efficient low rank approximation of the stochastic galerkin matrix in tensor formats in this article we describe an efficient approximation of the stochastic galerkin matrix which stems from a stationary diffusion equation the uncertain permeability coefficient is assumed to be a log normal random field with given covariance and mean functions the approximation is done in the canonical tensor format and then compared numerically with the tensor train and hierarchical tensor formats it will be shown that under additional assumptions the approximation error depends only on the smoothness of the covariance function and does not depend either on the number of random variables nor the degree of the multivariate hermite polynomials

numerical realization of dirichlet to neumann transparent boundary conditions for photonic crystal wave guides the computation of guided modes in photonic crystal wave guides is a key issue in the process of designing devices in photonic communications existing methods such as the super cell method provide an efficient computation of well confined modes however if the modes are not well confined the modelling error of the super cell method becomes prohibitive and advanced methods applying transparent boundary conditions for periodic media are needed in this work we demonstrate the numerical realization of a recently proposed dirichlet to neumann approach and compare the results with those of the super cell method for the resulting non linear eigenvalue problem we propose an iterative solution based on newton s method and a direct solution using chebyshev interpolation of the non linear operator based on the dirichlet to neumann approach we present a formula for the group velocity of guided modes that can serve as an objective function in the optimization of photonic crystal wave guides

combining data from two independent surveys a model assisted approach combining information from two or more independent surveys is a problem frequently encountered in survey sampling we consider the case of two independent surveys where a large sample from survey 1 collects only auxiliary information and a much smaller sample from survey 2 provides information on both the variables of interest and the auxiliary variables we propose a model assisted projection method of estimation based on a working model but the reference distribution is design based we generate synthetic or proxy values of a variable of interest by first fitting the working model relating the variable of interest to the auxiliary variables to the data from survey 2 and then predicting the variable of interest associated with the auxiliary variables observed in survey 1 the projection estimator of a total is simply obtained from the survey 1 weights and associated synthetic values we identify the conditions for the projection estimator to be asymptotically unbiased domain estimation using the projection method is also considered replication variance estimators are obtained by augmenting the synthetic data file for survey 1 with additional synthetic columns associated with the columns of replicate weights results from a simulation study are presented copyright 2012 oxford university press

an a posteriori error estimate for hp adaptive dg methods for convection diffusion problems on anisotropically refined meshes we prove an a posteriori error estimate for hp adaptive discontinuous galerkin methods for the numerical solution of convection diffusion equations on anisotropically refined rectangular elements the estimate yields global upper and lower bounds of the errors measured in terms of a natural norm associated with diffusion and a semi norm associated with convection the anisotropy of the underlying meshes is incorporated in the upper bound through an alignment measure we present a series of numerical experiments to test the feasibility of this approach within a fully automated hp adaptive refinement algorithm

weighted analytic regularity in polyhedra we explain a simple strategy to establish analytic regularity for solutions of second order linear elliptic boundary value problems the abstract framework presented here helps to understand the proof of analytic regularity in polyhedral domains given in the authors paper in m costabel m dauge s nicaise analytic regularity for linear elliptic systems in polygons and polyhedra math models methods appl sci 22 8 2012 we illustrate this strategy by considering problems set in smooth domains in corner domains and in polyhedra

on the stability of the boundary trace of the polynomial l2 projection on triangles and tetrahedra for the reference triangle or tetrahedron t we study the stability properties of the l 2 t projection p n onto the space of polynomials of degree n we show p nu l 2 t 2 c u l 2 t u h 1 t this implies optimal convergence rates for the approximation error u p nu l 2 t for all u h k t k 1 2

handwritten numeral recognition using gradient and curvature of gray scale image abstract in this paper the authors study on the use of gradient and curvature of the gray scale character image to improve the accuracy of handwritten numeral recognition three procedures based on curvature coefficient bi quadratic interpolation and gradient vector interpolation are proposed for calculating the curvature of the equi gray scale curves of an input image then two procedures to compose a feature vector of the gradient and the curvature are described the efficiency of the feature vectors are tested by recognition experiments for the handwritten numeral database iptp cdrom1 and nist sd3 and sd7 the experimental results show the usefulness of the curvature feature and recognition rate of 99 49 and 98 25 which are one of the highest rates ever reported for these databases h kato et al technical report of ieice pru95 3 1995 p 17 r a wilkinson et al technical report nistir 4912 august 1992 j geist et al technical report nistir 5452 june 1994 are achieved respectively

empirical likelihood for estimating equations with missing values we consider an empirical likelihood inference for parameters defined by general estimating equations when some components of the random observations are subject to missingness as the nature of the estimating equations is wide ranging we propose a nonparametric imputation of the missing values from a kernel estimator of the conditional distribution of the missing variable given the always observable variable the empirical likelihood is used to construct a profile likelihood for the parameter of interest we demonstrate that the proposed nonparametric imputation can remove the selection bias in the missingness and the empirical likelihood leads to more efficient parameter estimation the proposed method is further evaluated by simulation and an empirical study on a genetic dataset on recombinant inbred mice

jackknife variance estimation with survey data under hot deck imputation summary hot deck imputation is commonly employed for item nonresponse in sample surveys it is also a common practice to treat the imputed values as if they are true values and then compute the variance estimates using standard formulae this procedure however could lead to serious underestimation of the true variance when the proportion of missing values for an item is appreciable we propose a jackknife variance estimator for stratified multistage surveys which is obtained by first adjusting the imputed values for each pseudo replicate and then applying the standard jackknife formula the proposed jackknife variance estimator is shown to be consistent as the sample size increases assuming equal response probabilities within imputation classes and using a particular hot deck imputation

on the bias of the multiple imputation variance estimator in survey sampling summary multiple imputation is a method of estimating the variances of estimators that are constructed with some imputed data we give an expression for the bias of the multiple imputation variance estimator for data that are collected with a complex sample design the bias may be sizable for certain estimators such as domain means when a large fraction of the values are imputed a bias adjusted variance estimator is suggested

the dpg method for the stokes problem we discuss well posedness and convergence theory for the dpg method applied to a general system of linear partial differential equations pdes and specialize the results to the classical stokes problem the stokes problem is an iconic troublemaker for standard bubnov galerkin methods if discretizations are not carefully designed they may exhibit non convergence or locking by contrast dpg does not require us to treat the stokes problem in any special manner we illustrate and confirm our theoretical convergence estimates with numerical experiments

on balanced random imputation in surveys random imputation methods are often used in practice because they tend to preserve the distribution of the variable being imputed which is an important property when the goal is to estimate population quantiles however this type of imputation method introduces additional variability the imputation variance due to the random selection of residuals in this paper we propose a class of random balanced imputation methods under which the imputation variance is eliminated while the distribution of the variable being imputed is preserved the rationale behind balanced imputation is to select residuals at random so that appropriate constraints are satisfied we describe an algorithm for selecting the random residuals that can be viewed as an adaptation of the cube algorithm proposed in the context of balanced sampling deville tille 2004 results of a simulation study support our findings

a robust dpg method for convection dominated diffusion problems ii adjoint boundary conditions and mesh dependent test norms we introduce a dpg method for convection dominated diffusion problems the choice of a test norm is shown to be crucial to achieving robust behavior with respect to the diffusion parameter demkowicz and heuer 2011 18 we propose a new inflow boundary condition which regularizes the adjoint problem allowing the use of a stronger test norm the robustness of the method is proven and numerical experiments demonstrate the method s robust behavior

small sample degrees of freedom with multiple imputation an appealing feature of multiple imputation is the simplicity of the rules for combining the multiple complete data inferences into a final inference the repeated imputation inference rubin 1987 this inference is based on a t distribution and is derived from a bayesian paradigm under the assumption that the complete data degrees of freedom com are infinite but the number of imputations m is finite when com is small and there is only a modest proportion of missing data the calculated repeated imputation degrees of freedom m for the t reference distribution can be much larger than com which is clearly inappropriate following the bayesian paradigm we derive an adjusted degrees of freedom m with the following three properties for fixed m and estimated fraction of missing information m monotonically increases in com m is always less than or equal to com and m equals m when com is infinite a small simulation study demonstrates the superior frequentist performance when using m rather than m

parametric fractional imputation for missing data analysis under a parametric model for missing data the em algorithm is a popular tool for flnding the maximum likelihood estimates mle of the parameters of the model imputation when carefully done can be used to facilitate the parameter estimation by applying the complete sample estimators to the imputed dataset the basic idea is to generate the imputed values from the conditional distribution of the missing data given the observed data multiple imputation is a bayesian approach to generate the imputed values from the conditional distribution in this article parametric fractional imputation is proposed as a parametric approach for generating imputed values using fractional weights the e step of the em algorithm can be approximated by the weighted mean of the imputed data likelihood where the fractional weights are computed from the current value of the parameter estimates some computational e ciency can be achieved using the idea of importance sampling in the monte carlo approximation of the conditional expectation the resulting estimator of the specifled parameters will be identical to the mle under missing data if the fractional weights are adjusted using a calibration step the proposed imputation method provides e cient parameter estimates for the model parameters specifled and also provides reasonable estimates for parameters that are not part of the imputation model for example domain means thus the proposed imputation method is a useful tool for general purpose data analysis variance estimation is covered and results from a limited simulation study are presented

convergence of quasi optimal stochastic galerkin methods for a class of pdes with random coefficients in this work we consider quasi optimal versions of the stochastic galerkin method for solving linear elliptic pdes with stochastic coefficients in particular we consider the case of a finite number n of random inputs and an analytic dependence of the solution of the pde with respect to the parameters in a polydisc of the complex plane c n we show that a quasi optimal approximation is given by a galerkin projection on a weighted anisotropic total degree space and prove a sub exponential convergence rate as a specific application we consider a thermal conduction problem with non overlapping inclusions of random conductivity numerical results show the sharpness of our estimates

hp adaptive ipdg tdg fem for parabolic obstacle problems for a parabolic obstacle problem two equivalent hp fem discretization methods based on interior penalty discontinuous galerkin in space and discontinuous galerkin in time are presented the first approach is based on a variational inequality vi formulation and the second approach on a mixed method in which the non penetration condition is resolved by a lagrange multiplier the discrete lagrange multiplier is a linear combination of biorthogonal basis functions allowing to write the discrete vi constraints as a set of complementarity problems employing a penalized fischer burmeister non linear complementarity function the discrete mixed problem can be solved by a locally q quadratic converging semi smooth newton ssn method the hierarchical a posteriori error estimator for the vi formulation which under the saturation assumption is both efficient and reliable allows hp adaptivity the numerical experiments show improved convergence compared to uniform and h adaptive meshes furthermore an a priori error estimate is given for the vi formulation

the hp adaptive fem based on continuous sobolev embeddings isotropic refinements the aim of this paper is to present a new class of smoothness testing strategies in the context of hp adaptive refinements based on continuous sobolev embeddings in addition to deriving a modified form of the 1d smoothness indicators introduced in 26 they will be extended and applied to a higher dimensional framework a few numerical experiments in the context of the hp adaptive fem for a linear elliptic pde will be performed

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

alternative paradigms for the analysis of imputed survey data abstract rubin has offered multiple imputation as a general approach to inference from survey data sets with missing values filled in through imputation in many situations the multiple imputation variance estimator is consistent in turn this observation has lent support to a number of complex applications in fact however the multiple imputation variance estimator is inconsistent under some simple conditions this article extends previous work of rao and shao and of fay directed toward consistent variance estimation under wider conditions extensions of rao and shao s results to fractionally weighted imputation combines the estimation efficiency of multiple imputation and the consistency of the rao shao variance estimator

adjusted jackknife for imputation under unequal probability sampling without replacement imputation is commonly used to compensate for item non response in sample surveys if we treat the imputed values as if they are true values and then compute the variance estimates by using standard methods such as the jackknife we can seriously underestimate the true variances we propose a modified jackknife variance estimator which is defined for any without replacement unequal probability sampling design in the presence of imputation and non negligible sampling fraction mean ratio and random imputation methods will be considered the practical advantage of the method proposed is its breadth of applicability

high order methods as an alternative to using sparse tensor products for stochastic galerkin fem solutions of random elliptic boundary value problems admit efficient approximations by polynomials on the parameter domain each coefficient in such an expansion is a spatially dependent function and can be approximated within a hierarchy of finite element spaces if the finite elements are of sufficiently high order using just a single spatial mesh is predicted to achieve the same convergence rate with respect to the total number of degrees of freedom as sparse tensor product constructions and other multilevel stochastic galerkin approximations numerical computations for an elliptic two point boundary value problem confirm this and indicate no loss of accuracy for a single level method compared to using a sparse tensor product with the same total number of degrees of freedom

an analysis of discretizations of the helmholtz equation in l2 and in negative norms for a model helmholtz problem at high wavenumber k we present a wavenumber explicit error analysis in the l 2 and h 1 norms for the galerkin fem for the convergence in l 2 we show that the lowest order case p 1 is special in that the relative error in l 2 scales at best with k whereas it does not for higher order discretizations an alternative to the galerkin method with better dispersion properties is the optimally blended spectral finite element scheme of ainsworth and wajid 2010 for this method we present an error analysis in l 2 for the lowest order case p 1 in one dimension showing that the l 2 error is improved by a factor k compared to the lowest order galerkin fem

multiply robust imputation procedures for the treatment of item nonresponse in surveys summaryitem nonresponse in surveys is often treated through some form of imputation we introduce multiply robust imputation in finite population sampling this is closely related to multiple robustness which extends double robustness in practice multiple nonresponse models and multiple imputation models may be fitted each involving different subsets of covariates and possibly different link functions an imputation procedure is said to be multiply robust if the resulting estimator is consistent when all models but one are misspecified a jackknife variance estimator is proposed and shown to be consistent random and fractional imputation procedures are discussed a simulation study suggests that the proposed estimation procedures have low bias and high efficiency

fractional hot deck imputation to compensate for item nonresponse hot deck imputation procedures replace missing values with values that occur in the sample fractional hot deck imputation replaces each missing observation with a set of imputed values and assigns a weight to each imputed value under the model in which observations in an imputation cell are independently and identically distributed fractional hot deck imputation is shown to be an effective imputation procedure a consistent replication variance estimation procedure for estimators computed with fractional imputation is suggested simulations show that fractional imputation and the suggested variance estimator are superior to multiple imputation estimators in general and much superior to multiple imputation for estimating the variance of a domain mean

jackknife variance estimation for nearest neighbor imputation nearest neighbor imputation is a popular hot deck imputation method used to compensate for nonresponse in sample surveys although this method has a long history of application the problem of variance estimation after nearest neighbor imputation has not been fully investigated because nearest neighbor imputation is a nonparametric method a nonparametric variance estimation technique such as the jackknife is desired we show that the naive jackknife that treats imputed values as observed data produces serious underestimation we also show that rao and shao s adjusted jackknife or the jackknife with each pseudoreplicate reimputed which produces asymptotically unbiased and consistent jackknife variance estimators for other imputation methods such as mean imputation random hot deck imputation and ratio or regression imputation produces serious overestimation in the case of nearest neighbor imputation two partially reimputed and a partially adjusted jackknife variance estimators are proposed and s

a unified approach to linearization variance estimation from survey data after imputation for item nonresponse variance estimation after imputation is an important practical problem in survey sampling when deterministic imputation or stochastic imputation is used we show that the variance of the imputed estimator can be consistently estimated by a unifying linearize and reverse approach we provide some applications of the approach to regression imputation fractional categorical imputation multiple imputation and composite imputation results from a simulation study under a factorial structure for the sampling response and imputation mechanisms show that the proposed linearization variance estimator performs well in terms of relative bias assuming a missing at random response mechanism