on a local existence theorem of neumann problem for some quasilinear hyperbolic systems of 2nd order on considere l existence locale en temps des solutions pour un systeme hyperbolique quasilineaire avec des conditions aux limites de type neumann

existence of regular solutions for a quasilinear wave equation with the third boundary condition on etablit l existence locale en temps des solutions classiques du probleme aux valeurs limites et initiales suivant u tt t x i j 1 3 i a ij t x u t x j u t x f t x u t x x u t x t x 0 t r r 3 i j 1 3 a ij t u t i j u t t u t 0 t 0 t u 0 x u 0 x u t 0 x u 1 x x

fitting regression models to case control data by maximum likelihood summary we consider fitting categorical regression models to data obtained by either stratified or nonstratified case control or response selective sampling from a finite population with known population totals in each response category with certain models such as the logistic with appropriate constant terms a method variously known as conditional maximum likelihood breslow cain 1988 or pseudo conditional likelihood wild 1991 which involves the prospective fitting of a pseudo model results in maximum likelihood estimates of case control data we extend these results by showing the maximum likelihood estimates for any model can be found by iterating this process with a simple updating of offset parameters attention is also paid to estimation of the asymptotic covariance matrix one benefit of the results of this paper is the ability to obtain maximum likelihood estimates of the parameters of logistic models for stratified case control studies compare breslow cain 1988 scott wild 1991 using an ordinary logistic regression program even when the stratum constants are modelled

the dirichlet cauchy problem for nonlinear hyperbolic equations in a domain with edges abstract we study the dirichlet cauchy problem for nonlinear hyperbolic equation of second order in a domain with edges the aim of this paper is to prove the regularity of solution in weighted sobolev spaces

normal forms and quadratic nonlinear klein gordon equations on construit une transformation qui change l equation a non linearite cubique que l on sait resoudre a 3 1 dimensions on demontre que la solution du probleme original a le meme comportement asymptotique que l equation de klein gordon non lineaire

maximum likelihood estimation of logistic regression parameters under two phase outcome dependent sampling summary outcome dependent sampling increases the efficiency of studies of rare outcomes examples being case control studies in epidemiology and choice based sampling in econometrics two phase or double sampling is a standard technique for drawing efficient stratified samples we develop maximum likelihood estimation of logistic regression coefficients for a hybrid two phase outcome dependent sampling design an algorithm is given for determining the estimates by repeated fitting of ordinary logistic regression models simulation results demonstrate the efficiency loss associated with alternative pseudolikelihood and weighted likelihood methods for certain data configurations these results provide an efficient solution to the measurement error problem with validation sampling based on a discrete surrogate

local well posedness for membranes in the light cone gauge in this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge a hamiltonian reduction gives a system with one constraint the area preserving constraint the hamiltonian evolution equations corresponding to this system however fail to be hyperbolic making use of the area preserving constraint an equivalent system of evolution equations is found which is hyperbolic and has a well posed initial value problem we are thus able to solve the initial value problem for the hamiltonian evolution equations by means of this equivalent system we furthermore obtain a blowup criterion for the membrane evolution equations and show making use of the constraint that one may achieve improved regularity estimates

existence of periodic solutions in predator prey with watt type functional response and impulsive effects abstract in this paper the existence of a periodic solution and the permanence of a periodic watt type predator prey system where the prey disperses in patchy environment with two patches are investigated with the continuation theorem of coincidence degree theory we obtain the existence of a positive periodic solution for such a system we assume the watt type functional response within patch dynamics and provide a sufficient condition to guarantee the predator and prey species to be permanent furthermore we give numerical analysis to confirm our theoretical results it will be useful to ecosystem control

clustering methods based on variational analysis in the space of measures we formulate clustering as a minimisation problem in the space of measures by modelling the cluster centres as a poisson process with unknown intensity function we derive a ward type clustering criterion which under the poisson assumption can easily be evaluated explicitly in terms of the intensity function we show that asymptotically i e for increasing total intensity the optimal intensity function is proportional to a dimension dependent power of the density of the observations for fixed finite total intensity no explicit solution seems available however the ward type criterion to be minimised is convex in the intensity function so that the steepest descent method of molchanov and zuyev 2001 can be used to approximate the global minimum it turns out that the gradient is similar in form to the functional to be optimised if we discretise over a grid the steepest descent algorithm at each iteration step increases the current intensity function at those points where the gradient is minimal at the expense of regions with a large gradient value the algorithm is applied to a toy one dimensional example a simulation from a popular spatial cluster model and a real life dataset from strauss 1975 concerning the positions of redwood seedlings finally we discuss the relative merits of our approach compared to classical hierarchical and partition clustering techniques as well as to modern model based clustering methods using markov point processes and mixture distributions

blow up for quasi linear wave equations in three space dimensions we consider equations of the form u phi x t u u u 1a for a function u u x 1 x n t u x t here denotes the d alembertian square frac partial 2 partial t 2 vartriangle 1b and u represents the vector of first derivatives u that of second derivatives of u with respect to the x k and t on linearizing 1a shall go over into the classical wave equation u 0 this means that and its first derivatives with respect to u u u shall vanish for u u u 0

on some nonlinear hyperbolic systems with damping boundary conditions in recent years the effect of boundary damping on the solutions to interior initial boundary value problems for hyperbolic equations has been extensively studied in 111 quinn and russell considered the wave equation with damping boundary condition on a part of the boundary it was proved by control theoretic method that if the boundary where the boundary condition was posed was star shaped then the solution of the wave equation had polynomial decay rate later on chen in l got the exponential decay of solutions to the wave equation under the more restrictive assumptions on the boundary and also lagnese in 6 got the exponential decay of solutions to the three dimensional elastic wave equations with damping boundary condition on a part of the boundary provided the geometry of the boundary is suitably restricted as for the nonlinear problem greenberg and li in 131 considered the nonlinear conservation system in one space dimension with damping boundary condition and proved the global existence of smooth solution when the initial data are small shen and zheng 14 and nagasawa 9 proved the global existence of classical solutions to the system of one dimensional thermoelasticity and to the system of one dimensional nonlinear problem in higher space dimension respectively for the nonlinear problem in higher space dimension to our knowledge the works were done by qin lo and zajaczkowski 26 only for the nonlinear wave equation with damping boundary conditions based on chen s results in l in this paper our aim is to derive the decay rate of solutions to the linear hyperbolic system of second order with damping boundary condition without any assumptions on the geometry of the boundary by using the spectral analysis method cf section 2 below and then to prove the global existence of smooth solutions to the corresponding nonlinear system with applications to nonlinear elastodynamics and to nonlinear acoustic wave equations our approach to obtaining the rate of decay of solutions to linear problem is completely different from l 6 and lo

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

on the motion of a compact elastic body we study the problem of motion of a relativistic ideal elastic solid with free surface boundary by casting the equations in material form lagrangian coordinates by applying a basic theorem due to koch we prove short time existence and uniqueness for solutions close to a trivial solution this trivial or natural solution corresponds to a stress free body in rigid motion

large sample theory for semiparametric regression models with two phase outcome dependent sampling outcome dependent two phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by lawless kalbfleisch and wild 1999 under two phase sampling designs we show that the maximum likelihood estimators for both the parametric and nonparametric parts of the model are asymptotically normal and efficient the efficient influence function for the parametric part agrees with the more general information bound calculations of robins hsieh and newey 1995 by verifying the conditions of murphy and van der vaart 2000 for a least favorable parametric submodel we provide asymptotic justification for statistical inference based on profile likelihood

odds ratios for a continuous outcome variable without dichotomizing the loss of information from dichotomizing a continuous outcome is well documented in the literature one advantage of dichotomizing is that it allows estimation of odds ratio parameters through a logistic regression analysis the objective of this paper is to develop a new estimator of the same odds ratio parameters through regression analysis on the original continuous outcome without the inherent loss of information caused by dichotomizing through a mathematical asymptotic development the relative sample sizes required to attain a specified power when testing the odds ratio parameter are compared for the dichotomizing procedure and the proposed approach the comparison highlights the substantial sample size savings attained by the proposed approach particularly for large values of the odds ratio parameter and for small proportions of dichotomized successes or failures in a monte carlo simulation the variances and absolute biases of the two odds ratio estimators and the length of their respective confidence intervals again demonstrate the improvement attained by the proposed approach in addition coverage probabilities of the confidence intervals of the proposed approach converge quickly to the nominal levels the cost savings due to the reduction in required sample size when using this method make it a very attractive study design and analysis tool for medical researchers copyright 2004 john wiley sons ltd

mixed problems for fully nonlinear hyperbolic equations 1 i n the summation convention is used here i j n f 2 c l r is a bounded domain with smooth boundary f v the outer normal f2t 0 t x f2 and ft 0 t x f 0 t oo f and g satisfy some natural conditions which assure hyperbolicity the main result is concerned with classical solutions for small t assume that uoe ws l f2 n and ul e ws f2 n where s is an integer bigger than 1 n 2 this implies uo e c2 0 n under suitable assumptions the following holds

optimal approximation and quantisation abstract a number of interesting functionals f x of a finite point set x in the euclidean space can be represented as integrals of a function that depends on the integration variable y and x restricted onto a certain set c y x that is determined by y and x and satisfies separation and uniform boundedness conditions for instance c y x can be the voronoi cell generated by x that contains y we single out the general properties of c and that ensure that the normalised infimum of f x over all sets x with cardinality n converges to a limit that can be identified using a particular form of the considered functionals include those that appear in quantisation problems for probability measures and in finding the optimal approximation of a function by splines tangent planes and triangulated surfaces for instance it is shown that the minimum l approximation error normalised by n of a sufficiently smooth bivariate convex function f using the convex triangulation converges to the l 1 1 norm of the determinant of the second derivative of f times a certain absolute constant

on profile likelihood abstract we show that semiparametric profile likelihoods where the nuisance parameter has been profiled out behave like ordinary likelihoods in that they have a quadratic expansion in this expansion the score function and the fisher information are replaced by the efficient score function and efficient fisher information the expansion may be used among others to prove the asymptotic normality of the maximum likelihood estimator to derive the asymptotic chi squared distribution of the log likelihood ratio statistic and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance

the analysis of retrospective family studies summary case control samples allow straightforward calculation of estimates of the association between covariates and disease status by fitting a prospective logistic regression model in genetic studies of disease investigators often gather additional information on response and covariate variables from family members of cases and controls the objective is to model the responses of all the family members in terms of the covariate data whittemore 1995 has discussed maximum likelihood methods for fitting a special class of logistic models to family data collected according to a particular design in the present paper we show that we can obtain efficient semiparametric maximum likelihood estimates for an arbitrary multivariate binary regression model by fitting a modified prospective model for a wide class of retrospective designs however in contrast to the situation with simple case control studies the prospective model will differ from the original model even when the model is logistic

energy methods for quasilinear hyperbolic initial boundary value problems applications to elastodynamics the aim of this paper is to show how energy methods can be used to establish local in time existence of smooth solutions to certain initial boundary value problems for systems of quasilinear hyperbolic partial differential equations our particular objective is to treat the equations of nonlinear elastodynamics

variational analysis of functionals of poisson processes letf ii be a functional of a generally nonhomogeneous poisson process ii with intensity measure considering the expectatione f ii as a functional of from the cone m of positive finite measures we derive closed form expressions for its fra chet derivatives of all orders that generalize the perturbation analysis formulae for poisson processes variational methods developed for the space m allow us to obtain first and second order sufficient conditions for various types of constrained optimization problems fore f we study in detail optimization over the class of measures with a fixed total massa and develop a technique that often allows us to obtain the asymptotic behavior of the optimal intensity measure in the high intensity setting whena grows to infinity as a particular application we consider the problem of optimal placement of stations in the poisson model of a two layer telecommunication network

exact boundary controllability for 1 d quasilinear wave equations in this paper we present a unified constructive method to establish the local exact boundary controllability for 1 d quasilinear wave equations with boundary conditions of various types

the global existence of yang mills higgs fields in 4 dimensional minkowski space in this paper we complete the proof of global existence of yang mills higgs fields in 4 dimensional minkowski space by showing that an appropriate norm of the solutions cannot blow up in a finite time a key step in the proof is the demonstration that thel norm of the curvature is boundeda priori our results apply to any compact guage group and to any invariant higgs self coupling which is positive and of no higher than quartic degree

semiparametric methods for response selective and missing data problems in regression summary suppose that data are generated according to the model f ylx 0 g x where y is a response and x are covariates we derive and compare semiparametric likelihood and pseudolikelihood methods for estimating 0 for situations in which units generated are not fully observed and in which it is impossible or undesirable to model the covariate distribution the probability that a unit is fully observed may depend on y and there may be a subset of covariates which is observed only for a subsample of individuals our key assumptions are that the probability that a unit has missing data depends only on which of a finite number of strata that y x belongs to and that the stratum membership is observed for every unit applications include case control studies in epidemiology field reliability studies and broad classes of missing data and measurement error problems our results make fully efficient estimation of 0 feasible and they generalize and provide insight into a variety of methods that have been proposed for specific problems

analyticity of solutions for quasilinear wave equations and other quasilinear systems we prove the persistence of analyticity for classical solution of the cauchy problem for quasilinear wave equations with analytic data our results show that the analyticity of solutions stated by the cauchy kowalewski and ovsiannikov nirenberg theorems lasts till a classical solution exists moreover they show that if the equation and the cauchy data are analytic only in a part of space variables then a classical solution also is analytic in these variables the approach applies to other quasilinear equations and implies the persistence of the space analyticity and the partial space analyticity of their classical solutions

semiparametric likelihood ratio inference likelihood ratio tests and related confidence intervals for a real parameter in the presence of an infinite dimensional nuisance parameter are considered in all cases the estimator of the real parameter has an asymptotic normal distribution however the estimator of the nuisance parameter may not be asymptotically gaussian or may converge to the true parameter value at a slower rate than the square root of the sample size nevertheless the likelihood ratio statistic is shown to possess an asymptotic chi squared distribution the examples considered are tests concerning survival probabilities based on doubly censored data a test for presence of heterogeneity in the gamma frailty model a test for significance of the regression coefficient in cox s regression model for current status data and a test for a ratio of hazards rates in an exponential mixture model in both of the last examples the rate of convergence of the estimator of the nuisance parameter is less than the square root of the sample size

fitting logistic models under case control or choice based sampling on compare deux approches dans le cas important de l ajustement des modeles de regression logistique

a bayesian goodness of fit test and semiparametric generalization of logistic regression with measurement data summary logistic regression is a popular tool for risk analysis in medical and population health science with continuous response data it is common to create a dichotomous outcome for logistic regression analysis by specifying a threshold for positivity fitting a linear regression to the nondichotomized response variable assuming a logistic sampling model for the data has been empirically shown to yield more efficient estimates of odds ratios than ordinary logistic regression of the dichotomized endpoint we illustrate that risk inference is not robust to departures from the parametric logistic distribution moreover the model assumption of proportional odds is generally not satisfied when the condition of a logistic distribution for the data is violated leading to biased inference from a parametric logistic analysis we develop novel bayesian semiparametric methodology for testing goodness of fit of parametric logistic regression with continuous measurement data the testing procedures hold for any cutoff threshold and our approach simultaneously provides the ability to perform semiparametric risk estimation bayes factors are calculated using the savage dickey ratio for testing the null hypothesis of logistic regression versus a semiparametric generalization we propose a fully bayesian and a computationally efficient empirical bayesian approach to testing and we present methods for semiparametric estimation of risks relative risks and odds ratios when parametric logistic regression fails theoretical results establish the consistency of the empirical bayes test results from simulated data show that the proposed approach provides accurate inference irrespective of whether parametric assumptions hold or not evaluation of risk factors for obesity shows that different inferences are derived from an analysis of a real data set when deviations from a logistic distribution are permissible in a flexible semiparametric framework

local existence of solutions for the neumann problem of the nonlinear elastodynamic system outside a domain abstract in this paper we study the mixed initial boundary value problem of neumann type for the nonlinear elastic wave equation outside a domain the local existence of solutions to this problem is proved by iteration to get this result we prove the existence of solutions for the second order linear hyperbolic system with variable coefficients in sobolev spaces outside of a domain by using linear evolution operators and integro differential equations

local existence of solution for the initial boundary value problem of fully nonlinear wave equation on considere l existence locale par rapport au temps des solutions pour le probleme aux valeurs limites et initiales d une equation d onde totalement non lineaire

large sample theory of maximum likelihood estimates in semiparametric biased sampling models vardi ann statist 13 178 203 1985 introduced an s sample biased sampling model with known selection weight functions gave a condition under which the common underlying probability distribution g is uniquely estimable and developed simple procedure for computing the nonparametric maximum likelihood estimator npmle g n of g gill vardi and wellner thoroughly described the large sample properties of vardi s npmle giving results on uniform consistency convergence of n g n g to a gaussian process and asymptotic efficiency of g n gilbert lele and vardi considered the class of semiparametric s sample biased sampling models formed by allowing the weight functions to depend on an unknown finite dimensional parameter they extended vardi s estimation approach by developing a simple two step estimation procedure in which n is obtained by maximizing a profile partial likelihood and g n g n n is obtained by evaluating vardi s npmle at n here we examine the large sample behavior of the resulting joint mle n g n characterizing conditions on the selection weight functions and data in order that n g n is uniformly consistent asymptotically gaussian and efficient examples illustrated here include clinical trials especially hiv vaccine efficacy trials choice based sampling in econometrics and case control studies in biostatistics

transonic shock wave in an infinite nozzle asymptotically converging to a cylinder abstract we construct a single transonic shock wave pattern in an infinite nozzle asymptotically converging to a cylinder which is close to a uniform transonic shock wave in other words suppose there is a uniform transonic shock wave in an infinite cylinder nozzle which can be constructed easily if we perturbed the supersonic incoming flow and the infinite nozzle a little bit we can obtain a transonic wave near the uniform one as a consequence we can show that the uniform transonic wave is stable with respect to the perturbation of the incoming flow and nozzle wall based on the theory of g q chen m feldman existence and stability of multi dimensional transonic flows through an infinite nozzle of arbitrary cross sections arch ration mech anal 184 2007 185 242 the crucial parts of this paper are to derive the uniform schauder estimates of the linear elliptic equation for the infinite nozzle asymptotically converging to a cylinder

global smooth solutions of 3 d null form wave equations in exterior domains with neumann boundary conditions abstract the paper is devoted to investigating long time behavior of smooth small data solutions to 3 d quasilinear wave equations outside of compact convex obstacles with neumann boundary conditions concretely speaking when the surface of a 3 d compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition we prove that the smooth small data solution exists globally provided that the neumann boundary condition on the exterior domain is given one of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself as an application of the main result the global stability to 3 d static compressible chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude

maximum likelihood estimation with partially censored data suppose one observes independent samples of size n from both the mixture density int p x mid z d eta z and from the distribution eta the kernel p x mid z is known we show asymptotic normality and efficiency of the maximum likelihood estimator for eta

on the mixed problem for some quasilinear hyperbolic system with fully nonlinear boundary condition on demontre le theoreme d existence locale en temps des solutions classiques pour le probleme mixte pour des systemes d ordre 2 t 2 u t i p i t d 1 u t q t d 1 u t f t dans 0 t i p i t d 1 u t q t d 1 u t f t sur 0 t u 0 u 0 et t u 0 u 1 dans

the error in linear interpolation at the vertices of a simplex a formula for the error in multivariate quasi interpolation which reproduces the linear polynomials is given from it sharp pointwise l infty bounds for the error in linear interpolation interpolation by linear polynomials to function values at the vertices of a simplex are obtained the corresponding envelope theorem giving the optimal recovery of functions is discussed

tangent sets in the space of measures with applications to variational analysis we characterise the first and second order tangent sets in the linear space of signed measures with finite total variation and apply the obtained results to derive necessary optimality conditions for functionals on measures

analysis and geometry on configuration spaces abstract in this paper foundations are presented to a new systematic approach to analysis and geometry for an important class of infinite dimensional manifolds namely configuration spaces more precisely a differential geometry is introduced on the configuration space x over a riemannian manifold x this geometry is non flat even if x r d it is obtained as a natural lifting of the riemannian structure on x in particular a corresponding gradient divergence div and laplace beltrami operator h div gamma are constructed the associated volume elements i e all measures on x w r t which and div gamma become dual operators on l 2 x are identified as exactly the mixed poisson measures with mean measure equal to a multiple of the volume element dx on x in particular all these measures obey an integration by parts formula w r t vector fields on x the corresponding dirichlet forms e on l 2 x are therefore defined each is shown to be associated with a diffusion process which is thus the brownian motion on x and which is sub sequently identified as the usual independent infinite particle process on x the associated heat semigroup t t t 0 is calculated explicitly it is also proved that the diffusion process when started with is time ergodic or equivalently e gamma is irreducible or equivalently t t t 0 is ergodic if and only if is poisson measure z dx with intensity z dx for some z 0 furthermore it is shown that the laplace beltrami operator h div gamma gamma on l 2 x z dx is unitary equivalent to the second quantization of the laplacian x on x on the corresponding fock space n 0 l 2 x z dx n as another direct consequence of our results we obtain a representation of the lie algebra of compactly supported vector fields on x on poisson space finally generalizations to the case where dx is replaced by an absolutely continuous measure and also to interacting particle systems on x are described in particular the case where the mixed poisson measures are replaced by gibbs measures of ruelle type on x

poisson process fock space representation chaos expansion and covariance inequalities we consider a poisson process on an arbitrary measurable space with an arbitrary sigma finite intensity measure we establish an explicit fock space representation of square integrable functions of as a consequence we identify explicitly in terms of iterated difference operators the integrands in the wiener ito chaos expansion we apply these results to extend well known variance inequalities for homogeneous poisson processes on the line to the general poisson case the poincare inequality is a special case further applications are covariance identities for poisson processes on strictly ordered spaces and harris fkg inequalities for monotone functions of

optimum quantization and its applications abstract minimum sums of moments or equivalently distortion of optimum quantizers play an important role in several branches of mathematics fejes toth s inequality for sums of moments in the plane and zador s asymptotic formula for minimum distortion in euclidean d space are the first precise pertinent results in dimension d 2 in this article these results are generalized in the form of asymptotic formulae for minimum sums of moments resp distortion of optimum quantizers on riemannian d manifolds and normed d spaces in addition we provide geometric and analytic information on the structure of optimum configurations our results are then used to obtain information on i the minimum distortion of high resolution vector quantization and optimum quantizers ii the error of best approximation of probability measures by discrete measures and support sets of best approximating discrete measures iii the minimum error of numerical integration formulae for classes of holder continuous functions and optimum sets of nodes iv best volume approximation of convex bodies by circumscribed convex polytopes and the form of best approximating polytopes and v the minimum isoperimetric quotient of convex polytopes in minkowski spaces and the form of the minimizing polytopes

weak solutions and development of singularities of the su 2 σ model pour toutes donnees initiales d energie finie le modele sigma o k a des solutions faibles globales en chaque dimension d espace temps

a transmission problem for quasi linear wave equations we prove the local existence and uniqueness of solutions to a system of quasi linear wave equations involving a jump discontinuity in the lower order terms a continuation principle is also established

the numerical simulation of periodic solutions for a predator prey system in this article the existence and global stability of periodic solutions for a semi ratio dependent predator prey system with holling iv functional response and time delays are investigated using coincidence degree theory and lyapunov method sufficient conditions for the existence and global stability of periodic solutions are obtained a numerical simulation is given to illustrate the results

semiparametric efficient estimation of a conditional density with missing or mismeasured covariates summary pepe and fleming and carroll and wand have recently proposed estimators in a parametric model for the density of a random variable y conditional on a vector of covariates x v when data on one of the regressors x is missing for some study subjects we propose a new class of estimators that remains consistent and asymptotically normal even when the probability that x is missing depends on the observed v and y includes an estimator whose asymptotic variance attains the semiparametric variance bound for the model and when the data are missing completely at random includes an estimator that is asymptotically equivalent to the inefficient estimators proposed by pepe and fleming and by carroll and wand the optimal estimator in our class depends on the unknown probability law generating the data when the vector v of non missing regressors has at most two continuous components we propose an adaptive semiparametric efficient estimator and compare the performance of the proposed semiparametric efficient estimator with the estimators proposed by pepe and fleming and carroll and wand in a small simulation study when v has many continuous components we propose an alternative class of adaptive estimators that should have high efficiency

case control analysis with a continuous outcome variable it is not uncommon for a continuous outcome variable y to be dichotomized and analysed using logistic regression moser and coombs statist med 2004 23 1843 1860 provide a method for converting the output from a standard linear regression analysis using the original continuous outcome y to give much more efficient inferences about the same odds ratio parameters being estimated by the logistic regression however these results apply only to prospective studies this paper follows up moser and coombs by providing an efficient linear model based solution for data collected using case control studies gains in statistical efficiency of up to 240 per cent are obtained even with small to moderate odds ratios differences in design efficiency between case control and prospective sampling designs are found to be much smaller however when linear model based analyses are being used than they are when logistic regression analyses are being used

global solutions of nonlinear hyperbolic equations for small initial data on considere des systemes quasilineaires d equations hyperboliques d ordre 2 qui sont des deformations non lineaires de l equation d onde on etudie l existence globale et le comportement asymptotique des solutions du probleme de cauchy quand la donnee initiale est suffisamment petite

existence and stability of multidimensional transonic flows through an infinite nozzle of arbitrary cross sections we establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross sections including a slowly varying de laval nozzle the transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance uniform subsonic downstream flow at the exit at infinity and the slip boundary condition on the nozzle boundary our results indicate that if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow there exists a solution that consists of a c1 subsonic flow in the unbounded downstream region converging to a uniform velocity state at infinity and a c1 multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow and the shock is orthogonal to the nozzle boundary at every point of their intersection in order to construct such a transonic flow we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase in which the equation is elliptic and the free boundary is a transonic shock the free boundary conditions are determined by the rankine hugoniot conditions along the shock we further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain we also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

central limit theorems for u statistics of poisson point processes a u statistic of a poisson point process is defined as the sum f x1 xk over all possibly infinitely many k tuples of distinct points of the point process using the malliavin calculus the wiener ito chaos expansion of such a functional is computed and used to derive a formula for the variance central limit theorems for u statistics of poisson point processes are shown with explicit bounds for the wasserstein distance to a gaussian random variable as applications the intersection process of poisson hyperplanes and the length of a random geometric graph are investigated