long time large scale limit of the wigner transform for a system of linear oscillators in one dimension we consider the long time large scale behavior of the wigner transform w t x k of the wave function corresponding to a discrete wave equation on a 1 d integer lattice with a weak multiplicative noise this model has been introduced in basile et al in phys rev lett 96 2006 to describe a system of interacting linear oscillators with a weak noise that conserves locally the kinetic energy and the momentum the kinetic limit for the wigner transform has been shown in basile et al in arch rat mech 195 1 171 203 2009 in the present paper we prove that in the unpinned case there exists 0 0 such that for any 0 0 the weak limit of w t 3 2 x k as 1 satisfies a one dimensional fractional heat equation partial t w t x hat c partial x 2 3 4 w t x with hat c 0 in the pinned case an analogous result can be claimed for w t 2 x k but the limit satisfies then the usual heat equation

nonparametric estimation of a multivariate distribution in the presence of censoring summary this paper presents examples of situations in which one wishes to estimate a multivariate distribution from data that may be right censored a distinction is made between what we term homogeneous and heterogeneous censoring it is shown how a multivariate empirical survivor function must be constructed in order to be considered a nonparametric maximum likelihood estimate of the underlying survivor function a closed form solution similar to the product limit estimate of kaplan and meier is possible with homogeneous censoring but an iterative method such as the em algorithm is required with heterogeneous censoring an example is given in which an anomaly is produced if censored multivariate data are analyzed as a series of univariate variables this anomaly is shown to disappear if

survival curve estimation for informatively coarsened discrete event time data interval censored or more generally coarsened event time data arise when study participants are observed at irregular time periods and experience the event of interest in between study observations such data are often analysed assuming non informative censoring which can produce biased results if the assumption is wrong this paper extends the standard approach for estimating survivor functions to allow informatively interval censored data by incorporating various assumptions about the censoring mechanism into the model we include a bayesian extension in which final estimates are produced by mixing over a distribution of assumed censoring mechanisms we illustrate these methods with a natural history study of hiv infected individuals using assumptions elicited from an aids expert

nonparametric estimation of the concordance correlation coefficient under univariate censoring assessing agreement is often of interest in clinical studies to evaluate the similarity of measurements produced by different raters or methods on the same subjects lin s 1989 biometrics 45 255 268 concordance correlation coefficient ccc has become a popular measure of agreement for correlated continuous outcomes however commonly used estimation methods for the ccc do not accommodate censored observations and are therefore not applicable for survival outcomes in this article we estimate the ccc nonparametrically through the bivariate survival function the proposed estimator of the ccc is proven to be strongly consistent and asymptotically normal with a consistent bootstrap variance estimator furthermore we propose a time dependent agreement coefficient as an extension of lin s 1989 ccc for measuring the agreement between survival times among subjects who survive beyond a specified time point a nonparametric estimator is developed for the time dependent agreement coefficient as well it has the same asymptotic properties as the estimator of the ccc simulation studies are conducted to evaluate the performance of the proposed estimators a real data example from a prostate cancer study is used to illustrate the method

analysis of a nonsusceptible fraction with current status data in studies involving subclinical events times of events are often subject to interval censoring since their occurrence is only detected at inspection times when individuals are event free at an initial time and a single follow up inspection is made current status data are obtained in many settings however the population comprised a susceptible and a nonsusceptible subpopulation where only susceptible individuals will go on to experience the event then interest often lies primarily in identifying prognostic variables for susceptibility and secondarily in the event time distribution among the susceptible individuals we give a simple mixture model that facilitates estimation of the proportion of susceptible individuals covariate effects on the odds of susceptibility and the event time distribution under a current status observation scheme asymptotic relative efficiency of maximum likelihood estimators is considered based on the fisher information for a variety of settings em algorithms are proposed for parametric weakly parametric and nonparametric estimation of the event time distribution the methods are applied to motivating studies examining an immunological response to low molecular weight heparin in patients undergoing orthopedic surgery

a kernel method for incorporating information on disease progression in the analysis of survival summary this paper considers incorporating information on disease progression in the analysis of survival a three state model is assumed with the distribution of each transition estimated separately the distribution of survival following progression can depend on the time of progression kernel methods are used to give consistent estimators under general forms of dependence the estimators for the individual transitions are then combined into an overall estimator of the survival distribution a test statistic for equality of survival between treatment groups is proposed based on the tests of pepe fleming 1989 1991 in simulations the kernel method successfully incorporated dependence on the time of progression in some reasonable settings but under extreme forms of dependence the tests had substantial bias if survival beyond progression can be predicted fairly accurately then gains in power over standard methods that ignore progression can be substantial but the gains are smaller when survival beyond progression is more variable the methodology is illustrated with an application to a breast cancer clinical trial

macroscopic behavior of microscopic oscillations in harmonic lattices via wigner husimi transforms we consider the dynamics of infinite harmonic lattices in the limit of the lattice distance tending to 0 we allow for general polyatomic crystals but assume exact periodicity such that the system can be solved in principle by fourier transform and linear algebra methods

nonequilibrium statistical mechanics of hamiltonian rotators with alternated spins we consider a finite region of a d dimensional lattice of nonlinear hamiltonian rotators where neighbouring rotators have opposite alternated spins and are coupled by a small potential of size varepsilon a a ge 1 2 we weakly stochastically perturb the system in such a way that each rotator interacts with its own stochastic thermostat with a force of order varepsilon then we introduce action angle variables for the system of uncoupled rotators varepsilon 0 and note that the sum of actions over all nodes is conserved by the purely hamiltonian dynamics of the system with varepsilon 0 we investigate the limiting as varepsilon rightarrow 0 dynamics of actions for solutions of the varepsilon perturbed system on time intervals of order varepsilon 1 it turns out that the limiting dynamics is governed by a certain autonomous stochastic equation for the vector of actions this equation has a completely non hamiltonian nature this is a consequence of the fact that the system of rotators with alternated spins do not have resonances of the first order the varepsilon perturbed system has a unique stationary measure widetilde mu varepsilon and is mixing any limiting point of the family widetilde mu varepsilon of stationary measures as varepsilon rightarrow 0 is an invariant measure of the system of uncoupled integrable rotators there are plenty of such measures however it turns out that only one of them describes the limiting dynamics of the varepsilon perturbed system we prove that a limiting point of widetilde mu varepsilon is unique its projection to the space of actions is the unique stationary measure of the autonomous equation above which turns out to be mixing and its projection to the space of angles is the normalized lebesque measure on the torus mathbb t n the results and convergences which concern the behaviour of actions on long time intervals are uniform in the number n of rotators those concerning the stationary measures are uniform in n in some natural cases

bayesian models for multivariate current status data with informative censoring des donnees multivariees d etat consistent en un ensemble d indicatrices associees a la realisation de plusieurs evenements au moment d un examen nous nous interessons aux inferences sur les distributions jointes des temps d evenements les methodes conventionnelles d analyse des donnees de durees multiples ne peuvent etre utilisees parce que tous les temps d evenements sont censures et la censure peut etre informative nous prenons en compte la correlation des temps d evenements chez un sujet au moyen d une variable latente propre au sujet conditionnellement a laquelle les divers temps d evenements sont supposes independants nous supposons egalement que chaque evenement contribue independamment au risque de censure des fonctions en escalier non parametriques sont utilisees pour caracteriser les distributions de base des differents temps d evenements et des temps d examen les covariables et les effets specifiques du sujet sont incorpores grace au modele lineaire generalise un algorithme de monte carlo par chaines de markov est decrit pour l estimation des distributions a posteriori des inconnues les methodes sont illustrees par une application sur des donnees de sites multiples de tumeurs dans une etude de carcinogenicite animale

a nonparametric estimation procedure for a periodically observed three state markov process with application to aids estimation in a three state markov process with irreversible transitions in the presence of interval censored data is considered a nonparametric maximum likelihood procedure for the estimation of the cumulative transition intensities is presented a self consistent estimator of the parameters is defined and it is shown that the maximum likelihood estimator is a self consistent estimator this extends the idea of self consistency introduced by efron to the estimation of more than one parameter an algorithm based on selfconsistency equations is provided for the computation of the estimators

a non parametric maximum likelihood estimator for bivariate interval censored data we derive a non parametric maximum likelihood estimator for bivariate interval censored data using standard techniques for constrained convex optimization our approach extends those taken for univariate interval censored data we illustrate the estimator with bivariate data from an aids study

self averaging of wigner transforms in random media we establish the self averaging properties of the wigner transform of a mixture of states in the regime when the correlation length of the random medium is much longer than the wave length but much shorter than the propagation distance the main ingredients in the proof are the error estimates for the semiclassical approximation of the wigner transform by the solution of the liouville equations and the limit theorem for two particle motion along the characteristics of the liouville equations the results are applied to a mathematical model of the time reversal experiments for the acoustic waves and self averaging properties of the re transmitted wave are proved

energy transport in stochastically perturbed lattice dynamics we consider lattice dynamics with a small stochastic perturbation of order varepsilon and prove that for a space time scale of order varepsilon 1 the local spectral density wigner function evolves according to a linear transport equation describing inelastic collisions for an energy and momentum conserving chain the transport equation predicts a slow decay as 1 sqrt t for the energy current correlation in equilibrium this is in agreement with previous studies using a different method

maximum likelihood for interval censored data consistency and computation summary standard convex optimization techniques are applied to the analysis of interval censored data these methods provide easily verifiable conditions for the self consistent estimator proposed by turnbull 1976 to be a maximum likelihood estimator and for checking whether the maximum likelihood estimate is unique a sufficient condition is given for the almost sure convergence of the maximum likelihood estimator to the true underlying distribution function

nonparametric bivariate estimation with randomly censored data summary the estimation of a bivariate distribution function with randomly censored data is considered it is assumed that the censoring occurs independently of the lifetimes and that deaths and losses which occur simultaneously can be separated two estimators are developed a reduced sample estimator and a self consistent one it is shown that the latter estimator satisfies a nonparametric likelihood function and is unique up to the final uncensored values in any dimension it jumps at the points of double deaths in both dimensions some key word8 censored data kaplan meier estimator life table product limit estimator survival estimation

one dimensional harmonic lattice caricature of hydrodynamics second approximation the long time behavior of an infinite chain of coupled harmonic oscillators is studied in addition to a limiting hydrodynamic euler type equation the next approximation is investigated the corresponding equation is derived

nonparametric survival estimation using prognostic longitudinal covariates one of the primary problems facing statisticians who work with survival data is the loss of information that occurs with right censored data this research considers trying to recover some of this endpoint information through the use of a prognostic covariate which is measured on each individual we begin by defining a survival estimate which uses time dependent covariates to more precisely get at the underlying survival curves in the presence of censoring this estimate has a smaller asymptotic variance than the usual kaplan meier in the presence of censoring and reduces to the kaplan meier 1958 journal of the american statistical association 53 457 481 in situations where the covariate is not prognostic or no censoring occurs in addition this estimate remains consistent when the incorporated covariate contains information about the censoring process as well as survival information because the kaplan meier estimate is known to be biased in this situation due to informative censoring we recommend use of our estimate

kinetic limit for a chain of harmonic oscillators with a point langevin thermostat abstract we consider an infinite chain of coupled harmonic oscillators whose hamiltonian dynamics is perturbed by a random exchange of momentum between particles such that total energy and momentum are conserved modeling collision between atoms this random exchange is rarefied in the limit that corresponds to the hypothesis that in the macroscopic unit time only a finite number of collisions takes place the boltzmann grad limit furthermore the system is in contact with a langevin thermostat at temperature t through a single particle we prove that after the hyperbolic space time rescaling the wigner distribution describing the energy density of phonons in space frequency domain converges to a positive energy density function w t y k that evolves according to a linear kinetic equation with the interface condition at y 0 that corresponds to reflection transmission and absorption of phonons caused by the presence of the thermostat the paper extends the results of 15 where a harmonic chain with no inter particle scattering in contact with a langevin thermostat has been considered

asymptotics of the solutions of the stochastic lattice wave equation we consider the long time limit for the solutions of a discrete wave equation with weak stochastic forcing the multiplicative noise conserves energy and in the unpinned case also conserves momentum we obtain a time inhomogeneous ornstein uhlenbeck equation for the limit wave function that holds for both square integrable and statistically homogeneous initial data the limit is understood in the point wise sense in the former case and in the weak sense in the latter on the other hand the weak limit for square integrable initial data is deterministic

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

kaplan meier estimate on the plane estimation of the bivariate survival function from censored data is considered the product integral representation of univariate survival functions is generalized to the bivariate case and used to determine identifiability of the survival function of the partially observed data a bivariate analogue of the kaplan meier estimate is introduced and its almost sure consistency is studied extensions to the general multivariate case are sketched

kinetic limit for wave propagation in a random medium we study crystal dynamics in the harmonic approximation the atomic masses are weakly disordered in the sense that their deviation from uniformity is of the order e the dispersion relation is assumed to be a morse function and to suppress crossed recollisions we then prove that in the limit e 0 the disorder averaged wigner function on the kinetic scale time and space of order e 1 is governed by a linear boltzmann equation

one dimensional harmonic lattice caricature of hydrodynamics a higher correction corrections to the hydrodynamic limit for an infinite chain of coupled harmonic oscillators are obtained this makes more precise the asymptotic picture for this type of evolution of a system with infinitely many degrees of freedom

a simple nonparametric estimator of the bivariate survival function under univariate censoring summary in the presence of univariate censoring the bivariate survival function of paired failure times can be expressed as the ratio of the bivariate at risk probability to the survival function of the censoring time the use of this natural representation yields a very simple nonparametric estimator for the bivariate survival curve the estimator is strongly consistent and upon proper normalization converges weakly to a zero mean gaussian process with an easily estimated covariance function numerical studies demonstrate that both the survival curve estimator and its covariance function estimator perform markedly well for practical sample sizes applications to the correlation problem and to the interval estimation of the difference in median survival times are also studied

on nonparametric maximum likelihood estimation with interval censoring and left truncation summary a graph theoretical approach is employed to describe the support set of the nonparametric maximum likelihood estimator for the cumulative distribution function given interval censored and left truncated data a necessary and sufficient condition for the existence of a nonparametric maximum likelihood estimator is then derived two previously analysed data sets are revisited

non isothermal boundary in the boltzmann theory and fourier law in the study of the heat transfer in the boltzmann theory the basic problem is to construct solutions to the following steady problem v cdot nabla x f frac 1 rm k rm n q f f qquad x v in omega times mathbf r 3 quad quad 0 1 f x v n x cdot v 0 f x v prime n x cdot v prime dv prime quad x in partial omega quad quad 0 2 where is a bounded domain in mathbf r d 1 leq d leq 3 kn is the knudsen number and mu theta frac 1 2 pi theta 2 x rm exp frac v 2 2 theta x is a maxwellian with non constant non isothermal wall temperature x based on new constructive coercivity estimates for both steady and dynamic cases for theta theta 0 leq delta ll 1 and any fixed value of kn we construct a unique non negative solution fs to 0 1 and 0 2 continuous away from the grazing set and exponentially asymptotically stable this solution is a genuine non equilibrium stationary solution differing from a local equilibrium maxwellian as an application of our results we establish the expansion f s mu theta 0 delta f 1 o delta 2 and we prove that if the fourier law holds the temperature contribution associated to f1 must be linear in the slab geometry

nonparametric estimation of a bivariate survival function in the presence of censoring a new family of estimators of a bivariate survival function based on censored vectors is obtained from a decomposition of the bivariate survival function these estimators are uniformly consistent under bivariate censoring and are self consistent under univariate censoring

a rank test for bivariate time to event outcomes when one event is a surrogate in many clinical settings improving patient survival is of interest but a practical surrogate such as time to disease progression is instead used as a clinical trial s primary endpoint a time to first endpoint e g death or disease progression is commonly analyzed but may not be adequate to summarize patient outcomes if a subsequent event contains important additional information we consider a surrogate outcome very generally as one correlated with the true endpoint of interest settings of interest include those where the surrogate indicates a beneficial outcome so that the usual time to first endpoint of death or surrogate event is nonsensical we present a new two sample test for bivariate interval censored time to event data where one endpoint is a surrogate for the second less frequently observed endpoint of true interest this test examines whether patient groups have equal clinical severity if the true endpoint rarely occurs the proposed test acts like a weighted logrank test on the surrogate if it occurs for most individuals then our test acts like a weighted logrank test on the true endpoint if the surrogate is a useful statistical surrogate our test can have better power than tests based on the surrogate that naively handles the true endpoint in settings where the surrogate is not valid treatment affects the surrogate but not the true endpoint our test incorporates the information regarding the lack of treatment effect from the observed true endpoints and hence is expected to have a dampened treatment effect compared with tests based on the surrogate alone published 2016 this article is a u s government work and is in the public domain in the usa

an expectation maximization approach to nonlinear component analysis the proposal of considering nonlinear principal component analysis as a kernel eigenvalue problem has provided an extremely powerful method of extracting nonlinear features for a number of classification and regression applications whereas the utilization of mercer kernels makes the problem of computing principal components in possibly infinite dimensional feature spaces tractable there are still the attendant numerical problems of diagonalizing large matrices in this contribution we propose an expectation maximization approach for performing kernel principal component analysis and show this to be a computationally efficient method especially when the number of data points is large