l 1 stability estimates for n x n conservation laws let u t f u x 0 be a strictly hyperbolic n times n system of conservation laws each characteristic field being linearly degenerate or genuinely nonlinear in this paper we explicitly define a functional phi phi u v equivalent to the l 1 distance which is almost decreasing i e phi big u t v t big phi big u s v s big leq o ve cdot t s quad hbox for all t s geq 0 for every pair of e approximate solutions u v with small total variation generated by a wave front tracking algorithm the small parameter e here controls the errors in the wave speeds the maximum size of rarefaction fronts and the total strength of all non physical waves in u and in v from the above estimate it follows that front tracking approximations converge to a unique limit solution depending lipschitz continuously on the initial data in the vec l 1 norm this provides a new proof of the existence of the standard riemann semigroup generated by a n n system of conservation laws

a geometrical method for removing edge effects from kernel type nonparametric regression estimators abstract we introduce a simple geometric method for removing edge effects from kernel type nonparametric regression estimators it involves reflecting the data set in two estimated points thereby generating a new data set with three times the range of the original data the usual kernel type estimator may be applied to the new enlarged data set without any danger of edge effects this technique is applicable generally to both regularly spaced and randomly spaced designs and admits a natural analog of leave one out cross validation the new cross validation algorithm may be extended to the very ends of the design interval unlike its more conventional counterpart which must be downweighted at the ends of the interval to avoid edge effects

l2 contraction of large planar shock waves for multi dimensional scalar viscous conservation laws abstract we consider a l 2 contraction a l 2 type stability of large viscous shock waves for the multi dimensional scalar viscous conservation laws up to a suitable shift by using the relative entropy methods quite different from the previous results we find a new way to determine the shift function which depends both on the time and space variables and solves a viscous hamilton jacobi type equation with source terms moreover we do not impose any conditions on the anti derivative variables of the perturbation around the shock profile more precisely it is proved that if the initial perturbation around the viscous shock wave is suitably small in l 2 norm then the l 2 contraction holds true for the viscous shock wave up to a suitable shift function note that bv norm or the l norm of the initial perturbation and the shock wave strength can be arbitrarily large furthermore as the time t tends to infinity the l 2 contraction holds true up to a spatially homogeneous time dependent shift function in particular if we choose some special initial perturbations then l 2 convergence of the solutions towards the associated shock profile can be proved up to a time dependent shift

l 2 stability estimates for shock solutions of scalar conservation laws using the relative entropy method we consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension and we investigate the behavior of bounded l2 perturbations of shock wave solutions to the riemann problem using the relative entropy method we show that up to a time dependent translation of the shock the l2 norm of a perturbed solution relative to the shock wave is bounded above by the l2 norm of the initial perturbation

numerical approximations for stochastic differential games the markov chain approximation method is a widely used robust relatively easy to use and efficient family of methods for the bulk of stochastic control problems in continuous time for reflected jump diffusion type models it has been shown to converge under broad conditions and there are good algorithms for solving the numerical problems if the dimension is not too high versions of these methods have been used in applications to various two player differential and stochastic dynamic games for a long time and proofs of convergence are available for some cases mainly using pde type techniques in this paper purely probabilistic proofs of convergence are given for a broad class of such problems where the controls for the two players are separated in the dynamics and cost function and which cover a substantial class not dealt with in previous works discounted and stopping time cost functions are considered finite horizon problems and problems where the process is stopped on first hitting an a priori given boundary can be dealt with by adapting the methods of h j kushner and p dupuis numerical methods for stochastic control problems in continuous time 2nd ed springer verlag berlin new york 2001 as done in this paper for the treated problems the essential conditions are the weak sense existence and uniqueness of solutions an almost everywhere continuity condition and that a weak local consistency condition holds almost everywhere for the numerical approximations just as for the control problem there are extensions to problems with controlled variance and jumps

statistical analysis of repeated events forming renewal processes for each of several individuals a sequence of repeated events forming a renewal process is observed up to some censoring time the object is to estimate the average interevent time over the population of individuals as well as the variation of interevent times within and between individuals medical motivation comes from gastroenterology and concerns the occurrence of certain cyclic movements in the small bowel during the fasting state two statistical models are considered one is the standard variance component model adapted to censored data and the other is a recent intensity based model with a random proportionality factor representing interindividual variation these models are applied to the motility data and their advantages are discussed the intensity based model allows simple empirical bayes estimation of the expected interevent times for an individual in the presence of censoring

relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non bv perturbations we develop a theory based on relative entropy to show the uniqueness and l 2 stability up to a translation of extremal entropic rankine hugoniot discontinuities for systems of conservation laws typically 1 shocks n shocks 1 contact discontinuities and n contact discontinuities of large amplitude among bounded entropic weak solutions having an additional trace property the existence of a convex entropy is needed no bv estimate is needed on the weak solutions considered the theory holds without smallness conditions the assumptions are quite general for instance strict hyperbolicity is not needed globally for fluid mechanics the theory handles solutions with vacuums

no contractive metrics for systems of conservation laws soit u t f u x 0 un systeme 2 2 de lois de conservation satisfaisant certaines hypotheses generiques sur f dans un voisinage 7b n de l espace u on montre que pour chaque metrique non degeneree d sur l u espace il existe des etats u 1 et u 2 dans 7b n tels que d u x t u 1 dx est une fonction strictement croissante de t dans un voisinage de t 0 ou u est la solution admissible du systeme avec u x 0 u 1 x 0 u 2 0 x 1 u 1 x 1

strong traces for solutions of multidimensional scalar conservation laws in this paper we consider multidimensional scalar conservation laws without bv estimates defined in a subset d we show that with a non degeneracy hypothesis on the flux we can define a strong notion of trace at the boundary of reached by l 1 convergence

numerical approximations for stochastic differential games the ergodic case the markov chain approximation method is a widely used relatively easy to use and efficient family of methods for the bulk of stochastic control problems in continuous time for reflected jump diffusion type models it has been shown to converge under broad conditions and there are good algorithms for solving the numerical problems if the dimension is not too high we consider a class of stochastic differential games with a reflected diffusion system model and ergodic cost criterion and where the controls for the two players are separated in the dynamics and cost function it is shown that the value of the game exists and that the numerical method converges to this value as the discretization parameter goes to zero the actual numerical method solves a stochastic game for a finite state markov chain and ergodic cost criterion the essential conditions are nondegeneracy and that a weak local consistency condition hold almost everywhere for the numerical approximations just as for the control problem

survival models for cost data the forgotten additive approach the usage of the aalen additive approach is proposed to model cost data using a monte carlo simulation in a wide set of scenarios we showed that the aalen model is performing well and can be a reasonable alternative to the standard gamma regression models in addition with reference to the costami trial data we highlighted the ability of the aalen model to offer additional information about the relationships between costs and specific covariates as compared with standard regression techniques

diagnostic plots to reveal functional form for covariates in multiplicative intensity models abstract we show how plots based on the residuals from a proportional hazards model may be used to reveal the correct functional form for covariates in the model a smoothed plot of the martingale residues was suggested for this purpose by therneau grambsch and fleming 1990 biometrika 77 147 160 however its consistency required that the covariates be independent they also noted that the plot could be biased for large covariate effects we introduce two refinements which overcome these difficulties the first is based on a ratio of scatter plot smooths where the numerator is the smooth of the observed count plotted against the covariate and the denominator is a smooth of the expected count this is related to the arjas goodness of fit plot 1988 journal of the american statistical association 83 204 212 the second technique smooths the martingale residuals divided by the expected count using expected count as a weight this latter approach is related to a glm partial residual plot as well as to the iterative methods of hastie and tibshirani 1990 biometrics 46 1005 1016 and gentleman and crowley 1991 biometrics 47 1283 1296 applications to survival data sets are given

estimation of excess risk from case control data using aalen s linear regression model we introduce methods for statistical inference in aalen s non parametric linear regression model of disease incidence aalen 1989 statistics in medicine 8 907 925 from nested case control data these methods provide the basis for estimation of excess risk as a linear function of dose and absolute risk for a given exposure history the methods are illustrated by estimating excess and absolute risks associated with radon exposure and smoking from nested case control samples from the colorado plateau uranium miners cohort language en

global tests in the additive hazards regression model in this article we discuss testing for the effect of several covariates in the additive hazards regression model bhattacharyya and klein statist med 2005 24 14 2235 2240 note that an ad hoc weight function suggested by aalen statist med 1989 8 907 925 is inconsistent when used as a global test for comparing groups since the test statistic depends on which group is used as the baseline group we will suggest a simple alternative test that does not exhibit this problem this test is a natural extension of the logrank test we shall also discuss an alternative covariance estimator the tests are applied to a data set and a simulation study is performed

criteria on contractions for entropic discontinuities of systems of conservation laws we study the contraction properties up to shift for admissible rankine hugoniot discontinuities of n times n systems of conservation laws endowed with a convex entropy we first generalize the criterion developed in serre and vasseur j l ecole polytech 1 2014 using the spatially inhomogeneous pseudo distance introduced in vasseur contemp math ams 2013 our generalized criterion guarantees the contraction property for extremal shocks of a large class of systems including the euler system moreover we introduce necessary conditions for contraction specifically targeted for intermediate shocks as an application we show that intermediate shocks of the two dimensional isentropic magnetohydrodynamics do not verify any of our contraction properties we also investigate the contraction properties for contact discontinuities of the euler system for a certain range of contraction weights none of the results involve any smallness condition on the initial perturbation or on the size of the shock

a note on testing in aalen s additive hazards regression models aalen s additive hazards regression model is a useful alternative to the proportional hazards model for censored data regression when used to compare treatments this approach leads to weighted comparisons of the crude estimate of the hazard rate of each group as compared to a baseline group this is contrasted to the weighted log rank test from the proportional hazards model which compares each treatment s rate to the pooled rate we show in this brief note that aalen s suggestion for weights in this test leads to inconsistent tests in the sense that the test statistic depends on which group we pick for a baseline group we show that consistent tests are obtained by using common weight functions for all comparisons and we make some suggestions

the partly aalen s model for recurrent event data with a dependent terminal event recurrent event data are commonly observed in biomedical longitudinal studies in many instances there exists a terminal event which precludes the occurrence of additional repeated events and usually there is also a nonignorable correlation between the terminal event and recurrent events in this article we propose a partly aalen s additive model with a multiplicative frailty for the rate function of recurrent event process and assume a cox frailty model for terminal event time a shared gamma frailty is used to describe the correlation between the two types of events consequently this joint model can provide the information of temporal influence of absolute covariate effects on the rate of recurrent event process which is usually helpful in the decision making process for physicians an estimating equation approach is developed to estimate marginal and association parameters in the joint model the consistency of the proposed estimator is established simulation studies demonstrate that the proposed approach is appropriate for practical use we apply the proposed method to a peritonitis cohort data set for illustration

dynamic regression hazards models for relative survival a natural way of modelling relative survival through regression analysis is to assume an additive form between the expected population hazard and the excess hazard due to the presence of an additional cause of mortality within this context the existing approaches in the parametric semiparametric and non parametric setting are compared and discussed we study the additive excess hazards models where the excess hazard is on additive form this makes it possible to assess the importance of time varying effects for regression models in the relative survival framework we show how recent developments can be used to make inferential statements about the non parametric version of the model this makes it possible to test the key hypothesis that an excess risk effect is time varying in contrast to being constant over time in case some covariate effects are constant we show how the semiparametric additive risk model can be considered in the excess risk setting providing a better and more useful summary of the data estimators have explicit form and inference based on a resampling scheme is presented for both the non parametric and semiparametric models we also describe a new suggestion for goodness of fit of relative survival models which consists on statistical and graphical tests based on cumulative martingale residuals this is illustrated on the semiparametric model with proportional excess hazards we analyze data from the trace study using different approaches and show the need for more flexible models in relative survival

the gauss seidel numerical procedure for markov stochastic games consider the problem of value iteration for solving markov stochastic games one simply iterates backward via a jacobi like procedure the convergence of the gauss seidel form of this procedure is shown for both the discounted and ergodic cost problems under appropriate conditions with extensions to problems where one stops when a boundary is hit or if any one of the players chooses to stop with associated costs generally the gauss seidel procedure accelerates convergence

value set iteration for two person zero sum markov games we present a novel exact algorithm called value set iteration vsi for solving two person zero sum markov games mgs as a generalization of value iteration vi and as a general framework of combining multiple solution methods we introduce a novel operator in the value function space and iteratively apply the operator with any sequence of the set of policies extending chang s vsi for mdps into the mg setting we show that vsi for mgs converges to the equilibrium value function with at least linear convergence rate and establish that vsi can potentially improve the convergence speed in terms of the number of iterations by proper setting of the sequence of the set of policies

age dependent u shaped risk functions and aalen s additive risk model epidemiologic studies of time to some failure often show a quadratic relation between the risk of failure and covariate s we study the nadir for a given covariate i e the value of the covariate associated with the lowest risk supposing a u shape within aalen s additive risk model this model was applied since the effect of the covariate s is allowed to vary over time and as a consequence a given nadir can vary over time we propose a test for the null hypothesis that the nadir is time independent and if this is the case an estimate of the nadir large sample properties of the test statistic and estimator are derived the methods are illustrated with data where time to death is related to body mass index

martingale based residuals for survival models summary graphical methods based on the analysis of residuals are considered for the setting of the highly used cox 1972 regression model and for the andersen gill 1982 generalization of that model we start with a class of martingale based residuals as proposed by barlow prentice 1988 these residuals and or their transforms are useful for investigating the functional form of a covariate the proportional hazards assumption the leverage of each subject upon the estimates of 13 and the lack of model fit to a given subject 1 1 model consider a set of n independent subjects such that the counting process ni ni t t o for the ith subject in the set indicates the number of observed events experienced over time t the sample paths of the ni are step functions with jumps of size 1 and with ni 0 0 we assume that the intensity function for ni t is given by yi t da t zi t yi t ep z t dao t 1 where yi t is a 0 1 process indicating whether the ith subject is a risk at time t 13 is a vector of regression coefficients zi t is a p dimensional vector of covariate processes and ao is the baseline cumulative hazard function several familar survival models fit into this framework the andersen gill 1982 generalization of the cox 1972 model arises when ao t is completely unspecified the further restriction that yi t 1 until the first event or censoring and is 0 thereafter yields the cox model the parametric form ao t t yields a poisson model or an exponential if restricted to a single event per subject and ao t tp a weibull model our attention will focus primarily on the andersen gill and cox models however the

a nonparametric dynamic additive regression model for longitudinal data in this work we study additive dynamic regression models for longitudinal data these models provide a flexible and nonparametric method for investigating the time dynamics of longitudinal data the methodology is aimed at data where measurements are recorded at random time points we model the conditional mean of responses given the full internal history and possibly time varying covariates we derive the asymptotic distribution for a new nonparametric least squares estimator of the cumulative time varying regression functions based on the asymptotic results confidence bands may be computed and inference about time varying coefficients may be drawn we propose two estimators of the cumulative regression function one estimator that involves smoothing and one that does not the latter however has twice the variance as the smoothing based estimator goodness of fit of the model is considered using martingale residuals finally we also discuss how partly conditional mean models in which the mean of the response is regressed onto selected time varying covariates may be analysed in the same framework we apply the methods to longitudinal data on height development for cystic fibrosis patients

a linear regression model for the analysis of life times a linear model is suggested for the influence of covariates on the intensity function this approach is less vulnerable than the cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed a method of non parametric estimation of regression functions is presented this results in plots that may give information on the change over time in the influence of covariates a test method and two goodness of fit plots are also given the approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx

further results on the non parametric linear regression model in survival analysis this paper gives further developments of a non parametric linear regression model in survival analysis three subjects are studied first martingale residuals originally developed for the cox model are introduced for our linear model their theory is developed and they are shown to be useful for judging goodness of fit the second focus of the paper is on the use of bootstrap replications to judge which features of the cumulative regression plots are likely to reflect real phenomena and not merely random variation in particular this is applied to judging whether the effect of a covariate disappears over time a problem for which no formal test exists the third subject is density type or kernel estimation of the regression functions themselves this might give more direct information than the cumulative plots the approaches are illustrated by data from a clinical trial of carcinoma of the oropharynx and by survival times of grafts in renal patients

a partly parametric additive risk model summary aalen s additive risk model allows the influence of each covariate to vary separately over time although allowing greater flexibility of temporal structure than a cox model aalen s model is more limited in the number of covariates it can handle we introduce a partly parametric version of aalen s model in which the influence of only a few covariates varies nonparametrically over time and that of the remaining covariates is constant efficient procedures for fitting this new model are developed and studied the approach is applied to data from the medical research council s myelomatosis trials it is the first step of a taylor series expansion of a general hazard function about the zero of the covariate vector however in estimating the unknown functions in such a general model there is a variance bias trade off that may be critical in small and medium samples also after fitting the model one does not have parameters or formulae that are easily reported we propose a model that takes the additive structure of aalen s model and imposes parametric constraints to obtain a semiparametric submodel which may be more appropriate in some applications the model will be illustrated with data from clinical trials on myelomatosis covariates include treatment sex and four age strata which will be treated parametrically together with serum levels of haemoglobin and f32 microglobulin whose effects will be investigated nonparametrically the additive form can be interpreted loosely in terms of unobserved competing risks since the hazard function for the minimum of independent random vari ables is the sum of the hazard functions for the individual variables microglobulin levels are related to kidney function and tumour mass whereas haemoglobin is unaffected by kidney function hence one might anticipate that the hazard function associated with each covariate represents a different cause of death

a graphical method for assessing goodness of fit in cox s proportional hazards model abstract suggested here is a simple graphical method for studying the goodness of fit in cox s regression model for survival data the method is easy to use as it does not require the estimation of alternative models and only involves quantities similar to those already appearing in the partial likelihood expression that is needed in the parameter estimation the rationale behind the graphs is very intuitive they make a direct comparison between observed and expected failure frequencies as estimated from the model in a correctly specified model one anticipates an approximate balance between such frequencies otherwise there will typically be groups of individuals for which the expected frequencies are systematically too high or too low to match with the data and this shows in the graphs introduced here in the concrete applications of the method the individuals are stratified in a way that depends on what aspect of the model is being checked against data there is always one graph for each stratum s

weighted least squares estimation for aalen s additive risk model abstract cox s proportional hazards model has so far been the most popular model for the regression analysis of censored survival data however the additive risk model of aalen can provide a useful and biologically more plausible alternative aalen s model stipulates that the conditional hazard function for a subject whose covariates are y y 1 yp has the form h t y y t where 1 p is an unknown vector of hazard functions this article discusses inference for based on a weighted least squares wls estimator of the vector of cumulative hazard functions the asymptotic distribution of the wls estimator is derived and used to obtain confidence intervals and bands for the cumulative hazard functions both a grouped data and a continuous data version of the estimator are examined an extensive simulation study is carried out the method is applied to grouped data on the incidence of cancer mortality among japanese atomic bomb survivors

lp stability for entropy solutions of scalar conservation laws with strict convex flux abstract here we consider the scalar convex conservation laws in one space dimension with strictly convex flux which is in c 1 existence uniqueness and l 1 contractivity were proved by kru kov 14 using the relative entropy method leger showed that for a uniformly convex flux and for the shock wave solutions the l 2 norm of a perturbed solution relative to the shock wave is bounded by the l 2 norm of the initial perturbation here we generalize the result to l p norm for all 1 p also we show that for the non shock wave solution l p norm of the perturbed solution relative to the modified n wave is bounded by the l p norm of the initial perturbation for all 1 p

empirical bayes estimation for additive hazards regression models we develop a novel empirical bayesian framework for the semiparametric additive hazards regression model the integrated likelihood obtained by integration over the unknown prior of the nonparametric baseline cumulative hazard can be maximized using standard statistical software unlike the corresponding full bayes method our empirical bayes estimators of regression parameters survival curves and their corresponding standard errors have easily computed closed form expressions and require no elicitation of hyperparameters of the prior the method guarantees a monotone estimator of the survival function and accommodates time varying regression coefficients and covariates to facilitate frequentist type inference based on large sample approximation we present the asymptotic properties of the semiparametric empirical bayes estimates we illustrate the implementation and advantages of our methodology with a reanalysis of a survival dataset and a simulation study