existence and stability of periodic solutions for parabolic systems with time delays this paper is concerned with the existence and stability time periodic solutions for a class of coupled parabolic equations with time delay and time delays may appear in the nonlinear reaction functions the existence of time periodic solutions is for a class of locally lipschitz continuous reaction functions without any quasimonotone requirement our approach to the problem is by the method of upper and lower solution and using schauder fixed point theorem some methods for proving the stability of the periodic solution are also given the results for the general system can be applied to the standard parabolic equations without time delay and corresponding ordinary differential system finally a model arising from chemistry is used to illustrate the obtained results

inference on the quantile regression process tests based on the quantile regression process can be formulated like the classical kolmogorov smirnov and cramer von mises tests of goodness of fit employing the theory of bessel processes as in kiefer 1959 however it is frequently desirable to formulate hypotheses involving unknown nuisance parameters thereby jeopardizing the distribution free character of these tests we characterize this situation as the durbin problem since it was posed in durbin 1973 for parametric empirical processes in this paper we consider an approach to the durbin problem involving a martingale transformation of the parametric empirical process suggested by khmaladze 1981 and show that it can be adapted to a wide variety of inference problems involving the quantile regression process in particular we suggest new tests of the location shift and location scale shift models that underlie much of classical econometric inference the methods are illustrated with a reanalysis of data on unemployment durations from the pennsylvania reemployment bonus experiments the pennsylvania experiments conducted in 1988 89 were designed to test the efficacy of cash bonuses paid for early reemployment in shortening the duration of insured unemployment spells

quantile regression adjusting for dependent censoring from semicompeting risks in this work we study quantile regression when the response is an event time subject to potentially dependent censoring we consider the semi competing risks setting where time to censoring remains observable after the occurrence of the event of interest while such a scenario frequently arises in biomedical studies most of current quantile regression methods for censored data are not applicable because they generally require the censoring time and the event time be independent by imposing rather mild assumptions on the association structure between the time to event response and the censoring time variable we propose quantile regression procedures which allow us to garner a comprehensive view of the covariate effects on the event time outcome as well as to examine the informativeness of censoring an efficient and stable algorithm is provided for implementing the new method we establish the asymptotic properties of the resulting estimators including uniform consistency and weak convergence the theoretical development may serve as a useful template for addressing estimating settings that involve stochastic integrals extensive simulation studies suggest that the proposed method performs well with moderate sample sizes we illustrate the practical utility of our proposals through an application to a bone marrow transplant trial

instrumental variable quantile regression a robust inference approach abstract in this paper we develop robust inference procedures for an instrumental variables model defined by y d u where d u is strictly increasing in u and u is a uniform variable that may depend on d but is independent of a set of instrumental variables z the proposed inferential procedures are computationally convenient in typical applications and can be carried out using software available for ordinary quantile regression our inferential procedure arises naturally from an estimation algorithm and has the important feature of being robust to weak and partial identification and remains valid even in cases where identification fails completely the use of the proposed procedures is illustrated through two empirical examples

traveling wavefronts for time delayed reaction diffusion equation ii nonlocal nonlinearity abstract in this paper we study a class of time delayed reaction diffusion equation with local nonlinearity for the birth rate for all wavefronts with the speed c c where c 0 is the critical wave speed we prove that these wavefronts are asymptotically stable when the initial perturbation around the traveling waves decays exponentially as x but the initial perturbation can be arbitrarily large in other locations this essentially improves the stability results obtained by mei so li and shen m mei j w h so m y li s s p shen asymptotic stability of traveling waves for the nicholson s blowflies equation with diffusion proc roy soc edinburgh sect a 134 2004 579 594 for the speed c 2 d m e p d m with small initial perturbation and by lin and mei c k lin m mei on travelling wavefronts of the nicholson s blowflies equations with diffusion submitted for publication for c c with sufficiently small delay time r 0 the approach adopted in this paper is the technical weighted energy method used in m mei j w h so m y li s s p shen asymptotic stability of traveling waves for the nicholson s blowflies equation with diffusion proc roy soc edinburgh sect a 134 2004 579 594 but inspired by gourley s a gourley linear stability of travelling fronts in an age structured reaction diffusion population model quart j mech appl math 58 2005 257 268 and based on the property of the critical wavefronts the weight function is carefully selected and it plays a key role in proving the stability for any c c and for an arbitrary time delay r 0

simple resampling methods for censored regression quantiles abstract powell journal of econometrics 25 1984 303 325 journal of econometrics 32 1986 143 155 considered censored regression quantile estimators the asymptotic covariance matrices of his estimators depend on the error densities and are therefore difficult to estimate reliably the difficulty may be avoided by applying the bootstrap method hahn econometric theory 11 1995 105 121 calculation of the estimators however requires solving a nonsmooth and nonconvex minimization problem resulting in high computational costs in implementing the bootstrap we propose in this paper computationally simple resampling methods by convexfying powell s approach in the resampling stage a major advantage of the new methods is that they can be implemented by efficient linear programming simulation studies show that the methods are reliable even with moderate sample sizes

censored quantile regression with partially functional effects quantile regression offers a flexible approach to analyzing survival data allowing each covariate effect to vary with quantiles in practice constancy is often found to be adequate for some covariates in this paper we study censored quantile regression tailored to the partially functional effect setting with a mixture of varying and constant effects such a model can offer a simpler view regarding covariate survival association and moreover can enable improvement in estimation efficiency we propose profile estimating equations and present an iterative algorithm that can be readily and stably implemented asymptotic properties of the resultant estimators are established a simple resampling based inference procedure is developed and justified extensive simulation studies demonstrate efficiency gains of the proposed method over a naive two stage procedure the proposed method is illustrated via an application to a recent renal dialysis study

boundary control of an unstable heat equation via measurement of domain averaged temperature in this note a feedback boundary controller for an unstable heat equation is designed the equation can be viewed as a model of a thin rod with not only the heat loss to a surrounding medium stabilizing but also the heat generation inside the rod destabilizing the heat generation adds a destabilizing linear term on the right hand side of the equation the boundary control law designed is in the form of an integral operator with a known continuous kernel function but can be interpreted as a backstepping control law this interpretation provides a lyapunov function for proving stability of the system the control is applied by insulating one end of the rod and applying either dirichlet or neumann boundary actuation on the other

an adapted loss function for censored quantile regression in this article we study a novel approach for the estimation of quantiles when facing potential right censoring of the responses contrary to the existing literature on the subject the adopted st

existence of traveling wave solutions for a reaction diffusion equation with distributed delays abstract in this paper we consider a reaction diffusion equation with distributed delays special attention is paid to the existence of traveling wave solutions for special delay kernels using the linear chain trick and the geometric singular perturbation theory we investigate a natural connection between the existence of traveling wave solutions for the reaction diffusion equation with distributed delays and the existence of traveling wave solutions for the corresponding undelayed reaction diffusion equation we show that if the corresponding undelayed reaction diffusion equation has a traveling wave solution then for any sufficiently small delay the delayed reaction diffusion equation also has a traveling wave solution

censored regression quantiles using quantile regression to analyze survival times offers an valuable complement to traditional cox proportional hazards modelling unfortunately this approach has been hampered by the lack of a conditional quantile estimator for censored data that is directly analogous to the kaplan meier estimator and applies under standard assumptions for censored regression models here a recursively reweighted estimator of the regression quantile process is developed as a direct generalization of the kaplan meier estimator specifically the asymptotic behavior is directly analogous to that of the kaplan meier estimator and computation is essentially equivalent to current simplex methods for the quantile process in the uncensored case some preliminary examples suggest the strong potential of these methods as a complement to the use of cox models

global existence and uniform decay for wave equation with dissipative term and boundary damping in this paper we prove the existence uniqueness and uniform stability of strong and weak solutions of the nonlinear wave equation u t email protected b x u t f u 0 in bounded domains with nonlinear damped boundary conditions given by email protected email protected g u t 0 with restrictions on function f u g u t and b x we prove the existence by means of the glerkin method and obtain the asymptotic behavior by using of the multiplier technique from the idea of kmornik and zuazua see 7

diffusive monotonicity and threshold dynamics of delayed reaction diffusion equations abstract for abstract functional differential equations and reaction diffusion equations with delay an exponential ordering is introduced which takes into account the spatial diffusion the induced monotonicity of the solution semiflows is established and applied to describe the threshold dynamics extinction or persistence convergence to positive equilibria for a nonlocal and delayed reaction diffusion population model

approximate controllability of a system of parabolic equations with delay abstract in this paper we give necessary and sufficient conditions for the approximate controllability of the following system of parabolic equations with delay z t x t d z l z t b u t x t 0 r z 0 x t 0 r z 0 x 0 x x z s x s x s 0 x where is a bounded domain in r n d is an n n nondiagonal matrix whose eigenvalues are semi simple with nonnegative real part the control u l 2 0 r u l 2 0 r l 2 r m and b l u z with u l 2 r m z l 2 r n the standard notation z t x defines a function from 0 to r n with x fixed by z t x s z t s x s 0 here 0 is the maximum delay which is supposed to be finite we assume that the operator l l 2 0 z z is linear and bounded and 0 z l 2 0 z to this end first we reformulate this system into a standard first order delay equation secondly the semigroup associated with the first order delay equation on an appropriate product space is expressed as a series of strongly continuous semigroups and orthogonal projections related with the eigenvalues of the laplacian operator a 2 this representation allows us to reduce the controllability of this partial differential equation with delay to a family of ordinary delay equations finally we use the well known result on the rank condition for the approximate controllability of delay system to derive our main result

partial identification and inference in censored quantile regression abstract in this paper we study partial identification and inference in a linear quantile regression where the dependent variable is subject to possibly unknown dependent censoring characterized by an archimedean copula an outer set of the identified set for the regression coefficient is characterized via inequality constraints for one parameter ordered families of archimedean copulas we construct a simple confidence set by inverting an asymptotically pivotal statistic a bootstrap confidence set is also constructed sensitivity of the identified set to possible misspecification of the true copula and the finite sample performance of the boostrap confidence set are investigated numerically

median regression models for longitudinal data with dropouts summary recently median regression models have received increasing attention when continuous responses follow a distribution that is quite different from a normal distribution usual mean regression models may fail to produce efficient estimators whereas median regression models may perform satisfactorily in this article we discuss using median regression models to deal with longitudinal data with dropouts weighted estimating equations are proposed to estimate the median regression parameters for incomplete longitudinal data where the weights are determined by modeling the dropout process consistency and the asymptotic distribution of the resultant estimators are established the proposed method is used to analyze a longitudinal data set arising from a controlled trial of hiv disease volberding et al 1990 the new england journal of medicine 322 941 949 simulation studies are conducted to assess the performance of the proposed method under various situations an extension to estimation of the association parameters is outlined

entire solutions in bistable reaction diffusion equations with nonlocal delayed nonlinearity this paper is concerned with entire solutions for bistable reaction diffusion equations with nonlocal delay in one dimensional spatial domain here the entire solutions are defined in the whole space and for all time t r assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument we prove the existence of entire solutions which behave as two traveling wave solutions coming from both ends of the x axis and annihilating at a finite time furthermore we show that such an entire solution is unique up to space time translations and is liapunov stable a key idea is to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions in order to illustrate our main results two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are considered

markov chain marginal bootstrap markov chain marginal bootstrap mcmb is a new method for constructing confidence intervals or regions for maximum likelihood estimators of certain parametric models and for a wide class of m estimators of linear regression the mcmb method distinguishes itself from the usual bootstrap methods in two important aspects it involves solving only one dimensional equations for parameters of any dimension and produces a markov chain rather than a conditionally independent sequence it is designed to alleviate computational burdens often associated with bootstrap in high dimensional problems the validity of mcmb is established through asymptotic analyses and illustrated with empirical and simulation studies for linear regression and generalized linear models

two examples of ill posedness with respect to time delays revisited we revisit two examples of elastic control systems which are stabilized by boundary feedback and then destabilized when time delays occur in the feedback in the first example a wave equation with a feedback gain greater than or equal to one arbitrary divergence rates are obtained for small time delays in the second example a euler bernoulli beam any time delay results in an arbitrary divergence rate

partial rank estimation of duration models with general forms of censoring abstract in this paper we propose estimators for the regression coefficients in censored duration models which are distribution free impose no parametric specification on the baseline hazard function and can accommodate general forms of censoring the estimators are shown to have desirable asymptotic properties and monte carlo simulations demonstrate good finite sample performance among the data features the new estimators can accommodate are covariate dependent censoring double censoring and fixed individual or group specific effects we also examine the behavior of the estimator in an empirical illustration

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

dynamics for a type of general reaction diffusion model abstract in this paper we discuss the following reaction diffusion model which is a general form of many population models u t x t u t x u t x f u t x we study the oscillatory behavior of solutions about the positive equilibrium k of system with neumann boundary conditions sufficient and necessary conditions are obtained for global attractivity of the zero solution and acceptable conditions are established for the global attractivity of k these results improve and complement existing results for system without diffusion moreover when these results are applied to the diffusive nicholson s blowflies model and the diffusive model of hematopoiesis some new results are obtained for the latter

inference for censored quantile regression models in longitudinal studies we develop inference procedures for longitudinal data where some of the measurements are censored by fixed constants we consider a semi parametric quantile regression model that makes no distributional assumptions our research is motivated by the lack of proper inference procedures for data from biomedical studies where measurements are censored due to a fixed quantification limit in such studies the focus is often on testing hypotheses about treatment equality to this end we propose a rank score test for large sample inference on a subset of the covariates we demonstrate the importance of accounting for both censoring and intra subject dependency and evaluate the performance of our proposed methodology in a simulation study we then apply the proposed inference procedures to data from an aids related clinical trial we conclude that our framework and proposed methodology is very valuable for differentiating the influences of predictors at different locations in the conditional distribution of a response variable

hopf bifurcations in a reaction diffusion population model with delay effect abstract a reaction diffusion population model with a general time delayed growth rate per capita is considered the growth rate per capita can be logistic or weak allee effect type from a careful analysis of the characteristic equation the stability of the positive steady state solution and the existence of forward hopf bifurcation from the positive steady state solution are obtained via the implicit function theorem where the time delay is used as the bifurcation parameter the general results are applied to a food limited population model with diffusion and delay effects as well as a weak allee effect population model

further improvements in the calculation of censored quantile regressions censored quantile regressions of powell 1984 1986 are very powerful inferencing tools in economics and engineering as the calculation of censored quantile regressions involves minimizing a nonconvex and nondifferentiable function global optimization techniques can be the only breakthroughs the first implementation of a global optimization technique namely threshold accepting of fitzenberger and winker 1998 2007 is challenged by the genetic algorithm ga in this paper the results show that the ga provides substantial improvements over threshold accepting for cases with randomly distributed censoring points

not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks we present two examples of hyperbolic partial differential equations which are stabilized by boundary feedback controls and then destabilized by small delays in these controls we show that in a general case when the controls are distributed stabilized hyperbolic systems possess nontrivial periodic solutions if small time delays are introduced into their feedbacks we also indicate by means of an example that the general case of this phenomenon is harder to demonstrate for boundary control problems

estimation and inference of quantile regression for survival data under biased sampling abstractbiased sampling occurs frequently in economics epidemiology and medical studies either by design or due to data collecting mechanism failing to take into account the sampling bias usually leads to incorrect inference we propose a unified estimation procedure and a computationally fast resampling method to make statistical inference for quantile regression with survival data under general biased sampling schemes including but not limited to the length biased sampling the case cohort design and variants thereof we establish the uniform consistency and weak convergence of the proposed estimator as a process of the quantile level we also investigate more efficient estimation using the generalized method of moments and derive the asymptotic normality we further propose a new resampling method for inference which differs from alternative procedures in that it does not require to repeatedly solve estimating equations it is proved that the resampling method consistently estimates the asymptoti

stability analysis of heat flow with boundary time varying delay effect abstract in this paper we investigate the stabilization of heat flow with boundary time varying delay effect under some assumptions we prove exponential stability of the solution applying variable norm technique and modified lyapunov functional approach

reaction diffusion systems with time delays monotonicity invariance comparison and convergence in a recent paper we have obtained differential inequality results developed comparison theorems and established invariance criteria for mild solutions of abstract functional differential equations in a banach space the primary application for these results is to reaction diffusion systems in which the reaction nonlinearity contains time delays in the present paper we apply these results to reaction diffusion systems with time delays of the form u t d u f x u t x x u u n 0 x where is a bounded open set in r n with smooth boundary u r n d diag d 1 d n with d i 0

mixing enhancement in enzymatic chemical reactions by optimal tuning of flows abstract we consider the problem of mixing enhancement in enzymatic chemical reactions in moving fluids which are modeled by a reaction convection diffusion equation the problem is formulated as an optimal control problem using the flow field as a control variable by variational principles we prove the existence of an optimal flow and derive an optimality system that consists of nonlinear reaction convection diffusion equations and laplace s equations the uniqueness of the optimal flow is left open

quantile regression under random censoring censored regression models have received a great deal of attention in both the theoretical and applied econometric literature most of the existing estimation procedures for either cross sectional or panel data models are designed only for models with fixed censoring in this paper a new procedure for adapting these estimators designed for fixed censoring to models with random censoring is proposed this procedure is then applied to the clad and quantile estimators of powell j econom 25 1984 303 32 1986a 143 to obtain an estimator of the coefficients under a mild conditional quantile restriction on the error term that is applicable to samples exhibiting fixed or random censoring the resulting estimator is shown to have desirable asymptotic properties and performs well in a small scale simulation study

brief paper dynamic stabilization of an euler bernoulli beam equation with time delay in boundary observation an euler bernoulli beam equation under boundary control and delayed observation is considered an observer predictor based scheme is developed to stabilize the equation on a time interval where the observation is available the state is tracked by the observer when the observation is not available due to the delay the state is estimated by the predictor the estimation is then used in proportional feedback it is shown that the state of closed loop system decays exponentially for smooth initial values

travelling wave fronts in reaction diffusion systems with spatio temporal delays this paper deals with the existence of travelling wave fronts in reaction diffusion systems with spatio temporal delays our approach is to use monotone iterations and a nonstandard ordering for the set of profiles of the corresponding wave system new iterative techniques are established for a class of integral operators when the reaction term satisfies different monotonicity conditions following this the existence of travelling wave fronts for reaction diffusion systems with spatio temporal delays is established finally we apply the main results to a single species diffusive model with spatio temporal delay and obtain some existence criteria of travelling wave fronts by choosing different kernels

persistence of wavefronts in delayed nonlocal reaction diffusion equations we develop a perturbation argument based on existing results on asymptotic autonomous systems and the fredholm alternative theory that yields the persistence of traveling wavefronts for reaction diffusion equations with nonlocal and delayed nonlinearities when the time lag is relatively small this persistence result holds when the nonlinearity of the corresponding ordinary reaction diffusion system is either monostable or bistable we then illustrate this general result using five different models from population biology epidemiology and bio reactors

conditional quantile screening in ultrahigh dimensional heterogeneous data summary to accommodate the heterogeneity that is often present in ultrahigh dimensional data we propose a conditional quantile screening method which enables us to select features that contribute to the conditional quantile of the response given the covariates the method can naturally handle censored data by incorporating a weighting scheme through redistribution of the mass to the right moreover it is invariant to monotone transformation of the response and requires substantially weaker conditions than do alternative methods we establish sure independent screening properties for both the complete and the censored response cases we also conduct simulations to evaluate the finite sample performance of the proposed method and compare it with existing approaches

quantile regression for doubly censored data double censoring often occurs in registry studies when left censoring is present in addition to right censoring in this work we propose a new analysis strategy for such doubly censored data by adopting a quantile regression model we develop computationally simple estimation and inference procedures by appropriately using the embedded martingale structure asymptotic properties including the uniform consistency and weak convergence are established for the resulting estimators moreover we propose conditional inference to address the special identifiability issues attached to the double censoring setting we further show that the proposed method can be readily adapted to handle left truncation simulation studies demonstrate good finite sample performance of the new inferential procedures the practical utility of our method is illustrated by an analysis of the onset of the most commonly investigated respiratory infection pseudomonas aeruginosa in children with cystic fibrosis through the use of the u s cystic fibrosis registry

quantile calculus and censored regression quantile regression has been advocated in survival analysis to assess evolving covariate effects however challenges arise when the censoring time is not always observed and may be covariate dependent particularly in the presence of continuously distributed covariates in spite of several recent advances existing methods either involve algorithmic complications or impose a probability grid the former leads to difficulties in the implementation and asymptotics whereas the latter introduces undesirable grid dependence to resolve these issues we develop fundamental and general quantile calculus on cumulative probability scale in this article upon recognizing that probability and time scales do not always have a one to one mapping given a survival distribution these results give rise to a novel estimation procedure for censored quantile regression based on estimating integral equations a numerically reliable and efficient progressive localized minimization plmin algorithm is proposed for the computation this procedure reduces exactly to the kaplan meier method in the k sample problem and to standard uncensored quantile regression in the absence of censoring under regularity conditions the proposed quantile coefficient estimator is uniformly consistent and converges weakly to a gaussian process simulations show good statistical and algorithmic performance the proposal is illustrated in the application to a clinical study

uniform attractors for non autonomous parabolic equations with delays abstract the present paper is devoted to the asymptotic behavior of non autonomous parabolic equations with nonlinearity containing general delay and with time dependent external forces the existence uniqueness and regularity of solutions for the equation are obtained if the time dependent external forces is a translation compact function in l loc 2 r l 2 then the existences of uniform attractor for non autonomous dynamics system are provided and the structures of attractors are also studied which is the union of all bounded complete trajectory of the equation at a time moment finally the main results are applied to the population dynamics with distributed state dependent delay and with almost periodic external force and the uniform attractor and its kernel section are obtained

mixing enhancement by optimal flow advection we consider the problem of optimal mixing control our objective is to best enhance mixing by flow advection while the flow is optimized in the sense that it is almost steady and is of the least magnitude and the least rotation for this we define a mixing efficiency functional by penalizing the average of variance of a diffusive scalar the average of the flow and the average of its acceleration and strain tensor by variational principles we prove the existence of an optimal flow and derive optimality conditions that consist of a system of nonlinear advection diffusion equations wave equations and laplace s equation

pattern statistics and vandermonde matrices in this paper we determine some limit distributions of pattern statistics in rational stochastic models we present a general approach to analyze these statistics in rational models having an arbitrary number of strongly connected components we explicitly establish the limit distributions in most significant cases they are characterized by a family of unimodal density functions defined by means of confluent vandermonde matrices

method of lyapunov functionals construction in stability of delay evolution equations the investigation of stability for hereditary systems is often related to the construction of lyapunov functionals the general method of lyapunov functionals construction which was proposed by v kolmanovskii and l shaikhet and successfully used already for functional differential equations for difference equations with discrete time for difference equations with continuous time is used here to investigate the stability of delay evolution equations in particular partial differential equations

censored median regression using weighted empirical survival and hazard functions abstract for median regression models that regress the median of the survival time or a transform thereof on the covariates some semi parametric estimators that include the intercept component are introduced when the survival time may be censored these new median regression estimators do not require estimating the censoring distributions they can be viewed as an extension of the sample median to the censored regression model these estimators are based on some weighted empirical survival and hazard functions and are shown to be consistent and asymptotically normal they performed very well in various numerical studies the proposed procedures are illustrated in some real data examples

random generation of combinatorial structures from a uniform distribution abstract the class of problems involving the random generation of combinatorial structures from a uniform distribution is considered uniform generation problems are in computational difficulty intermediate between classical existence and counting problems it is shown that exactly uniform generation of efficiently verifiable combinatorial structures is reducible to approximate counting and hence is within the third level of the polynomial hierarchy natural combinatorial problems are presented which exhibit complexity gaps between their existence and generation and between their generation and counting versions it is further shown that for self reducible problems almost uniform generation and randomized approximate counting are inter reducible and hence of similar complexity

competing risks quantile regression quantile regression has emerged as a significant extension of traditional linear models and its potential in survival applications has recently been recognized in this paper we study quantile regression with competing risks data formulating the model based on conditional quantiles defined using the cumulative incidence function which includes as a special case an analog to the usual accelerated failure time model the proposed competing risks quantile regression model provides meaningful physical interpretations of covariate effects and moreover relaxes the constancy constraint on regression coefficients thereby providing a useful perhaps more flexible alternative to the popular subdistribution proportional hazards model we derive an unbiased monotone estimating equation for regression parameters in the quantile model the uniform consistency and weak convergence of the resulting estimators are established across a quantile continuum we develop inferences including covariance estimation second

estimation of high conditional quantiles for heavy tailed distributions estimation of conditional quantiles at very high or low tails is of interest in numerous applications quantile regression provides a convenient and natural way of quantifying the impact of covariates at different quantiles of a response distribution however high tails are often associated with data sparsity so quantile regression estimation can suffer from high variability at tails especially for heavy tailed distributions in this article we develop new estimation methods for high conditional quantiles by first estimating the intermediate conditional quantiles in a conventional quantile regression framework and then extrapolating these estimates to the high tails based on reasonable assumptions on tail behaviors we establish the asymptotic properties of the proposed estimators and demonstrate through simulation studies that the proposed methods enjoy higher accuracy than the conventional quantile regression estimates in a real application involving statistical downscaling of daily precipitation in

multiple imputation for m regression with censored covariates we develop a new multiple imputation approach for m regression models with censored covariates instead of specifying parametric likelihoods our method imputes the censored covariates by their conditional quantiles given the observed data where the conditional quantiles are estimated through fitting a censored quantile regression process the resulting estimator is shown to be consistent and asymptotically normal and it improves the estimation efficiency by using information from cases with censored covariates compared with existing methods the proposed method is more flexible as it does not require stringent parametric assumptions on the distributions of either the regression errors or the covariates the finite sample performance of the proposed method is assessed through a simulation study and the analysis of a c reactive protein dataset in the 2007 2008 national health and nutrition examination survey this article has supplementary material online

blow up phenomena for the weakly dissipative dullin gottwald holm equation revisited in this paper we investigate the cauchy problem for the weakly dissipative dullin gottwald holm equation we first establish the local well posedness result by kato s semigroup theory then we obtain the precise blow up scenario and present some blow up results for strong solutions to the equation finally we discuss the blow up rate of the wave breaking solutions this result complements the early one in the literature such as novruzov j math phys 54 092703 2013

quantile adaptive model free variable screening for high dimensional heterogeneous data we introduce a quantile adaptive framework for nonlinear variable screening with high dimensional heterogeneous data this framework has two distinctive features 1 it allows the set of active variables to vary across quantiles thus making it more flexible to accommodate heterogeneity 2 it is model free and avoids the difficult task of specifying the form of a statistical model in a high dimensional space our nonlinear independence screening procedure employs spline approximations to model the marginal effects at a quantile level of interest under appropriate conditions on the quantile functions without requiring the existence of any moments the new procedure is shown to enjoy the sure screening property in ultra high dimensions furthermore the quantile adaptive framework can naturally handle censored data arising in survival analysis we prove that the sure screening property remains valid when the response variable is subject to random right censoring numerical studies confirm the fine performance of the proposed method for various semiparametric models and its effectiveness to extract quantile specific information from heteroscedastic data

multiple imputation for cure rate quantile regression with censored data summary the main challenge in the context of cure rate analysis is that one never knows whether censored subjects are cured or uncured or whether they are susceptible or insusceptible to the event of interest considering the susceptible indicator as missing data we propose a multiple imputation approach to cure rate quantile regression for censored data with a survival fraction we develop an iterative algorithm to estimate the conditionally uncured probability for each subject by utilizing this estimated probability and bernoulli sample imputation we can classify each subject as cured or uncured and then employ the locally weighted method to estimate the quantile regression coefficients with only the uncured subjects repeating the imputation procedure multiple times and taking an average over the resultant estimators we obtain consistent estimators for the quantile regression coefficients our approach relaxes the usual global linearity assumption so that we can apply quantile regression to any particular quantile of interest we establish asymptotic properties for the proposed estimators including both consistency and asymptotic normality we conduct simulation studies to assess the finite sample performance of the proposed multiple imputation method and apply it to a lung cancer study as an illustration

existence of fast positive wavefronts for a non local delayed reaction diffusion equation abstract we establish the existence of a continuous family of fast positive wavefronts u t x x c t 0 for the non local delayed reaction diffusion equation u t t x u x x t x u t x r k x w g u t h w d w here 0 and 0 are fixed points of g c 2 r r and the non negative k is such that r k w e w d w is finite for every real we also prove that the fast wavefronts are non monotone if g h e h 1 1

the global attractor of a competitor competitor mutualist reaction diffusion system with time delays abstract the aim of this paper is to investigate the asymptotic behavior of time dependent solutions of a three species reaction diffusion system in a bounded domain under a neumann boundary condition the system governs the population densities of a competitor a competitor mutualist and a mutualist and time delays may appear in the reaction mechanism it is shown under a very simple condition on the reaction rates that the reaction diffusion system has a unique constant positive steady state solution and for any nontrivial nonnegative initial function the corresponding time dependent solution converges to the positive steady state solution an immediate consequence of this global attraction property is that the trivial solution and all forms of semitrivial solutions are unstable moreover the state state problem has no nonuniform positive solution despite possible spatial dependence of the reaction and diffusion all the conclusions for the time delayed system are directly applicable to the system without time delays and to the corresponding ordinary differential system with or without time delays

asymptotic stability of traveling wave fronts in nonlocal reaction diffusion equations with delay abstract this paper is concerned with the asymptotic stability of traveling wave fronts of a class of nonlocal reaction diffusion equations with delay under monostable assumption we prove that the traveling wave front is exponentially stable by means of the technical weighted energy method when the initial perturbation around the wave is suitable small in a weighted norm the exponential convergent rate is also obtained finally we apply our results to some population models and obtain some new results which recover complement and or improve a number of existing ones

existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay this paper is concerned with the existence uniqueness and globally asymptotic stability of traveling wave fronts in the quasi monotone reaction advection diffusion equations with nonlocal delay under bistable assumption we construct various pairs of super and subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing traveling wave front up to translation which is monotonically increasing and globally asymptotically stable with phase shift the influence of advection on the propagation speed is also considered comparing with the previous results our results recovers and or improves a number of existing ones in particular these results can be applied to a reaction advection diffusion equation with nonlocal delayed effect and a diffusion population model with distributed maturation delay some new results are obtained

an alternative estimator for the censored quantile regression model the paper introduces an alternative estimator for the linear censored quantile regression model the objective function is globally convex and the estimator is a solution to a linear programming problem hence a global minimizer is obtained in a finite number of simplex iterations the suggested estimator also applies to the case where the censoring point is an unknown function of a set of regressors it is shown that under fairly weak conditions the estimator has a n convergence rate and is asymptotically normal in the case of a fixed censoring point its asymptotic property is nearly equivalent to that of the estimator suggested by powell 1984 1986a a monte carlo study performed shows that the suggested estimator has very desirable small sample properties it precisely corrects for the bias induced by censoring even when there is a large amount of censoring and for relatively small sample sizes

nonmonotone travelling waves in a single species reaction diffusion equation with delay abstract we prove the existence of a continuous family of positive and generally nonmonotone travelling fronts for delayed reaction diffusion equations u t t x u t x u t x g u t h x when g c 2 r r has exactly two fixed points x 1 0 and x 2 k 0 recently nonmonotonic waves were observed in numerical simulations by various authors here for a wide range of parameters we explain why such waves appear naturally as the delay h increases for the case of g with negative schwarzian our conditions are rather optimal we observe that the well known mackey glass type equations with diffusion fall within this subclass of as an example we consider the diffusive nicholson s blowflies equation

survival analysis with median regression models abstract the median is a simple and meaningful measure for the center of a long tailed survival distribution to examine the covariate effects on survival a natural alternative to the usual mean regression model is to regress the median of the failure time variable or a transformation thereof on the covariates in this article we propose semiparametric procedures to make inferences for such median regression models with possibly censored observations our proposals can be implemented efficiently using a simulated annealing algorithm numerical studies are conducted to show the advantage of the new procedures over some recently developed methods for the accelerated failure time model a special type of mean regression models in the survival analysis the proposals discussed in the article are illustrated with a lung cancer data set

boundary feedback stabilization of an unstable heat equation in this paper we study the problem of boundary feedback stabilization for the unstable heat equation ut x t uxx x t a x u x t this equation can be viewed as a model of a heat conducting rod in which not only is the heat being diffused mathematically due to the diffusive term uxx but also the destabilizing heat is generating mathematically due to the term a u with a 0 we show that for any given continuously differentiable function a and any given positive constant l we can explicitly construct a boundary feedback control law such that the solution of the equation with the control law converges to zero exponentially at the rate of l this is a continuation of the recent work of boskovic krstic and liu ieee trans automat control 46 2001 pp 2022 2028 and balogh and krstic european j control 8 2002 pp 165 176

entire solutions in monostable reaction diffusion equations with delayed nonlinearity abstract entire solutions for monostable reaction diffusion equations with nonlocal delay in one dimensional spatial domain are considered a comparison argument is employed to prove the existence of entire solutions which behave as two traveling wave solutions coming from both directions some new entire solutions are also constructed by mixing traveling wave solutions with heteroclinic orbits of the spatially averaged ordinary differential equations and the existence of such a heteroclinic orbit is established using the monotone dynamical systems theory key techniques include the characterization of the asymptotic behaviors of solutions as t in term of appropriate subsolutions and supersolutions two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are given to illustrate main results

on the number of occurrences of a symbol in words of regular languages we study the random variable yn representing the number of occurrences of a symbol a in a word of length n chosen at random in a regular language l a b where the random choice is defined via a non negative rational formal series r of support l assuming that the transition matrix associated with r is primitive we obtain asymptotic estimates for the mean value and the variance of yn and present a central limit theorem for its distribution under a further condition on such a matrix we also derive an asymptotic approximation of the discrete fourier transform of yn that allows to prove a local limit theorem for yn further consequences of our analysis concern the growth of the coefficients in rational formal series in particular it turns out that for a wide class of regular languages l the maximum number of words of length n in l having the same number of occurrences of a given symbol is of the order of growth n n for some constant 1

three step censored quantile regression and extramarital affairs this article suggests very simple three step estimators for censored quantile regression models with a separation restriction on the censoring probability the estimators are theoretically attractive i e asymptotically as efficient as the celebrated powell s censored least absolute deviation estimator at the same time they are conceptually simple and have trivial computational expenses they are especially useful in samples of small size or models with many regressors with desirable finite sample properties and small bias the separation restriction costs a small reduction of generality relative to the canonical censored regression quantile model yet its main plausible features remain intact the estimator can also be used to estimate a large class of traditional models including the normal amemiya tobin model and many accelerated failure and proportional hazard models we illustrate the approach with an extramarital affairs example and contrast our findings with those of fair

joint estimation of quantile planes over arbitrary predictor spaces abstractin spite of the recent surge of interest in quantile regression joint estimation of linear quantile planes remains a great challenge in statistics and econometrics we propose a novel parameterization that characterizes any collection of noncrossing quantile planes over arbitrarily shaped convex predictor domains in any dimension by means of unconstrained scalar vector and function valued parameters statistical models based on this parameterization inherit a fast computation of the likelihood function enabling penalized likelihood or bayesian approaches to model fitting we introduce a complete bayesian methodology by using gaussian process prior distributions on the function valued parameters and develop a robust and efficient markov chain monte carlo parameter estimation the resulting method is shown to offer posterior consistency under mild tail and regularity conditions we present several illustrative examples where the new method is compared against existing approaches and is found to o

an example on the effect of time delays in boundary feedback stabilization of wave equations this note is concerned with the erect of time delays in boundary feedback stabilization schemes for wave equations the question to be addressed is whether such delays can destabilize a system which is uniformly asymptotically stable in the absence of delays