a globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions we analyze a new galerkin finite element method for numerically solving a linear convection dominated convection diffusion problem in two dimensions the method is shown to be convergent uniformly in the perturbation parameter of order h1 2 in a global energy norm which is stronger than the l2 norm this order is optimal in this norm for our choice of trial functions

on variance estimation with imputed survey data abstract unit nonresponse and item nonresponse both occur frequently in surveys unit nonresponse is customarily handled by weighting adjustment whereas item nonresponse is usually treated by some form of imputation in particular deterministic or stochastic imputation is often used to assign values for missing item responses we provide an account of some recent work on jackknife variance estimation based on adjusted imputed values using only a single imputation and hence a single completed data set we also present linearized versions of the jackknife variance estimators we study both stratified simple random sampling and stratified multistage sampling existing computer programs for jackknife and linearization variance estimation can be modified to implement the proposed variance estimators without requiring the creation and permanent retention of supplemental data sets but for secondary analyses the completed data set must include information on response status for each item as well as on the im

uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems i reaction diffusion type abstract we consider the bilinear finite element method on a shishkin mesh for the singularly perturbed elliptic boundary value problem 2 2 u x 2 2 u y 2 a x y u f x y in two space dimensions by using a very sophisticated asymptotic expansion of han et al 1 and the technique we used in 2 we prove that our method achieves almost second order uniform convergence rate in l2 norm numerical results confirm our theoretical analysis

crosswind smear and pointwise errors in streamline diffusion finite element methods for a model convection dominated singularly perturbed convection diffusion prob lem it is shown that crosswind smear in the numerical streamline diffusion finite element method is minimized by introducing a judicious amount of artificial crosswind diffusion the ensuing method with piecewise linear elements converges with a pointwise accuracy of almost h 5 4 under local smoothness assumptions 1 introduction the streamline diffusion method is a finite element method for convection dominated convection diffusion problems which combines formal high accuracy with decent stability properties the method was introduced in the case of stationary problems by hughes and brooks 7 cf raithby and torrance 14 and wahlbin 15 for earlier thoughts in this direction the mathematical analysis of the method was started in johnson and navert 8 and continued with extensions to e g time dependent problems in navert 12 johnson navert and pitkaranta 9 and johnson and saranen 10 in these papers local error estimates in l2 of order o h k 1 2 in regions of smoothness with piecewise polynomial finite elements of degree k were derived together with estimates stating as a typical example that in the zero diffusion limit a sharp discontinuity in the exact solution across a streamline will be captured in a numerical crosswind layer of width 0 h1 2 essentially the purpose of the present paper is first to improve the result just mentioned on numerical crosswind smear to 0 h3 4 the improvement from 0 h1 2 to 0 h3 4 is obtained by adding a small amount 0 h3 2 of artificial crosswind diffusion to the method in the piecewise linear case k 1 this does not destroy the known o h3 2 accuracy in l2 in smooth regions using our first result we then obtain our second main result localized pointwise error estimates of order 0 h5 4 in regions of smoothness the previously known best pointwise error estimate in the piecewise linear situation is 0 h1 2 another consequence is a global l estimate of order 0 h 2 in the presence of typical crosswind and downwind singularities we shall consider the model problem of finding u u x y such that

necessary convergence conditions for upwind schemes in the two dimensional case this paper considers nine point difference schemes for a two dimensional boundary value singular perturbation problem without turning points and parabolic boundary layers necessary conditions are given for the uniform convergence in the sense of the maximum norm of a scheme using these conditions several widely used schemes are analysed it is shown that some common schemes are not uniformly convergent in and that in some cases we are able to compute uniquely free parameters in the scheme some remarks on the treatment of a problem with a parabolic boundary layer are given

on variance estimation with imputed survey data comment unit nonresponse and item nonresponse both occur frequently in surveys unit nonresponse is customarily handled by weighting adjustment whereas item nonresponse is usually treated by some form of imputation in particular deterministic or stochastic imputation is often used to assign values for missing item responses we provide an account of some recent work on jackknife variance estimation based on adjusted imputed values using only a single imputation and hence a single completed data set we also present linearized versions of the jackknife variance estimators we study both stratified simple random sampling and stratified multistage sampling existing computer programs for jackknife and linearization variance estimation can be modified to implement the proposed variance estimators without requiring the creation and permanent retention of supplemental data sets but for secondary analyses the completed data set must include information on response status for each item as well as on the imputation class

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

pointwise error estimates for a streamline diffusion finite element scheme pointwise error estimates for a streamline diffusion scheme for solving a model convection dominated singularly perturbed convection diffusion problem are given these estimates improve pointwise error estimates obtained by johnson et al 5

constrained bayes estimation with applications abstract bayesian techniques are widely used in these days for simultaneous estimation of several parameters in compound decision problems often however the main objective is to produce an ensemble of parameter estimates whose histogram is in some sense close to the histogram of population parameters this is for example the situation in subgroup analysis where the problem is not only to estimate the different components of a parameter vector but also to identify the parameters that are above and the others that are below a certain specified cutoff point we have proposed in this paper bayes estimates in a very general context that meet this need these estimates are obtained by matching the first two moments of the histogram of the estimates and the posterior expectations of the first two moments of the histogram of the parameters and minimizing subject to these conditions the posterior expectation of the euclidean distance between the estimates and the parameters several applications of the m

big islands in dispersing billiard like potentials abstract we derive a rigorous estimate of the size of islands in both phase space and parameter space appearing in smooth hamiltonian approximations of scattering billiards the derivation includes the construction of a local return map near singular periodic orbits for an arbitrary scattering billiard and for the general smooth billiard potentials thus universality classes for the local behavior are found moreover for all scattering geometries and for many types of natural potentials which limit to the billiard flow as a parameter 0 islands of polynomial size in appear this suggests that the loss of ergodicity via the introduction of the physically relevant effect of smoothening of the potential in modeling for example scattering molecules may be of physically noticeable effect

lardy s regularization of a singularly perturbed elliptic pde in this paper we consider an elliptic partial differential equation where a small parameter is multiplied with one or both of the second derivatives viewing it as an ill posed problem lardy s regularization method is applied to approximate the solution convergence of the regularized solution to the original is proved numerical examples have been included for illustrating the method

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

multiple imputation after 18 years abstract multiple imputation was designed to handle the problem of missing data in public use data bases where the data base constructor and the ultimate user are distinct entities the objective is valid frequency inference for ultimate users who in general have access only to complete data software and possess limited knowledge of specific reasons and models for nonresponse for this situation and objective i believe that multiple imputation by the data base constructor is the method of choice this article first provides a description of the assumed context and objectives and second reviews the multiple imputation framework and its standard results these preliminary discussions are especially important because some recent commentaries on multiple imputation have reflected either misunderstandings of the practical objectives of multiple imputation or misunderstandings of fundamental theoretical results then criticisms of multiple imputation are considered and finally comparisons are made to alt

a noninformative bayesian approach to interval estimation in finite population sampling abstract a noninformative bayesian approach to interval estimation in finite population sampling is discussed given the sample this method introduces the polya distribution as a pseudo posterior distribution over the unobserved members of the population in many cases this distribution yields interval estimates similar to those of standard frequentist theory in addition it can be used in situations where the standard methods are difficult to apply for example in producing an interval estimate for the ratio of two medians we also consider related point estimation problems and observe that estimators derived from the pseudo posterior often perform better than classical alternatives

uniform high order difference schemes for a singularly perturbed two point boundary value problem on construit une famille de schemas aux differences finies uniformement precis pour le probleme du type eu a x u b x u f x on donne une analyse complete de l erreur de discretisation basee sur les resultats de stabilite on presente des essais numeriques

stable regions and singular trajectories in chaotic soft wall billiards abstract we present numerical and experimental results for the development of islands of stability in atom optics billiards with soft walls as the walls are soften stable regions appear near singular periodic trajectories in converging focusing and dispersing billiards and are surrounded by areas of stickiness in phase space the size of these islands depends on the softness of the potential in a very sensitive way

escape probability for classically chaotic systems abstract a statistical approach to study the escape of an ensemble of particles from classical chaotic systems is proposed the universal kinetic decay laws exponential and algebraic are found through the velocity angle distribution and shown to be specific of distinct motion regimes in the billiards with a small opening on the basis of the particular case of the dispersing sinai billiard the escape probability is given in explicit form and the temporal and geometrical conditions are enunciated to make controlled observations of decay dynamics in numerical experiments

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

a decision theoretic approach to imputation in finite population sampling abstract consider the situation where observations are missing at random from a simple random sample drawn from a finite population in certain cases it is of interest to create a full set of sample values such that inferences based on the full set will have the stated frequentist properties even though the statistician making those inferences is unaware that some of the observations were missing in the original sample this article gives a bayesian decision theoretic solution to this problem when one is primarily interested in making inferences about the population mean

showalter regularization of a singularly perturbed pde in this paper we consider an elliptic partial differential equation where a small parameter is multiplied with one or both of the second derivatives viewing it as an ill posed problem showalter s regularization method is applied to approximate the solution convergence of the regularized solution to the original is proved a numerical example has been included for illustrating the method

lavrentiev regularization of a singularly perturbed elliptic pde this paper considers a reaction diffusion equation with a small parameter multiplied with the derivatives considering this as an ill posed problem lavrentiev regularization method is used to formulate the related well posed problem pointwise a priori estimates of the regularized solutions and of the regularization error are also derived the regularized equations are solved numerically via the central difference scheme it is suggested that any other suitable discretization might also be used to solve the regularized problems also it is found that with a comparatively small number of grid points the numerical solution of the regularized equation comes up as a good approximation to the original solution

a semiparametric transformation approach to estimating usual daily intake distributions abstract the distribution of usual intakes of dietary components is important to individuals formulating food policy and to persons designing nutrition education programs the usual intake of a dietary component for a person is the long run average of daily intakes of that component for that person because it is impossible to directly observe usual intake for an individual it is necessary to develop an estimator of the distribution of usual intakes based on a sample of individuals with a small number of daily observations on a subsample of the individuals daily intake data for individuals are nonnegative and often very skewed also there is large day to day variation relative to the individual to individual variation and the within individual variance is correlated with the individual means we suggest a methodology for estimating usual intake distributions that allows for varying degrees of departure from normality and recognizes the measurement error associated with one day dietary intakes the est