a posteriori error control for distributed elliptic optimal control problems with control constraints discretized by hp finite elements abstract a distributed elliptic control problem with control constraints is considered which is formulated as a three field problem and consists of two variational equations for the state and the co state variables as well as of a variational inequality for the control variable two discretization approaches with h p finite elements are discussed in the first discretization approach all variables state co state and control are discretized a semi smooth newton method is introduced for solving the resulting algebraic system in the second discretization approach only the state and the co state variables are discretized whereas the control is determined by projection a simple fixed point scheme is presented for the iterative solution of this approach the main focus of the paper is on the derivation of reliable and efficient a posteriori error estimates which enables h p adaptive mesh refinements in particular the estimates can be applied to the iteration solutions so that they can be used as a stopping criterion of the iterative solution schemes in several numerical experiments the order of convergence of the adaptive discretization approaches and the efficiency as well as the reliability of the a posteriori error estimates are studied

envelope constrained h filtering with fading measurements and randomly occurring nonlinearities in this paper the envelope constrained h filtering problem is investigated for a class of discrete time varying stochastic systems over a finite horizon the system under consideration involves fading measurements randomly occurring nonlinearities rons and mixed multiplicative and additive noises a novel envelope constrained performance criterion is proposed to better quantify the transient dynamics of the filtering error process over the finite horizon the purpose of the problem addressed is to design a time varying filter such that both the h performance and the desired envelope constraints are achieved at each time step by utilizing the stochastic analysis techniques combined with the ellipsoid description on the estimation errors sufficient conditions are established in the form of recursive matrix inequalities rmis reflecting both the envelope information and the desired h performance index the filter gain matrix is characterized by means of the solvability of the deduced rmis finally a simulation example is provided to show the effectiveness of the proposed filtering design scheme

a missing composite covariate in survival analysis a case study of the chinese longitudinal health and longevity survey we estimate a cox proportional hazards model where one of the covariates measures the level of a subject s cognitive functioning by grading the total score obtained by the subject on the items of a questionnaire a case study is presented where the sample includes partial respondents who did not answer some questionnaire items the total score takes hence the form of an interval censored variable and as a result the level of cognitive functioning is missing on some subjects we handle the partial respondents by taking a likelihood based approach where survival time is jointly modelled with the censored total score and the size of the censoring interval estimates are obtained by an e m type algorithm that reduces to the iterative maximization of three complete log likelihood functions derived from two augmented data sets with case weights alternated with weights updating this methodology is exploited to assess the mini mental state examination index as a prognostic factor of survival in a sample of chinese older adults

imputing missing covariate values for the cox model multiple imputation is commonly used to impute missing data and is typically more efficient than complete cases analysis in regression analysis when covariates have missing values imputation may be performed using a regression model for the incomplete covariates on other covariates and importantly on the outcome with a survival outcome it is a common practice to use the event indicator d and the log of the observed event or censoring time t in the imputation model but the rationale is not clear we assume that the survival outcome follows a proportional hazards model given covariates x and z we show that a suitable model for imputing binary or normal x is a logistic or linear regression on the event indicator d the cumulative baseline hazard h 0 t and the other covariates z this result is exact in the case of a single binary covariate in other cases it is approximately valid for small covariate effects and or small cumulative incidence if we do not know h 0 t we approximate it by the nelson aalen estimator of h t or estimate it by cox regression we compare the methods using simulation studies we find that using logt biases covariate outcome associations towards the null while the new methods have lower bias overall we recommend including the event indicator and the nelson aalen estimator of h t in the imputation model

averaging techniques yield reliable a posteriori finite element error control for obstacle problems the reliability of frequently applied averaging techniques for a posteriori error control has recently been established for a series of finite element methods in the context of second order partial differential equations this paper establishes related reliable and efficient a posteriori error estimates for the energy norm error of an obstacle problem on unstructured grids as a model example for variational inequalities the surprising main result asserts that the distance of the piecewise constant discrete gradient to any continuous piecewise affine approximation is a reliable upper error bound up to known higher order terms consistency terms and a multiplicative constant

an adaptive wavelet collocation method for solving optimal control of elliptic variational inequalities of the obstacle type abstract this paper presents a fast computational technique based on the wavelet collocation method for the numerical solution of an optimal control problem governed by elliptic variational inequalities of obstacle type in this problem the solution divides the domain into contact and noncontact sets the boundary between the contact and noncontact sets is a free boundary which is not known a priori and the solution is not smooth on it accordingly a very fine grid is needed in order to obtain a solution with a reasonable accuracy in this paper our aim is to propose an adaptive scheme in order to generate an appropriate and economic irregular dyadic mesh for finding the optimal control and state functions the irregular mesh will be generated such that its density around the free boundary is higher than in other places and high resolution computations are focused on these zones to this aim we use an adaptive wavelet collocation method and take advantage of the fast wavelet transform of compact supported interpolating wavelets to develop a multi level algorithm which generates an adaptive computational grid using this adaptive grid takes less cpu time than using a full regular mesh at each step of the algorithm the active set method is used for solving the optimality system of the obstacle problem on the adapted mesh finally the numerical examples are presented to show the validity and efficiency of the technique

large sample significance levels from multiply imputed data using moment based statistics and an f reference distribution abstract we present a procedure for computing significance levels from data sets whose missing values have been multiply imputed data this procedure uses moment based statistics m 3 repeated imputations and an f reference distribution when m we show first that our procedure is essentially the same as the ideal procedure in cases of practical importance and second that its deviations from the ideal are basically a function of the coefficient of variation of the canonical ratios of complete to observed information for small m our procedure s performance is largely governed by this coefficient of variation and the mean of these ratios using simulation techniques with small m we compare our procedure s actual and nominal large sample significance levels and conclude that it is essentially calibrated and thus represents a definite improvement over previously available procedures furthermore we compare the large sample power of the procedure as a function of m and other factors such as the di

multiple imputation in cox regression when there are time varying effects of covariates in cox regression it is important to test the proportional hazards assumption and sometimes of interest in itself to study time varying effects tves of covariates tves can be investigated with log hazard ratios modelled as a function of time missing data on covariates are common and multiple imputation is a popular approach to handling this to avoid the potential bias and efficiency loss resulting from a complete case analysis two multiple imputation methods have been proposed for when the substantive model is a cox proportional hazards regression an approximate method imputing missing covariate values for the cox model in statistics in medicine 2009 by white and royston and a substantive model compatible method multiple imputation of covariates by fully conditional specification accommodating the substantive model in statistical methods in medical research 2015 by bartlett et al at present neither accommodates tves of covariates we extend them to do so for a general form for the tves and give specific details for tves modelled using restricted cubic splines simulation studies assess the performance of the methods under several underlying shapes for tves our proposed methods give approximately unbiased tve estimates for binary covariates with missing data but for continuous covariates the substantive model compatible method performs better the methods also give approximately correct type i errors in the test for proportional hazards when there is no tve and gain power to detect tves relative to complete case analysis ignoring tves at the imputation stage results in biased tve estimates incorrect type i errors and substantial loss of power in detecting tves we also propose a multivariable tve model selection algorithm the methods are illustrated using data from the rotterdam breast cancer study r code is provided

a posteriori error control and adaptivity of hp finite elements for mixed and mixed hybrid methods abstract in this paper mixed and mixed hybrid methods for h and h p adaptive finite elements on quadrilateral meshes are discussed for variational equations and in particular for variational inequalities the main result is the derivation of reliable error estimates for mixed methods for the obstacle problem the estimates rely on the use of a post processing of the potential in h 1 and on the introduction of a certain lagrange multiplier which is associated with the obstacle constraints the error estimates consist of the dual norm of the residual which is defined by an appropriate approximation of the lagrange multiplier plus some computable remainder terms in numerical experiments the applicability of the post processing procedure on quadrilateral meshes with multilevel hanging nodes is verified and the use of the estimates in h and h p adaptive schemes is demonstrated by means of convergence rates and effectivity indices

multiple imputation of missing blood pressure covariates in survival analysis this paper studies a non response problem in survival analysis where the occurrence of missing data in the risk factor is related to mortality in a study to determine the influence of blood pressure on survival in the very old 85 years blood pressure measurements are missing in about 12 5 per cent of the sample the available data suggest that the process that created the missing data depends jointly on survival and the unknown blood pressure thereby distorting the relation of interest multiple imputation is used to impute missing blood pressure and then analyse the data under a variety of non response models one special modelling problem is treated in detail the construction of a predictive model for drawing imputations if the number of variables is large risk estimates for these data appear robust to even large departures from the simplest non response model and are similar to those derived under deletion of the incomplete records

multiple imputation for an incomplete covariate that is a ratio we are concerned with multiple imputation of the ratio of two variables which is to be used as a covariate in a regression analysis if the numerator and denominator are not missing simultaneously it seems sensible to make use of the observed variable in the imputation model one such strategy is to impute missing values for the numerator and denominator or the log transformed numerator and denominator and then calculate the ratio of interest we call this passive imputation alternatively missing ratio values might be imputed directly with or without the numerator and or the denominator in the imputation model we call this active imputation in two motivating datasets one involving body mass index as a covariate and the other involving the ratio of total to high density lipoprotein cholesterol we assess the sensitivity of results to the choice of imputation model and as an alternative explore fully bayesian joint models for the outcome and incomplete ratio fully bayesian approaches using winbugs were unusable in both datasets because of computational problems in our first dataset multiple imputation results are similar regardless of the imputation model in the second results are sensitive to the choice of imputation model sensitivity depends strongly on the coefficient of variation of the ratio s denominator a simulation study demonstrates that passive imputation without transformation is risky because it can lead to downward bias when the coefficient of variation of the ratio s denominator is larger than about 0 1 active imputation or passive imputation after log transformation is preferable 2013 the authors statistics in medicine published by john wiley sons ltd

a posteriori error estimations for mixed finite element approximations to the navier stokes equations a posteriori estimates for mixed finite element discretizations of the navier stokes equations are derived we show that the task of estimating the error in the evolutionary navier stokes equations can be reduced to the estimation of the error in a steady stokes problem as a consequence any available procedure to estimate the error in a stokes problem can be used to estimate the error in the nonlinear evolutionary problem a practical procedure to estimate the error based on the so called postprocessed approximation is also considered both the semidiscrete in space and the fully discrete cases are analyzed some numerical experiments are provided

mixed finite element methods of higher order for model contact problems this paper presents mixed finite element methods of higher order for a simplified signorini problem and an idealized frictional problem the discretization is based on a mixed variational formulation proposed by haslinger et al which is extended to higher order finite elements to guarantee the unique existence of the solution of the mixed method a discrete inf sup condition is proven approximation results of the p method of finite elements and some inverse estimates for higher order polynomials are applied numerical results confirm the theoretical findings

optimal pulse shape design for digital communication systems by projections onto convex sets recent developments in dsp hardware has made it possible to use almost any pulse shape for digital data trans mission this resulted in a search for algorithms capable of constructing pulse shapes matching to the properties of a given channel the projection onto convex sets technique is suitable for the solution of this problem particularly because of its ffexibility in modeling a variety of constraints the use of the technique for the optimal pulse shape design problem is demonstrated through a detailed example from power line communications i introduction ince nyquist s invention of the intersymbol interference isi the optimal pulse shaping problem for digital data transmission over channels with various properties has been investigated by a number of researchers 1 7 the main differences between various digital nyquist pulse design al gorithms published in the literature are the type of the filter fir or iir they choose to generate the pulse shape and the formulation and solution of the optimization problem some of these approaches use general optimization techniques and they can handle additional constraints if needed however addition of each new constraint requires reformulation of the problem and the solution algorithm the projections onto convex sets pocs technique is an optimization method introduced in the 1960 s 8 a number of successful applications of the pocs technique in the signal processing area have been reported in the recent years 9 ll the pocs technique is attractive for optimum pulse shape design particularly because of its modular way of formulating problems with many constraints in this technique the addition of new constraints or removal of some of the existing ones does not require reformulation it is also possible to handle certain inconsistent requirements in the pocs formulation 12 if there are nonintersecting convex sets it is possible to find the vector which is as close as possible to one set of constraints while satisfying the rest

extrapolating a band limited function from its samples taken in a finite interval a band limited signal of finite energy can be reconstructed from its samples taken at the nyquist rate moreover the reconstruction is stable a feature crucial for implementation a small error in the sample values generates only a correspondingly small error in the resulting signal the nyquist sample values are mutually independent so that knowledge of them in a given interval t leq t leq 0 provides hardly any information about the behavior of the signal outside the interval however when the samples are taken at a greater rate a case referred to as over sampling they are interrelated and this redundancy can be exploited in various ways to improve the behavior of the reconstruction procedure a natural question is whether it can also be used to form accurate estimates of the signal outside the interval of observation this problem is relevant as well to prediction theory with oversampling when t infty so that the samples are known on the entire half line t they determine the signal everywhere although the reconstruction is now no longer stable here we examine the case of finite t of course a finite amount of data can yield only limited accuracy we prove that the samples can be used to form an approximation to the signal outside the sampling interval with an error which asymptotically as t rightarrow infty decreases exponentially in t over a range which grows linearly with t however as in the limiting case these approximations are not useful in practice since they require the sample values to be known exactly in the presence of measurement error the nature of the results changes good approximations are now available for only a bounded distance outside the interval of observation regardless of its length and their accuracy and range of validity can be increased only by improving the precision of sample reading since physical measurements are never perfect it is this conclusion which counts for applications the same results hold for the extrapolation of bounded band limited signals

mean square convergence of adaptive envelope constrained filtering a new type of adaptive filtering scheme for solving an envelope constrained filter design problem in a stochastic environment has been presented the steady state stochastic analysis of the adaptive scheme is established in the sense of the mean square it is shown that if a given initial point is in a neighborhood of the origin the adaptive scheme with a fixed step size produces a filter that converges in the mean square sense to within an upper boundary of the noise free optimum filter numerical examples involving pulse compression and channel equalization are presented to illustrate the convergence characteristics of the adaptive scheme operating in a stochastic environment

a new interpolation theorem with application to pulse transmission an interpolation theorem is determined for the case when there are a finite number of arbitrarily placed sampling instants and the interpolation function is the output of a known filter they are also the interpolation functions with the specified properties that have minimum energy the theorem is used to determine the input to a communications channel given a finite number of samples of its output this provides a generalization of matched filters and a perspective on the benefits of fractionally spaced equalization the theorem is also used to construct masks of a family of pulses that are specified by the range of pulse voltages at a finite number of sampling instants the theory determines how the pulse masks thus constructed is transformed when the pulse family is transmitted through a filter such as a length of transmission line

a posteriori error control of h p finite elements for variational inequalities of the first and second kind in this paper residual based a posteriori error estimates for variational inequalities including those of the second kind are proposed the variational formulation and its discretizations are considered in an abstract framework of general banach spaces the main idea is to express the residual in terms of some lagrange multipliers which can be obtained for instance by some post processing the residual itself is defined for an arbitrary element of the trial space the error of this element and of the solution of the variational inequality is then estimated by the dual norm of the residual plus some computable remainder terms this concept is applied to a variety of frictional contact problems such as signorini and obstacle problems as well as to the bingham fluid problem the applicability of the estimates is confirmed by several numerical experiments in particular the general framework allows for the discretization with h p adaptivity which leads to nearly exponential convergence rates in most cases

multiple imputation for interval estimation from simple random samples with ignorable nonresponse abstract several multiple imputation techniques are described for simple random samples with ignorable nonresponse on a scalar outcome variable the methods are compared using both analytic and monte carlo results concerning coverages of the resulting intervals for the population mean using m 2 imputations per missing value gives accurate coverages in common cases and is clearly superior to single imputation m 1 in all cases the performances of the methods for various m can be predicted well by linear interpolation in 1 m 1 between the results for m 2 and m as a rough guide to assure coverages of interval estimates within 2 of the nominal level when using the preferred methods the number of imputations per missing value should increase from 2 to 3 as the nonresponse rate increases from 10 to 60

mixed finite element methods for unilateral problems convergence analysis and numerical studies in this paper we propose and study different mixed variational methods in order to approximate with finite elements the unilateral problems arising in contact mechanics the discretized unilateral conditions at the candidate contact interface are expressed by using either continuous piecewise linear or piecewise constant lagrange multipliers in the saddle point formulation a priori error estimates are established and several numerical studies corresponding to the different choices of the discretized unilateral conditions are achieved

a comparison of multiple imputation and fully augmented weighted estimators for cox regression with missing covariates several approaches exist for handling missing covariates in the cox proportional hazards model the multiple imputation mi is relatively easy to implement with various software available and results in consistent estimates if the imputation model is correct on the other hand the fully augmented weighted estimators fawes recover a substantial proportion of the efficiency and have the doubly robust property in this paper we compare the fawes and the mi through a comprehensive simulation study for the mi we consider the multiple imputation by chained equation and focus on two imputation methods bayesian linear regression imputation and predictive mean matching simulation results show that the imputation methods can be rather sensitive to model misspecification and may have large bias when the censoring time depends on the missing covariates in contrast the fawes allow the censoring time to depend on the missing covariates and are remarkably robust as long as getting either the conditional expectations or the selection probability correct due to the doubly robust property the comparison suggests that the fawes show the potential for being a competitive and attractive tool for tackling the analysis of survival data with missing covariates

a posteriori error estimates for fully discrete nonlinear parabolic problems abstract we present estimates for the spatial error in fully discrete approximations to nonlinear parabolic problems that extend the a posteriori estimates for the continuous time semi discretization introduced in de frutos and novo j de frutos j novo a posteriori error estimation with the p version of the finite element method for nonlinear parabolic differential equations comput methods appl mech engrg 191 2002 4893 4904 the error indicator is defined as the difference between the fully discrete galerkin and the fully discrete postprocessed approximations we prove that the main term of the temporal error in both the fully discrete galerkin and the postprocessed approximation is the same as a consequence the spatial approximation error can be independently estimated with regard to the time approximation error some numerical experiments are provided

a penalty approach to iterative algorithms for envelope constrained filter design the discrete time envelope constrained ec filtering problem can be formulated as a quadratic programming qp problem with affine inequality constraints this qp problem is approximated by an unconstrained minimization problem with two parameters descent direction based algorithms are applied to solve the unconstrained problem iteratively it is shown that these algorithms converge

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

a posteriori error estimators for obstacle problems another look we show that a posteriori estimators for the obstacle problem are easily obtained from the theory for linear equations the theory would be even simpler if the lagrange multiplier does not have a nonconforming contribution as it has in actual finite element computations

envelope constrained filters adaptive algorithms we consider an envelope constrained ec optimal filter design problem involving a quadratic cost function and a number of linear inequality constraints using the duality theory and the space transformation function the optimal solution of the dual problem can be computed by finding the limiting point of an ordinary differential equation given in terms of the gradient flow an iterative algorithm is developed via discretizing the differential equation from the primal dual relationship the corresponding sequence of approximate solutions in the original ec filtering problem is obtained based on these results an adaptive algorithm is constructed for solving the stochastic ec filtering problem in which the input signal is corrupted by an additive random noise for illustration a practical example is solved for both noise free and noisy cases

a posteriori error estimates of higher order finite elements for frictional contact problems abstract in this paper a posteriori estimates are derived for higher order finite element methods and frictional contact problems the discretization is based on a mixed approach where the geometrical and frictional constraints are captured by lagrange multipliers the use of higher order polynomials leads to a certain non conformity in the discretization which requires special attention in the error analysis as a main result an error estimation is proposed which consists of the dual norm of a residual plus some computable remainder terms the residual is estimated by well known a posteriori error estimates for variational equations the remainder terms represent typical sources resulting from the non conforming mixed discretization numerical experiments confirm the applicability of the a posteriori estimates to adaptive mesh refinements