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

homogenization limits and wigner transforms we present a theory for carrying out homogenization limits for quadratic functions called energy densities of solutions of initial value problems ivps with anti self adjoint spatial pseudo differential operators pdos the approach is based on the introduction of phase space wigner matrix measures that are calculated by solving kinetic equations involving the spectral properties of the pdo the weak limits of the energy densities are then obtained by taking moments of the wigner measure the very general theory is illustrated by typical examples like semi classical limits of schrodinger equations with or without a periodic potential the homogenization limit of the acoustic equation in a periodic medium and the classical limit of the dirac equation 1997 john wiley sons inc

efficient estimation for the proportional hazards model with interval censoring the maximum likelihood estimator mle for the proportional hazards model with case 1 interval censored data is studied it is shown that the mle for the regression parameter is asymptotically normal with n convergence rate and achieves the information bound even though the mle for the baseline cumulative hazard function only converges at n 1 3 rate estimation of the asymptotic variance matrix for the mle of the regression parameter is also considered to prove our main results we also establish a general theorem showing that the mle of the finite dimensional parameter in a class of semiparametric models is asymptotically efficient even though the mle of the infinite dimensional parameter converges at a rate slower than n the results are iliustrated by applying them to a data set from a tumorigenicity study

an efficient semiparametric estimator for binary response models this paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function where this function can be characterized by an index the estimator is shown to be consistent asymptotically normally distributed and to achieve the semiparametric efficiency bound monte carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known and that the small sample behavior of the estimator in other cases is good

interval censored survival data a generalized linear modelling approach a method is described for weak parametric modelling of arbitrarily interval censored survival data using generalized linear models the method makes use of an associated bernoulli model with standard errors based on the observed information matrix three types of models are discussed additive and multiplicative hazard models with piecewise constant baseline hazard and a proportional hazards model with discrete baseline survivor function these models may be fitted in the statistical package glim

efficient estimation of the partly linear additive cox model the partly linear additive cox model is an extension of the linear cox model and allows flexible modeling of covariate effects semiparametrically we study asymptotic properties of the maximum partial likelihood estimator of this model with right censored data using polynomial splines we show that with a range of choices of the smoothing parameter the number of spline basis functions required for estimation of the nonparametric components the estimator of the finite dimensional regression parameter is root n consistent asymptotically normal and achieves the semiparametric information bound rates of convergence for the estimators of the nonparametric components are obtained they are comparable to the rates in nonparametric regression implementation of the estimation approach can be done easily and is illustrated by using a simulated example

linear regression with current status data abstract in survival analysis a linear model often provides an adequate approximation after a suitable transformation of the survival times and possibly of the covariates this article proposes a semiparametric regression method for estimating the regression parameter in the linear model without specifying the distribution of the random error where the response variable is subject to so called case 1 interval censoring the method uses a constructed random sieve likelihood and constraints combining the benefits of semiparametric likelihood with estimating equations the estimation procedure is implemented and the asymptotic distributions for the estimated regression parameter and for the profile likelihood ratio statistic are obtained in addition some model diagnostics aspects are described finally the small sample operating characteristics of the proposed method is examined via simulations and its usefulness is illustrated on datasets from an animal tumorigenicity study and from a hiv study

an atomic energy lower bound that agrees with scott s correction abstract in this paper we prove that the energy of an atom with nuclear charge z is greater than c tf z 7 3 q 8 z 2 o z 17 9 log z atomic units as z q is the number of spin states q 2 for electrons and c tf is the thomas fermi constant for such systems

a semiparametric proportional odds regression model for the analysis of current status data abstract an approach to covariate analysis of current status data is described the method is applicable when the logit of the conditional probability of survival given the covariates is some increasing function of time plus a linear combination of the covariates the approach is based on approximating the infinite dimensional nuisance parameter the baseline log odds of failure with a step function and carrying out a maximum likelihood procedure the resulting finite dimensional parameter estimates for the regression parameters are shown to be asymptotically normal and semiparametric efficient numerical studies with small and moderate samples are discussed

regression with interval censored data summary interval censored data result when survival times are not known exactly but are only known to have occurred between intermittent examination times here the accelerated failure time model is treated for interval censored data a class of score statistics that may be used for estimation and confidence procedures is proposed an adaptive procedure based on estimating the optimal member of the class of score statistics is explored

on estimation of partially linear transformation models we study a general class of partially linear transformation models which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis a new martingale based estimating equation approach consisting of both global and kernel weighted local estimation equations is developed for estimating the parametric and nonparametric covariate effects in a unified manner we show that with a proper choice of the kernel bandwidth parameter one can obtain the consistent and asymptotically normal parameter estimates for the linear effects asymptotic properties of the estimated nonlinear effects are established as well we further suggest a simple resampling method to estimate the asymptotic variance of the linear estimates and show its effectiveness to facilitate the implementation of the new procedure an iterative algorithm is developed numerical examples are given to illustrate the finite sample performance of the procedure supplementary materials are available online

penalized log likelihood estimation for partly linear transformation models with current status data we consider partly linear transformation models applied to current status data the unknown quantities are the transformation function a linear regression parameter and a nonparametric regression effect it is shown that the penalized mle for the regression parameter is asymptotically normal and efficient and converges at the parametric rate although the penalized mle for the transformation function and nonparametric regression effect are only n 1 3 consistent inference for the regression parameter based on a block jack knife is investigated we also study computational issues and demonstrate the proposed methodology with a simulation study the transformation models and partly linear regression terms coupled with new estimation and inference techniques provide flexible alternatives to the cox model for current status data analysis

the free path in a high velocity random flight process associated to a lorentz gas in an external field we investigate the asymptotic behavior of the free path of a variable density random flight model in an external field as the initial velocity of the particle goes to infinity the random flight models we study arise naturally as the boltzmann grad limit of a random lorentz gas in the presence of an external field by analyzing the time duration of the free path we obtain exact forms for the asymptotic mean and variance of the free path in terms of the external field and the density of scatterers as a consequence we obtain a diffusion approximation for the joint process of the particle observed at reflection times and the amount of time spent in free flight

penalized quasi likelihood estimation in partial linear models consider a partial linear model where the expectation of a random variable y depends on covariates x z through f theta 0 x m 0 z with theta 0 an unknown parameter and m 0 an unknown function we apply the theory of empirical processes to derive the asymptotic properties of the penalized quasi likelihood estimator

distribution free maximum likelihood estimator of the binary choice model1 is a given function of the exogenous variables z and unknown parameters 9 representing the systematic component of the utility difference and f is the distribution function of the random component of the utility difference this paper describes a method of estimating the parameters 9 without assuming any functional form for the distribution function f and proves that this estimator is consistent f is also consistently estimated the method uses maximum likelihood estimation in which the likelihood is maximized not only over the parameter 9 but also over a space which contains all distribution functions

estimation and testing in a two sample generalized odds rate model abstract the generalized odds ratio for a survival variable t is defined as t t c c 1 1 sc t sc t for c 0 and log s t for c 0 where s t pr t t this ratio coincides with the integrated hazard for c 0 and the odds ratio for c 1 when the distribution of t depends on a covariate vector we assume that conditionally on the covariates log t t c is linear in the covariates this model is a generalization of the proportional hazard model phm which has an interpretation both as a phm with random nuisance effects clayton and cuzick 1986 and as a proportional odds rate model with the odds rate defined from the response times of series systems harrington and fleming 1982 and bickel 1986a considered rank tests for this semiparametric model clayton and cuzick 1986 considered estimation we use the odds rate representation to define a class of estimates of the proportionality parameter in the two sample case we show that the estimates are consistent and asymptotica

locally efficient estimation with current status data and time dependent covariates abstract in biostatistical applications interest often focuses on the estimation of the distribution of a failure time variable t if one observes only whether or not t exceeds an observed monitoring time c then the data structure is called current status data also known as interval censored data case i we extend the data structure by allowing the presence of a possibly time dependent covariate process which is observed up till the monitoring time c we follow the approach of robins and rotnitzky by modeling the hazard of c conditional on the failure time variable and the covariate process i e the missingness or censoring process under the restriction that the missingness monitoring process satisfies coarsening at random because of the curse of dimensionality no globally efficient nonparametric estimators with a good practical performance at moderate sample sizes exist we introduce an inverse probability of censoring weighted estimator of the distribution and of smooth functionals of this di

computationally simple accelerated failure time regression for interval censored data summary an approach is presented for fitting the accelerated failure time model to interval censored data that does not involve computing the nonparametric maximum likelihood estimate of the distribution function at the residuals the approach involves estimating equations computed with the examination times from the same individual treated as if they had actually been obtained from different individuals the dependence between different measurements obtained from the same individual is then accounted for in the calculation of the standard error of the regression coefficients the approach is applicable to interval censored data in settings in which examinations continue to occur regardless of whether the failure time has occurred simulations are presented to assess the behaviour of the approach and the methodology is illustrated through an application to data from an aids clinical trial

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

varying coefficient transformation models with censored data summary a maximum likelihood method with spline smoothing is proposed for linear transformation models with varying coefficients the estimation and inference procedures are computationally easy under some regularity conditions the estimators are proved to be consistent and asymptotically normal a simulation study using the stanford transplant data is presented to show that the proposed method performs well with a finite sample and is easy to use in practice

testing parametric versus semiparametric modeling in generalized linear models abstract we consider a generalized partially linear model e y x t g x t m t where g is a known function is an unknown parameter vector and m is an unknown function we introduce a test statistic that allows one to decide between a parametric and a semiparametric model a m is linear i e m t t t for a parameter vector and b m is a smooth nonlinear function under linearity a we show that the test statistic is asymptotically normal moreover we prove that the bootstrap works asymptotically simulations suggest that in small samples the bootstrap outperforms the calculation of critical values from the normal approximation the practical performance of the test is demonstrated in applications to data on east west german migration and credit scoring

diffusion in a weakly random hamiltonian flow we consider the motion of a particle governed by a weakly random hamiltonian flow we identify temporal and spatial scales on which the particle trajectory converges to a spatial brownian motion the main technical issue in the proof is to obtain error estimates for the convergence of the solution of the stochastic acceleration problem to a momentum diffusion we also apply our results to the system of random geometric acoustics equations and show that the energy density of the acoustic waves undergoes a spatial diffusion

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

sufficiency of condition ψ for local solvability in two dimensions on etablit l existence de solutions locales de l equation pu f ou p est un operateur pseudodifferentiel classique a 2 dimensions de type principal d ordre m qui satisfait la condition la partie imaginaire p 2 du symbole principal de p ne change pas de signe de a le long d une bicaracteristique orientee de la partie reelle p 1 du symbole principal

a proof of scott s correction for matter this paper contains a strengthening of stability of matter which in particular shows that thomas fermi theory which is already known to give the leading order contribution to the energy of matter if supplemented with the so called scott correction is correct uniformly in the number of nuclei new more precise estimates of the volume of matter also follow

additive hazards regression with current status data current status data arise when the only knowledge about the failure time of interest is whether the failure occurs before or after a random monitoring time we propose to analyse such data by the semiparametric additive hazards model which specifies that the hazard function for the failure time associated with a set of possibly time dependent covariates is the sum of an arbitrary baseline hazard function and a regression function of covariates under certain conditions on the monitoring time one can make inferences about the regression parameters of the additive hazards model by using the familiar asymptotic theory and software for the proportional hazards model with right censored data an application to a carcinogenicity experiment is provided

semiparametric probit models with univariate and bivariate current status data summary multivariate current status data are frequently encountered in biomedical and public health studies semiparametric regression models have been extensively studied for univariate current status data but most existing estimation procedures are computationally intensive involving either penalization or smoothing techniques it becomes more challenging for the analysis of multivariate current status data in this article we study the maximum likelihood estimations for univariate and bivariate current status data under the semiparametric probit regression models we present a simple computational procedure combining the expectation maximization algorithm with the pool adjacent violators algorithm for solving the monotone constraint on the baseline function asymptotic properties of the maximum likelihood estimators are investigated including the calculation of the explicit information bound for univariate current status data as well as the asymptotic consistency and convergence rate for bivariate current status data extensive simulation studies showed that the proposed computational procedures performed well under small or moderate sample sizes we demonstrate the estimation procedure with two real data examples in the areas of diabetic and hiv research

semiparametric bayes proportional odds models for current status data with underreporting current status data are a type of interval censored event time data in which all the individuals are either left or right censored for example our motivation is drawn from a cross sectional study which measured whether or not fibroid onset had occurred by the age of an ultrasound exam for each woman we propose a semiparametric bayesian proportional odds model in which the baseline event time distribution is estimated nonparametrically by using adaptive monotone splines in a logistic regression model and the potential risk factors are included in the parametric part of the mean structure the proposed approach has the advantage of being straightforward to implement using a simple and efficient gibbs sampler whereas alternative semiparametric bayes event time models encounter problems for current status data the model is generalized to allow systematic underreporting in a subset of the data and the methods are applied to an epidemiologic study of uterine fibroids

maximum likelihood estimation in semiparametric regression models with censored data summary semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies the presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models we present several classes of semiparametric regression models which extend the existing models in important directions we construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters the maximum likelihood estimators are consistent and asymptotically normal with efficient variances we develop simple and stable numerical techniques to implement the corresponding inference procedures extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings applications to three medical studies yield important new insights we conclude that there is no reason theoretical or numerical not to use maximum likelihood estimation for semiparametric regression models we discuss several areas that need further research

sieve maximum likelihood estimator for semiparametric regression models with current status data in a randomized controlled clinical trial study where the response variable of interest is the time to occurrence of a certain event it is often too expensive or even impossible to observe the exact time however the current status of the subject at a random time of inspection is much more natural feasible and practical in terms of cost effectiveness this article considers a semiparametric regression model that consists of parametric and nonparametric regression components a sieve maximum likelihood estimator mle is proposed to estimate the regression parameter allowing exploration of the nonlinear relationship between a certain covariate and the response function asymptotic properties of the proposed sieve mles are discussed under some mild conditions the estimators are shown to be strongly consistent moreover the estimators of the unknown parameters are asymptotically efficient and normally distributed and the estimator of the nonparametric function has an optimal convergence rate simula

quantum diffusion of the random schrodinger evolution in the scaling limit we consider random schrodinger equations on r d for d 3 with a homogeneous anderson poisson type random potential denote by the coupling constant and psi t the solution with initial data psi 0 the space and time variables scale as x sim lambda 2 varkappa 2 text and t sim lambda 2 varkappa text with 0 varkappa varkappa 0 left d right we prove that in the limit 0 the expectation of the wigner distribution of psi t converges weakly to the solution of a heat equation in the space variable x for arbitrary l 2 initial data

efficiency bounds for distribution free estimators of the binary choice and the censored regression models we derive lower bounds on the asymptotic variances for regular distribution free estimators of the parameters of the binary choice model and the censored regression tobit model a distribution free or semiparametric estimator is one that does not require any assumption about the distribution of the stochastic error term in the model apart from regularity conditions for the binary choice model we obtain an explicit lower bound for the asymptotic variance for the slope parameters or more generally the parameters of a nonlinear regression function in the underlying latent variable model but we find that there is no regular semiparametric estimator of the constant term identified by requiring the error distribution to have zero median lower bounds are also obtained under the further assumption that the error distribution is symmetric and in this case there is a finite lower bound for the constant term too comparison of the bounds with those for the classical parametric problem shows the loss of information due to lack of a priori knowledge of the functional form of the error distribution we give the conditions for equality of the parametric and semiparametric lower bounds in which case adaptive estimation may be possible both with and without the assumption of a symmetric error distribution in general adaptive estimation is not possible but one special case where these conditions hold is when the regression function is linear and the explanatory variables have a multivariate normal distribution the tobit model considered here is the censored nonlinear regression model with a fixed censoring point we again give an explicit lower bound for the asymptotic variance for the regression parameters this time including a constant term if the error term has zero median comparison with the corresponding lower bound for the parametric case shows that adaptive estimation is in general not possible for this model

analysis of transformation models with censored data summary in this paper we consider a class of semi parametric transformation models under which an unknown transformation of the survival time is linearly related to the covariates with various completely specified error distributions this class of regression models includes the proportional hazards and proportional odds models inference procedures derived from a class of generalised estimating equations are proposed to examine the covariate effects with censored observations numerical studies are conducted to investigate the properties of our proposals for practical sample sizes these transformation models coupled with the new simple inference procedures provide many useful alternatives to the cox regression model in survival analysis

asymptotic optimality for c_p c_l cross validation and generalized cross validation discrete index set c p c l cross validation and generalized cross validation are useful data driven techniques for selecting a good estimate from a proposed class of linear estimates the asymptotic behaviors of these procedures are studied some easily interpretable conditions are derived to demonstrate the asymptotic optimality it is argued that cross validation and generalized cross validation can be viewed as some special ways of applying c l applications in nearest neighbor nonparametric regression and in model selection are discussed in detail

large sample confidence regions based on subsamples under minimal assumptions in this article the construction of confidence regions by approximating the sampling distribution of some statistic is studied the true sampling distribution is estimated by an appropriate normalization of the values of the statistic computed over subsamples of the data in the i i d context the method has been studied by wu in regular situations where the statistic is asymptotically normal the goal of the present work is to prove the method yields asymptotically valid confidence regions under minimal conditions essentially all that is required is that the statistic suitably normalized possesses a limit distribution under the true model unlike the bootstrap the convergence to the limit distribution need not be uniform in any sense the method is readily adapted to parameters of stationary time series or more generally homogeneous random fields for example an immediate application is the construction of a confidence interval for the spectral density function of a homogeneous random field