adaptive anisotropic wavelet collocation method on general curvilinear coordinate systems a new general framework for an adaptive anisotropic wavelet collocation method a awcm for the solution of partial differential equations is developed this proposed framework addresses two major shortcomings of existing wavelet based adaptive numerical methodologies namely the reliance on a rectangular domain and the curse of anisotropy i e drastic over resolution of sheet and filament like features arising from the inability of the wavelet refinement mechanism to distinguish highly correlated directional information in the solution the a awcm addresses both of these challenges by incorporating coordinate transforms into the adaptive wavelet collocation method for the solution of pdes the resulting integrated framework leverages the advantages of both the curvilinear anisotropic meshes and wavelet based adaptive refinement in a complimentary fashion resulting in greatly reduced cost of resolution for anisotropic features the proposed adaptive anisotropic wavelet collocation method retains the a priori error control of the solution and fully automated mesh refinement while offering new abilities through the flexible mesh geometry including body fitting the new a awcm is demonstrated for a variety of cases including parabolic diffusion acoustic scattering and unsteady external flow

empirical likelihood ratio confidence regions than are those based on student s t statistic an effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable the method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain algorithms exist for finding the unique global minimum at a superlinear rate of convergence a byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points the multivariate empirical likelihood regions are justified for functions of several means such as variances correlations and regression parameters and for statistics with linear estimating equations an algorithm is given for computing profile empirical likelihoods for these statistics

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

a dynamically adaptive multilevel wavelet collocation method for solving partial differential equations in a finite domain a dynamically adaptive multilevel wavelet collocation method is developed for the solution of partial differential equations the multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution high resolution computations are performed only in regions where sharp transitions occur the scheme handles general boundary conditions the method is applied to the solution of the one dimensional burgers equation with small viscosity a moving shock problem and a nonlinear thermoacoustic wave problem the results indicate that the method is very accurate and efficient

semiparametric pseudo likelihoods in generalized linear models with nonignorable missing data we consider identifiability and estimation in a generalized linear model in which the response variable and some covariates have missing values and the missing data mechanism is nonignorable and unspecified we adopt a pseudo likelihood approach that makes use of an instrumental variable to help identifying unknown parameters in the presence of nonignorable missing data explicit conditions for the identifiability of parameters are given some asymptotic properties of the parameter estimators based on maximizing the pseudo likelihood are established explicit asymptotic covariance matrix and its estimator are also derived in some cases for the numerical maximization of the pseudo likelihood we develop a two step iteration algorithm that decomposes a nonconcave maximization problem into two problems of maximizing concave functions some simulation results and an application to a dataset from cotton factory workers are also presented

empirical likelihood estimation for finite populations and the effective usage of auxiliary information summary in finite population inference problems auxiliary population information is often available we show in this paper that the empirical likelihood method can be naturally applied to such problems to make effective use of the auxiliary information we prove that the resulting estimates have smaller asymptotic variances than the usual estimates which do not use auxiliary information a bahadur type representation for empirical likelihood sample quantiles is given simulation results show that the empirical likelihood estimates perform well among a number of competitors and are model robust

on estimating distribution functions and quantiles from survey data using auxiliary information summary ratio and difference estimators of a population distribution function under a general sampling design are obtained using auxiliary population information the relative mean errors and relative mean square errors of these estimators and a model based estimator of chambers dunstan 1986 are compared through a simulation study the advantages of the design based estimators over the model based estimator under model misspecifications especially for large samples are demonstrated ratio and difference estimators of a population quantile are also studied

a comparison of estimates of natural mortality from fish tagging experiments summary tagging experiments in which recaptures have to be made by professional fishermen are considered the methods put forward are shown to be maximum likelihood solutions and expressions are derived for the variances of the estimators optimal conditions for the experiment are found and cases of questionable behaviour are identified

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

wamr an adaptive wavelet method for the simulation of compressible reacting flow part i accuracy and efficiency of algorithm abstract the wavelet adaptive multiresolution representation wamr method provides a robust method for controlling spatial grid adaptation fine grid spacing in regions where a solution varies greatly i e near steep gradients or near singularities and a much coarser grid where the solution varies slowly subsequently a wide range of spatial scales often demanded in challenging continuum physics problems can be efficiently captured furthermore the wavelet transform provides a direct measure of local error at each collocation point effectively producing automatically verified solutions the method is applied to the solution of unsteady compressible reactive flow equations and includes detailed diffusive transport and chemical kinetics models accuracy and performance of the method are examined on several test problems the sparse grids produced by the wamr method exhibit an impressive compression of the solution reducing the number of collocation points used by factors of many orders of magnitude when compared to uniform grids of equivalent resolution

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

stable hp mixed finite elements based on the hellinger reissner principle in the hellinger reissner formulation for linear elasticity both the displacement u and the stress are taken as unknowns giving rise to a saddle point problem we present new pairings of quadrilateral trunk finite element spaces for this method and prove stability and optimality in terms of both h and p the effect of mesh shape regularity on the stability constant is explicitly tracked our results provide a theoretical basis for recent numerical experiments in the context of a mixed p formulation for viscoelasticity that showed these spaces worked well computationally

wavelet galerkin solutions for one dimensional partial differential equations in this paper we describe how wavelets may be used to solve partial differential equations these problems are currently solved by techniques such as finite differences finite elements and multi grid the wavelet method however offers several advantages over traditional methods wavelets have the ability to represent functions at different levels of resolution thereby providing a logical means of developing a hierarchy of solutions furthermore compactly supported wavelets such as those due to daubechies1 are localized in space which means that the solution can be refined in regions of high gradient e g stress concentrations without having to regenerate the mesh for the entire problem in order to demonstrate the wavelet technique we consider the one dimensional counterpart of helmholtz s equation by comparison with a simple finite difference solution to this problem with periodic boundary conditions we show how a wavelet technique may be efficiently developed dirichlet boundary conditions are then imposed using the capacitance matrix method described by proskurowski and widlund2 and others the convergence rates of the wavelet solutions are examined and they are found to compare extremely favourably to the finite difference solutions preliminary investigations also indicate that the wavelet technique is a strong contender to the finite element method at least for problems with simple geometries

toward a universal h p adaptive finite element strategy part 2 a posteriori error estimation abstract in this second paper of the series on h p adaptive finite element methods we present five different techniques for a posteriori error estimation of h p methods for linear elliptic boundary value problems the techniques are referred to as the residual estimation method the duality method the subdomain residual method a method based on interpolation theory and a post processing method the present study examines the theory and behavior of such techniques applied specifically to h p adaptive finite element methods several numerical examples illustrate the efficiency of the methods

use of empirical likelihood to calibrate auxiliary information in partly linear monotone regression models in statistical analysis a regression model is needed if one is interested in finding the relationship between a response variable and covariates when the response depends on the covariate then it may also depends on the function of this covariate if one has no knowledge of this functional form but expect for monotonic increasing or decreasing then the isotonic regression model is preferable estimation of parameters for isotonic regression models is based on the pool adjacent violators algorithm pava where the monotonicity constraints are built in with missing data people often employ the augmented estimating method to improve estimation efficiency by incorporating auxiliary information through a working regression model however under the framework of the isotonic regression model the pava does not work as the monotonicity constraints are violated in this paper we develop an empirical likelihood based method for isotonic regression model to incorporate the auxiliary information since the monotonicity constraints still hold the pava can be used for parameter estimation simulation studies demonstrate that the proposed method can yield more efficient estimates and in some situations the efficiency improvement is substantial we apply this method to a dementia study

a semiparametric method of multiple imputation in this paper we describe how to use multiple imputation semiparametrically to obtain estimates of parameters and their standard errors when some individuals have missing data the methods given require the investigator to know or be able to estimate the process generating the missing data but requires no full distributional form for the data the method is especially useful for non standard problems such as estimating the median when data are missing

a transformation approach in linear mixed effects models with informative missing responses we consider a linear mixed effects model in which the response panel vector has missing components and the missing data mechanism depends on observed data as well as missing responses through unobserved random effects using a transformation of the data that eliminates the random effects we derive asymptotically unbiased and normally distributed estimators of certain model parameters estimators of model parameters that cannot be estimated using the transformed data are also constructed and their asymptotic unbiasedness and normality are established simulation results are presented to examine the finite sample performance of the proposed estimators and a real data example is discussed

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

a fast adaptive wavelet collocation algorithm for multidimensional pdes a fast multilevel wavelet collocation method for the solution of partial differential equations in multiple dimensions is developed the computational cost of the algorithm is independent of the dimensionality of the problem and is o n where n is the total number of collocation points the method can handle general boundary conditions the multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution high resolution computations are performed only in regions where singularities or sharp transitions occur numerical results demonstrate the ability of the method to resolve localized structures such as shocks which change their location and steepness in space and time the present results indicate that the method has clear advantages in comparison with well established numerical algorithms

a hybrid wavelet based adaptive immersed boundary finite difference lattice boltzmann method for two dimensional fluid structure interaction abstract a second generation wavelet based adaptive finite difference lattice boltzmann method fd lbm is developed in this paper in this approach the adaptive wavelet collocation method awcm is firstly to the best of our knowledge incorporated into the fd lbm according to the grid refinement criterion based on the wavelet amplitudes of density distribution functions an adaptive sparse grid is generated by the omission and addition of collocation points on the sparse grid the finite differences are used to approximate the derivatives to eliminate the special treatments in using the fd based derivative approximation near boundaries the immersed boundary method ibm is also introduced into fd lbm by using the adaptive technique the adaptive code requires much less grid points as compared to the uniform mesh code as a consequence the computational efficiency can be improved to justify the proposed method a series of test cases including fixed boundary cases and moving boundary cases are invested a good agreement between the present results and the data in previous literatures is obtained which demonstrates the accuracy and effectiveness of the present awcm ib lbm

the g scheme a framework for multi scale adaptive model reduction the numerical solution of mathematical models for reaction systems in general and reacting flows in particular is a challenging task because of the simultaneous contribution of a wide range of time scales to the system dynamics however the dynamics can develop very slow and very fast time scales separated by a range of active time scales an opportunity to reduce the complexity of the problem arises when the fast active and slow active time scales gaps becomes large we propose a numerical technique consisting of an algorithmic framework named the g scheme to achieve multi scale adaptive model reduction along with the integration of the differential equations des the method is directly applicable to initial value odes and by using the method of lines pdes we assume that the dynamics is decomposed into active slow fast and when applicable invariant subspaces the g scheme introduces locally a curvilinear frame of reference defined by a set of orthonormal basis vectors with corresponding coordinates attached to this decomposition the evolution of the curvilinear coordinates associated with the active subspace is described by non stiff des whereas that associated with the slow and fast subspaces is accounted for by applying algebraic corrections derived from asymptotics of the original problem adjusting the active des dynamically during the time integration is the most significant feature of the g scheme since the numerical integration is accomplished by solving a number of des typically much smaller than the dimension of the original problem with corresponding saving in computational work to demonstrate the effectiveness of the g scheme we present results from illustrative as well as from relevant problems

an adaptive multilevel wavelet collocation method for elliptic problems an adaptive multilevel wavelet collocation method for solving multi dimensional elliptic problems with localized structures is described the method is based on multi dimensional second generation wavelets and is an extension of the dynamically adaptive second generation wavelet collocation method for evolution problems int j comp fluid dyn 17 2003 151 wavelet decomposition is used for grid adaptation and interpolation while a hierarchical finite difference scheme which takes advantage of wavelet multilevel decomposition is used for derivative calculations the multilevel structure of the wavelet approximation provides a natural way to obtain the solution on a near optimal grid in order to accelerate the convergence of the solver an iterative procedure analogous to the multigrid algorithm is developed the overall computational complexity of the solver is o n where n is the number of adapted grid points the accuracy and computational efficiency of the method are demonstrated for the solution of two and three dimensional elliptic test problems

a local anisotropic adaptive algorithm for the solution of low mach transient combustion problems a novel numerical algorithm for the simulation of transient combustion problems at low mach and moderately high reynolds numbers is presented these problems are often characterized by the existence of a large disparity of length and time scales resulting in the development of directional flow features such as slender jets boundary layers mixing layers or flame fronts this makes local anisotropic adaptive techniques quite advantageous computationally in this work we propose a local anisotropic refinement algorithm using for the spatial discretization unstructured triangular elements in a finite element framework for the time integration the problem is formulated in the context of semi lagrangian schemes introducing the semi lagrange galerkin slg technique as a better alternative to the classical semi lagrangian sl interpolation the good performance of the numerical algorithm is illustrated by solving a canonical laminar combustion problem the flame vortex interaction first a premixed methane air flame vortex interaction with simplified transport and chemistry description test i is considered results are found to be in excellent agreement with those in the literature proving the superior performance of the slg scheme when compared with the classical sl technique and the advantage of using anisotropic adaptation instead of uniform meshes or isotropic mesh refinement as a more realistic example we then conduct simulations of non premixed hydrogen air flame vortex interactions test ii using a more complex combustion model which involves state of the art transport and chemical kinetics in addition to the analysis of the numerical features this second example allows us to perform a satisfactory comparison with experimental visualizations taken from the literature

the h p and h p versions of the finite element method in 1 dimension this paper is the first one in the series of three which are addressing in detail the properties of the three basic versions of the finite element method in the one dimensional setting the main emphasis is placed on the analysis when the exact solution has singularity of x type the first part analyzes thep version the second theh version and generalh p version and the final third part addresses the problems of the adaptiveh p version

efficient and doubly robust imputation for covariate dependent missing responses in this article we study a well known response missing data problem missing data is an ubiquitous problem in medical and social science studies imputation is one of the most popular methods for dealing with missing data the most commonly used imputation that makes use of covariates is regression imputation in which the regression model can be parametric semiparametric or nonparametric parametric regression imputation is efficient but is not robust against misspecification of the regression model although nonparametric regression imputation such as nearest neighbor imputation and kernel regression imputation is model free it is not efficient especially if the dimension of covariate vector is high the well known problem of curse of dimensionality semiparametric regression imputation such as partially linear regression imputation can reduce the dimension of the covariate in nonparametric regression fitting but is not robust against misspecification of the linear component in the regression

the h p and h p versions of the finite element method in 1 dimension part ii the error analysis of the h and h p versions the paper is the second in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimensional setting the first part 1 analyzed thep version the present one concentrates on theh andh p versions

solving hyperbolic pdes using interpolating wavelets a method is presented for adaptively solving hyperbolic pdes the method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids the adaptability is performed automatically by thresholding the wavelet coefficients operations such as differentiation and multiplication are fast and simple due to the one to one correspondence between point values and wavelet coefficients in the interpolating basis treatment of boundary conditions is simplified in this sparse point representation spr numerical examples are presented for one and two dimensional problems it is found that the proposed method outperforms a finite difference method on a uniform grid for certain problems in terms of flops

an adaptive wavelet collocation method for fluid structure interaction at high reynolds numbers two mathematical approaches are combined to calculate high rey nolds number incompressible fluid structure interaction a wavelet method to dynamically adapt the computational grid to flow intermittency and obstacle motion and brinkman penalization to enforce solid boundaries of arbitrary complexity we also implement a wavelet based multilevel solver for the poisson problem for the pressure at each time step the method is applied to two dimensional flow around fixed and moving cylinders for reynolds numbers in the range 3 times 10 1 le re le 10 5 the compression ratios of up to 1000 are achieved for the first time it is demonstrated in actual dynamic simulations that the compression scales like re 1 2 over five orders of magnitude while computational complexity scales like re this represents a significant improvement over the classical complexity estimate of re 9 4 for two dimensional turbulence

estimation with survey data under nonignorable nonresponse or informative sampling nonresponse is a very common phenomenon in survey sampling nonignorable nonresponse that is a response mechanism that depends on the values of the variable having nonresponse is the most difficult type of nonresponse to handle this article studies a likelihood based estimation method for data with nonignorable nonresponse the likelihood is semiparametric in the sense that it consists of a parametric component for the response mechanism such as a logistic model and a nonparametric component for the distribution of the variable of interest and the covariates we show how auxiliary information can be augmented to improve the efficiency of estimators asymptotic distributions for the resulting parameter estimates are derived a simulation study shows that the proposed method gives promising results the method can also be applied to problems with two phase sampling in which the second phase sampling is informative

a pseudo empirical likelihood approach for stratified samples with nonresponse nonresponse is common in surveys when the response probability of a survey variable y depends on y through an observed auxiliary categorical variable z i e the response probability of y is conditionally independent of y given z a simple method often used in practice is to use z categories as imputation cells and construct estimators by imputing nonrespondents or reweighting respondents within each imputation cell this simple method however is inefficient when some z categories have small sizes and ad hoc methods are often applied to collapse small imputation cells assuming a parametric model on the conditional probability of z given y and a nonparametric model on the distribution of y we develop a pseudo empirical likelihood method to provide more efficient survey estimators our method avoids any ad hoc collapsing small z categories since reweighting or imputation is done across z categories asymptotic distributions for estimators of population means based on the pseudo empirical likelihood method are derived for variance estimation we consider a bootstrap procedure and its consistency is established some simulation results are provided to assess the finite sample performance of the proposed estimators

semiparametric bayesian estimation for marginal parametric potential outcome modeling application to causal inference we propose a new semiparametric bayesian model for causal inference in which assignment to treatment depends on potential outcomes the model uses the probit stick breaking process mixture proposed by chung and dunson 2009 a variant of the dirichlet process mixture modeling in contrast to previous bayesian models the proposed model directly estimates the parameters of the marginal parametric model of potential outcomes while it relaxes the strong ignorability assumption and requires no parametric model assumption for the assignment model and conditional distribution of the covariate vector the proposed estimation method is more robust than maximum likelihood estimation in that it does not require knowledge of the full joint distribution of potential outcomes covariates and assignments in addition the method is more efficient than fully nonparametric bayes methods we apply this model to infer the differential effects of cognitive and noncognitive skills on the wages of production and nonprodu

interpolation through an iterative scheme abstract a new method of interpolation is generated through an iterative scheme on dyadic rationals the process is linear local and produces almost twice differentiable functions a fundamental interpolating function is analyzed error formulas are derived the method is applied for curve fitting

galerkin wavelet methods for two point boundary value problems anti derivatives of wavelets are used for the numerical solution of differential equations optimal error estimates are obtained in the applications to two point boundary value problems of second order the orthogonal property of the wavelets is used to construct efficient iterative methods for the solution of the resultant linear algebraic systems numerical examples are given