delayed feedback control of periodic orbits without torsion in nonautonomous chaotic systems theory and experiment we demonstrate theoretically and experimentally that the unstable delayed feedback controller is an efficient tool for stabilizing torsion free unstable periodic orbits in nonautonomous chaotic systems to improve the global control performance we introduce a two step control algorithm the problem of a linear stability of the system under delayed feedback control is treated analytically theoretical results are confirmed by electronic circuit experiments for a forced double well oscillator

unified hybridization of discontinuous galerkin mixed and continuous galerkin methods for second order elliptic problems we introduce a unifying framework for hybridization of finite element methods for second order elliptic problems the methods fitting in the framework are a general class of mixed dual finite element methods including hybridized mixed continuous galerkin nonconforming and a new wide class of hybridizable discontinuous galerkin methods the distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements since the associated matrix is sparse symmetric and positive definite these methods can be efficiently implemented moreover the framework allows in a single implementation the use of different methods in different elements or subdomains of the computational domain which are then automatically coupled finally the framework brings about a new point of view thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom

bayesian random threshold estimation in a cox proportional hazards cure model in this paper we develop a bayesian approach to estimate a cox proportional hazards model that allows a threshold in the regression coefficient based on a threshold in a covariate when some fraction of subjects are not susceptible to the event of interest a data augmentation scheme with latent binary cure indicators is adopted to simplify the markov chain monte carlo implementation given the binary cure indicators the cox cure model reduces to a standard cox model and a logistic regression model furthermore the threshold detection problem reverts to a threshold problem in a regular cox model the baseline cumulative hazard for the cox model is formulated non parametrically using counting processes with a gamma process prior simulation studies demonstrate that the method provides accurate point and interval estimates application to a data set of oropharynx cancer patients suggests a significant threshold in age at diagnosis such that the effect of gender on disease specific survival changes after the threshold

inverse regression estimation for censored data an inverse regression methodology for assessing predictor performance in the censored data setup is developed along with inference procedures and a computational algorithm the technique developed here allows for conditioning on the unobserved failure time along with a weighting mechanism that accounts for the censoring the implementation is nonparametric and computationally fast this provides an efficient methodological tool that can be used especially in cases where the usual modeling assumptions are not applicable to the data under consideration it can also be a good diagnostic tool that can be used in the model selection process we have provided theoretical justification of consistency and asymptotic normality of the methodology simulation studies and two data analyses are provided to illustrate the practical utility of the procedure

convergence of adaptive finite element methods for general second order linear elliptic pdes we prove convergence of adaptive finite element methods afems for general nonsymmetric second order linear elliptic pdes thereby extending the result of morin nochetto and siebert it siam j numer anal 38 2000 pp 466 488 it siam rev 44 2002 pp 631 658 the proof relies on quasi orthogonality which accounts for the bilinear form not being a scalar product together with novel error and oscillation reduction estimates which now do not decouple we show that afems are a contraction for the sum of energy error plus oscillation numerical experiments including oscillatory coefficients and both coercive and noncoercive convection diffusion pde illustrate the theory and yield optimal meshes

quasi optimal convergence rate of an adaptive discontinuous galerkin method we analyze an adaptive discontinuous finite element method adfem for symmetric second order linear elliptic operators the method is formulated on nonconforming meshes made of simplices or quadrilaterals with any polynomial degree and in any dimension geq2 we prove that the adfem is a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops we design a refinement procedure that maintains the level of nonconformity uniformly bounded and prove that the approximation classes using continuous and discontinuous finite elements are equivalent the geometric decay and the equivalence of classes are instrumental in deriving the optimal cardinality of the adfem we show that the adfem and the afem on nonconforming meshes yields a decay rate of energy error plus oscillation in terms of the number of degrees of freedom as dictated by the best approximation for this combined nonlinear quantity

estimation in a cox regression model with a change point according to a threshold in a covariate we consider a nonregular cox model for independent and identically distributed right censored survival times with a change point according to the unknown threshold of a covariate the maximum partial likelihood estimators of the parameters and the estimator of the baseline cumulative hazard are studied we prove that the estimator of the change point is n consistent and the estimator of the regression parameters are n 1 2 consistent and we establish the asymptotic distributions of the estimators the estimators of the regression parameters and of the baseline cumulative hazard are adaptive in the sense that they do not depend on the knowledge of the change point

pyragas stabilizability via delayed feedback with periodic control gain abstract in this paper for the unstable periodic solution of nonlinear differential equation pyragas stabilizability problem is studied an algorithm of stabilization via periodical delayed feedback is obtained the consideration is based on the theory of nonstationary stabilization

feedback and adaptive finite element solution of one dimensional boundary value problems this paper examines the concepts of feedback and adaptivity for the finite element method the model problem concernsc 0 elements of arbitrary fixed degree for a one dimensional two point boundary value problem three different feedback methods are introduced and a detailed analysis of their adaptivity is given

pointwise error estimates for discontinuous galerkin methods with lifting operators for elliptic problems in this article we prove some weighted pointwise estimates for three discontinuous galerkin methods with lifting operators appearing in their corresponding bilinear forms we consider a dirichlet problem with a general second order elliptic operator

maximum likelihood estimation in the proportional odds model abstract we consider maximum likelihood estimation of the parameters in the proportional odds model with right censored data the estimator of the regression coefficient is shown to be asymptotically normal with efficient variance the maximum likelihood estimator of the unknown monotonic transformation of the survival time converges uniformly at a parametric rate to the true transformation estimates for the standard errors of the estimated regression coefficients are obtained by differentiation of the profile likelihood and are shown to be consistent a likelihood ratio test for the regression coefficient is also considered

testing for threshold effects in regression models in this article we develop a general method for testing threshold effects in regression models using sup likelihood ratio lr type statistics although the sup lr type test statistic has been considered in the literature our method for establishing the asymptotic null distribution is new and nonstandard the standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function the article provides an alternative novel method that can be used to establish the asymptotic null distribution even when the usual quadratic approximation is intractable we illustrate the usefulness of our approach in the examples of the maximum score estimation maximum likelihood estimation quantile regression and maximum rank correlation estimation we establish consistency and local power properties of the test we provide some simulation results and also an empirical application to tipping in racial segregation this ar

an analysis of transformations revisited rebutted abstract in a paper written in 1964 box and cox described a method for estimating transformations and showed how in suitable cases valuable increases in simplicity and efficiency were possible since that time this technique has enjoyed wide practical use and considerable success however a recent theoretical paper by bickel and doksum 1981 seems to suggest that serious dangers are associated with the employment of this method and speaks of instability and cost of estimation of the transformation these difficulties seem to be associated with 1 examples which common sense would rule out namely situations where the effect of transformation on the data is almost linear so that it is a matter of indifference which transformation is used 2 the idea that it makes sense to state conclusions in terms of a number measured on an arbitrary scale 3 failure to take proper account of the jacobian of the transformation

likelihood ratio tests for a changepoint with survival data summary we consider the likelihood ratio test for a changepoint or lag of the effect of some covariates e g treatment in regression modelling of survival data subject to right censoring asymptotic distributions under null hypotheses are derived numerical examples are used to illustrate the implementation of the procedure finally we apply the theory to data from a large randomised cancer prevention trial

energy norm a posteriori error estimation for mixed discontinuous galerkin approximations of the maxwell operator in this paper we develop the a posteriori error estimation of mixed discontinuous galerkin finite element approximations of the maxwell operator in particular by employing suitable helmholtz decompositions of the error together with the conservation properties of the underlying method computable upper bounds on the error measured in terms of a natural mesh dependent energy norm are derived numerical experiments testing the performance of our a posteriori error bounds for problems with both smooth and singular analytical solutions are presented

inference under right censoring for transformation models with a change point based on a covariate threshold we consider linear transformation models applied to right censored survival data with a change point in the regression coefficient based on a covariate threshold we establish consistency and weak convergence of the nonparametric maximum likelihood estimators the change point parameter is shown to be n consistent while the remaining parameters are shown to have the expected root n consistency we show that the procedure is adaptive in the sense that the nonthreshold parameters are estimable with the same precision as if the true threshold value were known we also develop monte carlo methods of inference for model parameters and score tests for the existence of a change point a key difficulty here is that some of the model parameters are not identifiable under the null hypothesis of no change point simulation studies establish the validity of the proposed score tests for finite sample sizes

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

adaptive finite element methods with convergence rates adaptive finite element methods for numerically solving elliptic equations are used often in practice only recently 12 17 have these methods been shown to converge however this convergence analysis says nothing about the rates of convergence of these methods and therefore does in principle not guarantee yet any numerical advantages of adaptive strategies versus non adaptive strategies the present paper modifies the adaptive method of morin nochetto and siebert 17 for solving the laplace equation with piecewise linear elements on domains in 2 by adding a coarsening step and proves that this new method has certain optimal convergence rates in the energy norm which is equivalent to the h1 norm namely it is shown that whenever s 0 and the solution u is such that for each n 1 it can be approximated to accuracy o n s in the energy norm by a continuous piecewise linear function on a triangulation with n cells using complete knowledge of u then the adaptive algorithm constructs an approximation of the same type with the same asymptotic accuracy while using only information gained during the computational process moreover the number of arithmetic computations in the proposed method is also of order o n for each n 1 the construction and analysis of this adaptive method relies on the theory of nonlinear approximation

an equilibrated a posteriori error estimator for the interior penalty discontinuous galerkin method interior penalty discontinuous galerkin ipdg methods for second order elliptic boundary value problems have been derived from a mixed variational formulation of the problem numerical flux functions across interelement boundaries play an important role in that theory residual type a posteriori error estimators for ipdg methods have been derived and analyzed by many authors including the convergence analysis of the resulting adaptive schemes typically the effectivity indices deteriorate with increasing polynomial order of the ipdg methods the situation is more favorable for a posteriori error estimators derived by means of the so called hypercircle method equilibrated fluxes are obtained by using a mixed method and an extension operator for brezzi douglas marini elements and this can be done in the same way for all the discontinuous galerkin methods that fit into a known unified framework the hypercircle method immediately provides the reliability of the estimator whereas its efficiency can be

change point estimation under adaptive sampling we consider the problem of locating a jump discontinuity change point in a smooth parametric regression model with a bounded covariate it is assumed that one can sample the covariate at different values and measure the corresponding responses budget constraints dictate that a total of n such measurements can be obtained a multistage adaptive procedure is proposed where at each stage an estimate of the change point is obtained and new points are sampled from its appropriately chosen neighborhood it is shown that such procedures accelerate the rate of convergence of the least squares estimate of the change point further the asymptotic distribution of the estimate is derived using empirical processes techniques the latter result provides guidelines on how to choose the tuning parameters of the multistage procedure in practice the improved efficiency of the procedure is demonstrated using real and synthetic data this problem is primarily motivated by applications in engineering systems

quasi optimal convergence rate for an adaptive hybridizable c 0 discontinuous galerkin method for kirchhoff plates in this paper we present an adaptive hybridizable c 0 discontinuous galerkin hcdg method for kirchhoff plates a reliable and efficient a posteriori error estimator is produced for this hcdg method quasi orthogonality and discrete reliability are established with the help of a postprocessed bending moment and the discrete helmholtz decomposition based on these the contraction property between two consecutive loops and complexity of the adaptive hcdg method are studied thoroughly the key points in our analysis are a postprocessed normal normal continuous bending moment from the hcdg method solution and a lifting of jump residuals from inter element boundaries to element interiors

convergence of adaptive discontinuous galerkin approximations of second order elliptic problems a residual type a posteriori error estimator is introduced and analyzed for a discontinuous galerkin formulation of a model second order elliptic problem with dirichlet neumann type boundary conditions an adaptive algorithm using this estimator together with specific marking and refinement strategies is constructed and shown to achieve any specified error level in the energy norm in a finite number of cycles the convergence rate is in effect linear with a guaranteed error reduction at every cycle results of numerical experiments are presented

optimal tests when a nuisance parameter is present only under the alternative this paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null for example the results apply to tests of structural change with unknown changepoint the testing problem considered is nonstandard and the classical asymptotic optimality results for the lagrange multiplier wald and likelihood ratio do not apply a weighted average power criterion is used here to generate optimal tests this criterion is similar to that used by a wald 1943 to obtain the classical asymptotic optimality properties of wald tests in regular testing problems copyright 1994 by the econometric society

a multilevel discontinuous galerkin method a variable v cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented an analysis under a mild regularity assumption shows that the preconditioner is uniform the interior penalty method is then combined with a discontinuous galerkin scheme to arrive at a discretization scheme for an advection diffusion problem for which an error estimate is proved a multigrid algorithm for this method is presented and numerical experiments indicating its robustness with respect to diffusion coefficient are reported

convergence of adaptive finite element methods adaptive finite element methods fems have been widely used in applications for over 20 years now in practice they converge starting from coarse grids although no mathematical theory has been able to prove this assertion ensuring an error reduction rate based on a posteriori error estimators together with a reduction rate of data oscillation information missed by the underlying averaging process we construct a simple and efficient adaptive fem for elliptic partial differential equations we prove that this algorithm converges with linear rate without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance extensions to higher order elements and applications to saddle point problems are discussed as well

a posteriori error estimates for a discontinuous galerkin method applied to elliptic problems log number r74 abstract a posteriori error estimates for locally mass conservative methods for subsurface flow are presented these methods are based on discontinuous approximation spaces and referred to as discontinuous galerkin methods in the case where penalty terms are added to the bilinear form one obtains the nonsymmetric interior penalty galerkin methods in a previous work we proved optimal rates of convergence of the methods applied to elliptic problems here h adaptivity is investigated for flow problems in 2d we derive global explicit estimators of the error in the l 2 norm and we numerically investigate an implicit indicator of the error in the energy norm model problems with discontinuous coefficients are considered

predicting survival probabilities with semiparametric transformation models abstract prediction of survival probabilities for future patients is one of the main goals of fitting survival data with regression models in this article we consider a large class of semiparametric transformation models which includes the well known proportional hazards and proportional odds models for the analysis of failure time data specifically we propose pointwise and simultaneous confidence interval procedures for the survival probability of future patients with specific covariates these procedures can be easily implemented through simulation and are illustrated with the data from two well known clinical studies

semiparametric estimation of a binary response model with a change point due to a covariate threshold this paper is concerned with semiparametric estimation of a threshold binary response model the estimation method considered in the paper is semiparametric since the parameters for a regression function are finite dimensional while allowing for heteroskedasticity of unknown form in particular the paper considers manski 1975 1985 s maximum score estimator the model in this paper is irregular because of a change point due to an unknown threshold in a covariate this irregularity coupled with the discontinuity of the objective function of the maximum score estimator complicates the analysis of the asymptotic behavior of the estimator sufficient conditions for the identification of parameters are given and the consistency of the estimator is obtained it is shown that the estimator of the threshold parameter is n consistent and the estimator of the remaining regression parameters is cube root n consistent furthermore we obtain the asymptotic distribution of the estimators it turns out that a suitably normalized estimator of the regression parameters converges weakly to the distribution to which it would converge weakly if the true threshold value were known and likewise for the threshold estimator

superconvergence of the local discontinuous galerkin method for elliptic problems on cartesian grids in this paper we present a superconvergence result for the local discontinuous galerkin ldg method for a model elliptic problem on cartesian grids we identify a special numerical flux for which the l2 norm of the gradient and the l2 norm of the potential are of orders k 1 2 and k 1 respectively when tensor product polynomials of degree at most k are used for arbitrary meshes this special ldg method gives only the orders of convergence of k and k 1 2 respectively we present a series of numerical examples which establish the sharpness of our theoretical results

robust inference for univariate proportional hazards frailty regression models we consider a class of semiparametric regression models which are one parameter extensions of the cox j roy statist soc ser b 34 1972 187 220 model for right censored univariate failure times these models assume that the hazard given the covariates and a random frailty unique to each individual has the proportional hazards form multiplied by the frailty the frailty is assumed to have mean 1 within a known one parameter family of distributions inference is based on a nonparametric likelihood the behavior of the likelihood maximizer is studied under general conditions where the fitted model may be misspecified the joint estimator of the regression and frailty parameters as well as the baseline hazard is shown to be uniformly consistent for the pseudo value maximizing the asymptotic limit of the likelihood appropriately standardized the estimator converges weakly to a gaussian process when the model is correctly specified the procedure is semiparametric efficient achieving the semiparametric information bound for all parameter components it is also proved that the bootstrap gives valid inferences for all parameters even under misspecification we demonstrate analytically the importance of the robust inference in several examples in a randomized clinical trial a valid test of the treatment effect is possible when other prognostic factors and the frailty distribution are both misspecified under certain conditions on the covariates the ratios of the regression parameters are still identifiable the practical utility of the procedure is illustrated on a non hodgkin s lymphoma dataset

proportional hazards model with a change point for clustered event data in many epidemiology studies family data with survival endpoints are collected to investigate the association between risk factors and disease incidence sometimes the risk of the disease may change when a certain risk factor exceeds a certain threshold finding this threshold value could be important for disease risk prediction and diseases prevention in this work we propose a change point proportional hazards model for clustered event data the model incorporates the unknown threshold of a continuous variable as a change point in the regression the marginal pseudo partial likelihood functions are maximized for estimating the regression coefficients and the unknown change point we develop a supremum test based on robust score statistics to test the existence of the change point the inference for the change point is based on the m out of n bootstrap we establish the consistency and asymptotic distributions of the proposed estimators the finite sample performance of the proposed method is demonstrated via extensive simulation studies finally the strong heart family study dataset is analyzed to illustrate the methods

testing when a parameter is on the boundary of the maintained hypothesis this paper considers testing problems where several of the standard regularity conditions fail to hold we consider the case where i parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and ii there may be a nuisance parameter that appears under the alternative hypothesis but not under the null the paper establishes the asymptotic null and local alternative distributions of quasi likelihood ratio rescaled quasi likelihood ratio wald and score tests in this case the results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models examples treated in the paper are i tests of the null hypothesis of no conditional heteroskedasticity in a garch 1 1 regression model and ii tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with possibly correlated random coefficients

on the linear transformation model for censored data recently cheng wei ying 1995 1997 proposed a class of estimation procedures for semi parametric linear transformation models with censored observations when the support of the censoring variable is shorter than that of the failure time the estimators are asymptotically biased in this paper we present a simple modification of cheng s estimation procedures for the regression parameters through extensive numerical studies with practical sample sizes we find that the new proposals perform well but the original interval estimators may not have correct coverage probabilities when censoring is heavy prediction procedures for the survival probabilities of future subjects are also modified accordingly

convergence analysis of an adaptive interior penalty discontinuous galerkin method we study the convergence of an adaptive interior penalty discontinuous galerkin ipdg method for a two dimensional model second order elliptic boundary value problem based on a residual type a posteriori error estimator we prove that after each refinement step of the adaptive scheme we achieve a guaranteed reduction of the global discretization error in the mesh dependent energy norm associated with the ipdg method in contrast to recent work on adaptive ipdg methods o karakashian and f pascal convergence of adaptive discontinuous galerkin approximations of second order elliptic problems preprint university of tennessee knoxville tn 2007 the convergence analysis does not require multiple interior nodes for refined elements of the triangulation in fact it will be shown that bisection of the elements is sufficient the main ingredients of the proof of the error reduction property are the reliability and a perturbed discrete local efficiency of the estimator a bulk criterion that takes care of a proper selection of edges and elements for refinement and a perturbed galerkin orthogonality property with respect to the energy inner product the results of numerical experiments are given to illustrate the performance of the adaptive method

proportional odds regression and sieve maximum likelihood estimation summary this paper introduces under a censoring mechanism an estimation procedure for the baseline function and the regression parameters in the proportional odds model based on the sieve maximum likelihood method the procedure uses monotone splines of variable orders and knots as approximations for the baseline function and an approximately unbiased estimator of the comparative kullback leibler risk to select the best approximation the procedure adapts to various unknown structures of the baseline function such as spatial structures and smoothness of an unknown degree the proposed procedure is implemented for right censored and so called case 2 interval censored data the estimated regression parameters are shown to be asymptotically normal and efficient the small sample operating characteristics of the proposed procedure are examined via simulations and are illustrated on a dataset from a study of breast cancer patients

a posteriori error estimates for a discontinuous galerkin approximation of second order elliptic problems several a posteriori error estimators are introduced and analyzed for a discontinuous galerkin formulation of a model second order elliptic problem in addition to residual type estimators we introduce some estimators that are couched in the ideas and techniques of domain decomposition results of numerical experiments are presented

change point in stochastic design regression and the bootstrap in this paper we study the consistency of dierent bootstrap procedures for constructing condence intervals cis for the unique jump discontinuity change point in an otherwise smooth regression function in a stochastic design setting this problem exhibits nonstandard asymptotics and we argue that the standard bootstrap procedures in regression fail to provide valid condence intervals for the change point we propose a version of smoothed bootstrap illustrate its remarkable nite sample performance in our simulation study and prove the consistency of the procedure the m out of n bootstrap procedure is also considered and shown to be consistent we also provide sucient conditions for any bootstrap procedure to be consistent in this scenario

an a priori error analysis of the local discontinuous galerkin method for elliptic problems in this paper we present the first a priori error analysis for the local discontinuous galerkin ldg method for a model elliptic problem for arbitrary meshes with hanging nodes and elements of various shapes we show that for stabilization parameters of order one the l2 norm of the gradient and the l2 norm of the potential are of order k and k 1 2 respectively when polynomials of total degree at least k are used if stabilization parameters of order h 1 are taken the order of convergence of the potential increases to k 1 the optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains

stopping criteria for adaptive finite element solvers we consider a family of practical stopping criteria for linear solvers for adaptive finite element methods for symmetric elliptic problems a contraction property between two consecutive levels of refinement of the adaptive algorithm is shown when a family of smallness criteria for the corresponding linear solver residuals are assumed on each level or refinement more importantly based on known and new results for the estimation of the residuals of the conjugate gradient method we show that the smallness criteria give rise to practical stopping criteria for the iterations of the linear solver which guarantees that the inexact adaptive algorithm converges a series of numerical experiments highlights the practicality of the theoretical developments

an adaptive discontinuous finite volume method for elliptic problems an adaptive discontinuous finite volume method is developed and analyzed in this paper we prove that the adaptive procedure achieves guaranteed error reduction in a mesh dependent energy norm and has a linear convergence rate numerical results are also presented to illustrate the theoretical analysis

a posteriori estimates for the bubble stabilized discontinuous galerkin method in this paper two reliable and efficient a posteriori error estimators for the bubble stabilized discontinuous galerkin bsdg method for diffusion reaction problems in two and three dimensions are derived the theory is followed by some numerical illustrations

convergence analysis of an adaptive continuous interior penalty finite element method for the helmholtz equation abstract we are concerned with an adaptive continuous interior penalty finite element method for the helmholtz equation a convergence result with explicit constraints on the wave number k and the initial mesh size h 0 is derived in particular it is shown that if k 1 s h 0 s is sufficiently small where 1 2 s 1 depends on the regularity of the weak solution of the model problem then the adaptive continuous interior penalty finite element method is a contraction with respect to the sum of the energy error and a scaled error estimator numerical experiments are provided to verify the theoretical findings and show advantages of the adaptive continuous interior penalty finite element method

adaptive symmetric interior penalty galerkin method for boundary control problems we investigate an a posteriori error analysis of adaptive finite element approximations of linear quadratic boundary optimal control problems under bilateral box constraints which act on a neumann boundary control we use a symmetric interior galerkin method as discretization technique an efficient and reliable residual type error estimator is introduced by invoking data oscillations we then derive local upper and lower a posteriori error estimates for the boundary control problem adaptive mesh refinement indicated by a posteriori error estimates is applied numerical results are presented to illustrate the performance of the adaptive finite element approximation

asymptotic theory for the correlated gamma frailty model the frailty model is a generalization of cox s proportional hazard model where a shared unobserved quantity in the intensity induces a positive correlation among the survival times murphy showed consistency and asymptotic normality of the nonparametric maximum likelihood estimator npmle for the shared gamma frailty model without covariates in this paper we extend this result to the correlated gamma frailty model and we allow for covariates we discuss the definition of the nonparametric likelihood function in terms of a classical proof of consistency for the maximum likelihood estimator which goes back to wald our proof of the consistency for the npmle is essentially the same as the classical proof for the maximum likelihood estimator a new central limit theorem for processes of bounded variation is given furthermore we prove that a consistent estimator for the asymptotic variance of the npmle is given by the inverse of a discrete observed information matrix

convergence of an adaptive discontinuous galerkin method for elliptic interface problems abstract we prove a basic error contraction result of an adaptive discontinuous galerkin method for an elliptic interface problem the interface conditions considered model mass transfer of solutes through semi permeable membranes and other filtering processes the adaptive algorithm is based on a residual type a posteriori error estimator with a bulk refinement criterion the a posteriori error bound is derived under the assumption that the triangulation is aligned with the interfaces although crucially extremely general curved element shapes are also allowed resolving the interface geometry exactly as a corollary convergence of the adaptive discontinuous galerkin method for non essential neumann and or robin type boundary conditions posed on general curved boundaries also follows numerical experiments are also presented

systematic experimental exploration of bifurcations with noninvasive control we present a general method for systematically investigating the dynamics and bifurcations of a physical nonlinear experiment in particular we show how the odd number limitation inherent in popular noninvasive control schemes such as pyragas time delayed or washout filtered feedback control can be overcome for tracking equilibria or forced periodic orbits in experiments to demonstrate the use of our noninvasive control we trace out experimentally the resonance surface of a periodically forced mechanical nonlinear oscillator near the onset of instability around two saddle node bifurcations folds and a cusp bifurcation

asymptotics for change point models under varying degrees of mis specification change point models are widely used by statisticians to model drastic changes in the pattern of observed data least squares maximum likelihood based estimation of change points leads to curious asymptotic phenomena when the change point model is correctly specified such estimates generally converge at a fast rate n and are asymptotically described by minimizers of a jump process under complete mis specification by a smooth curve i e when a change point model is fitted to data described by a smooth curve the rate of convergence slows down to n1 3 and the limit distribution changes to that of the minimizer of a continuous gaussian process in this paper we provide a bridge between these two extreme scenarios by studying the limit behavior of change point estimates under varying degrees of model mis specification by smooth curves which can be viewed as local alternatives we find that the limiting regime depends on how quickly the alternatives approach a change point model we unravel a family of intermediate limits that can transition at least qualitatively to the limits in the two extreme scenarios the theoretical results are illustrated via a set of carefully designed simulations we also demonstrate how inference for the change point parameter can be performed in absence of knowledge of the underlying scenario by resorting to subsampling techniques that involve estimation of the convergence rate

data oscillation and convergence of adaptive fem data oscillation is intrinsic information missed by the averaging process associated with finite element methods fem regardless of quadrature ensuring a reduction rate of data oscillation together with an error reduction based on a posteriori error estimators we construct a simple and efficient adaptive fem for elliptic partial differential equations pdes with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance

energy norm a posteriori error estimation for discontinuous galerkin methods in this paper we present a residual based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous galerkin approximations of elliptic problems the theory is developed for an elliptic model problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed we also present some illustrating numerical examples

phase reduction theory based treatment of extended delayed feedback control algorithm in the presence of a small time delay mismatch the delayed feedback control dfc methods are noninvasive which means that the control signal vanishes if the delay time is adjusted to be equal to the period of a target unstable periodic orbit upo if the delay time differs slightly from the upo period a nonvanishing periodic control signal is observed we derive an analytical expression for this period for a general class of multiple input multiple output systems controlled by an extended dfc algorithm our approach is based on the phase reduction theory adapted to systems with time delay the analytical results are supported by numerical simulations of the controlled rossler system

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

error reduction and convergence for an adaptive mixed finite element method an adaptive mixed finite element method amfem is designed to guarantee an error reduction also known as saturation property after each refinement step the error for the fine mesh is strictly smaller than the error for the coarse mesh up to oscillation terms this error reduction property is established here for the raviart thomas finite element method with a reduction factor p 1 uniformly for the l 2 norm of the flux errors our result allows for linear convergence of a proper adaptive mixed finite element algorithm with respect to the number of refinement levels the adaptive algorithm surprisingly does not require any particular mesh design unlike the conforming finite element method the new arguments are a discrete local efficiency and a quasi orthogonality estimate the proof does not rely on duality or on regularity

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

quasi optimal a priori interface error bounds and a posteriori estimates for the interior penalty method in this work we show quasi optimal interface error estimates for solutions obtained by the symmetric interior penalty discontinuous galerkin method it is proved that the numerical solution restricted to an interface converges with order lvert ln h rvert h k 1 under suitable regularity requirements where the logarithmic factor is only present in the lowest order case i e k 1 for this case we also derive and analyze two a posteriori error estimators which demonstrate that the jump terms of the discrete fluxes are not essential to obtain local efficiency and reliability we support our analysis by numerical results and demonstrate that the interface approximation can be locally postprocessed to obtain discrete solutions of order h k 1 2 in the energy norm

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f

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

convergence analysis of an adaptive nonconforming finite element method an adaptive nonconforming finite element method is developed and analyzed that provides an error reduction due to the refinement process and thus guarantees convergence of the nonconforming finite element approximations the analysis is carried out for the lowest order crouzeix raviart elements and leads to the linear convergence of an appropriate adaptive nonconforming finite element algorithm with respect to the number of refinement levels important tools in the convergence proof are a discrete local efficiency and a quasi orthogonality property the proof does neither require regularity of the solution nor uses duality arguments as a consequence on the data control no particular mesh design has to be monitored