the marginal distributions of multivariate failure time data this model has a nested structure in that it allows different baseline hazard functions among distinct failure types and imposes a common baseline hazard function on the failure times of the same type we prove that the maximum quasi partial likelihood estimator for the vector of regression parameters under the independence working assumption is consistent and asymptotically normal with a covariance matrix for which a consistent estimator is provided furthermore we establish the uniform consistency and joint weak convergence of the aalen breslow type estimators for the cumulative baseline hazard functions and develop a resampling technique to approximate the joint distribution of these processes which enables one to make simultaneous inference about the survival functions over the time axis and across failure types finally we assess the small sample pro

some large deviation results for dynamical systems we prove some large deviation estimates for continuous maps of compact metric spaces and apply them to attractors in differentiable dynamics rate of escape problems and to shift spaces

semiparametric regression for the mean and rate functions of recurrent events the counting process with the cox type intensity function has been commonly used to analyse recurrent event data this model essentially assumes that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process recently pepe and cai and lawless and co workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the poisson type assumption in this paper we provide a rigorous justification of such robust procedures through modern empirical process theory furthermore we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean rate model the advantages of the robust procedures are demonstrated through simulation studies an illustration with multiple infection data taken from a clinical study on chronic granulomatous disease is also provided