local linear regression smoothers and their minimax efficiencies in this paper we introduce a smooth version of local linear regression estimators and address their advantages the mse and mise of the estimators are computed explicitly it turns out that the local linear regression smoothers have nice sampling properties and high minimax efficiency they are not only efficient in rates but also nearly efficient in constant factors in the nonparametric regression context the asymptotic minimax lower bound is developed via the heuristic of the hardest onedimensional subproblem of donoho and liu connections of the minimax risk with the modulus of continuity are made the lower bound is also applicable for estimating conditional mean regression and conditional quantiles for both fixed and random design regression problems

hybrid boundary element analysis for surface cracks at first a hybrid boundary element method used for linear elastic fracture analysis of surface crack is established by introducing the relative displacement fundamental function into the first and the second kind of boundary integral equations then the numerical approaches including the classification of the boundaries the division of the elements the computation of the hyper singular integral etc are presented in detail finally numerical examples for axial semi elliptical surface crack and circumferential quasi semi elliptical surface crack in a cylinder are demonstrated to check the proposed method the numerical results show that the proposed method has a high accuracy for analysis of the stress intensity factor of surface crack

covariate adjusted regression mue11er wa1d ucdavis edu summary we introduce covariate adjusted regression for situations where both predictors and response in a regression model are not directly observable but are contaminated with a multiplicative factor that is determined by the value of an unknown function of an observable covariate we demonstrate how the regression coefficients can be estimated by establishing a connection to varying coefficient regression the proposed covariate adjustment method is illustrated with an analysis of the regression of plasma fibrinogen concentration as response on serum transferrin level as predictor for 69 haemodialysis patients in this example both response and predictor are thought to be influenced in a multiplicative fashion by body mass index a bootstrap hypothesis test enables us to test the significance of the regression parameters we establish consistency and convergence rates of the parameter estimators for this new covariate adjusted regression model simulation studies demonstrate the efficacy of the proposed method

clt for linear spectral statistics of large dimensional sample covariance matrices let bn 1 n t1 2nxnx nt1 2n where xn xij is n n with i i d complex standardized entries having finite fourth moment and t1 2n is a hermitian square root of the nonnegative definite hermitian matrix tn the limiting behavior as n with n n approaching a positive constant of functionals of the eigenvalues of bn where each is given equal weight is studied due to the limiting behavior of the empirical spectral distribution of bn it is known that these linear spectral statistics converges a s to a nonrandom quantity this paper shows their rate of convergence to be 1 n by proving after proper scaling that they form a tight sequence moreover if exppx211 0 and expp x11 4 2 or if x11 and tn are real and exppx411 3 they are shown to have gaussian limits

analysis of repeated measurements using nonparametric smoothers and randomization tests the mixed model analysis of variance anova which is commonly applied to repeated measurements taken over time depends on specialized assumptions about the error distribution and fails to exploit information contained in the ordering of the data points over time this paper describes a procedure that overcomes these disadvantages while preserving familiar features of the mixed model anova group profiles are estimated by nonparametric smoothing of observed mean profiles group and time main effects and the group by time interaction effect are tested using randomization tests results of zerbe 1979 journal of the american statistical association 74 215 221 are used to construct f test approximations for the randomization tests of the group and group by time effects a new approximate f test for time effect is proposed a simulation study demonstrates that the approximations perform well and that smoothing increases the power of the tests for time main effect and group by time interaction the procedure is applied to data on hormone levels in cows

algorithms for strong coupling procedures abstract this paper considers algorithms for computing the response of a coupled problem with a partitioned approach one important example treated here is fluid structure interaction fsi often procedures or even software exists to solve each sub problem separately and one wants to couple both this setting seems to allow only the so called weak coupling which is not sufficient for some problems the so called strong coupling is often a totally implicit formulation where the system components are evaluated at the same time level this usually requires an iterative procedure the fsi problem is cast as an abstract differential algebraic equation dae for which the coupling procedures are developed with the partitioned approach one simple and frequently used computational procedure is similar to a block gauss seidel iteration it is shown why this approach may experience difficulties and how they may be circumvented with newton like methods still staying in the partitioned framework the functional and software engineering requirements for the simulation interface are described and analysed some simple coupled example problems demonstrate how the proposed procedures work

efficient estimation and inferences for varying coefficient models abstract this article deals with statistical inferences based on the varying coefficient models proposed by hastie and tibshirani local polynomial regression techniques are used to estimate coefficient functions and the asymptotic normality of the resulting estimators is established the standard error formulas for estimated coefficients are derived and are empirically tested a goodness of fit test technique based on a nonparametric maximum likelihood ratio type of test is also proposed to detect whether certain coefficient functions in a varying coefficient model are constant or whether any covariates are statistically significant in the model the null distribution of the test is estimated by a conditional bootstrap method our estimation techniques involve solving hundreds of local likelihood equations to reduce the computational burden a one step newton raphson estimator is proposed and implemented the resulting one step procedure is shown to save computational cost on an order of tens with no

local polynomial regression analysis of clustered data this paper proposes a classical weighted least squares type of local polynomial smoothing for the analysis of clustered data with the key idea of using generalised inverses of correlation matrices the estimator has a simple closed form expression simplicity is achieved also for nonparametric generalised linear models with arbitrary link function via a transformation our approach can be characterised by local observations with local variances which yields intuitively correct results in the sense that correct incorrect specification of within cluster correlation has respective positive negative effects the approach is a natural extension of classical local polynomial smoothing consequently existing theory can be largely carried over and important issues such as bandwidth selection can be tackled in the classical fashion moreover the approach can handle various types of covariate such as cluster level subject level or partially cluster level numerical studies support the theoretical results the method is illustrated with a real example on luteinising hormone levels in cows

balanced model reduction via the proper orthogonal decomposition a new method for performing a balanced reduction of a high order linear system is presented the technique combines the proper orthogonal decomposition and concepts from balanced realization theory the method of snapshotsisused to obtainlow rank reduced rangeapproximationsto thesystemcontrollability and observability grammiansineitherthetimeorfrequencydomain theapproximationsarethenusedtoobtainabalancedreducedorder model the method is particularly effective when a small number of outputs is of interest it is demonstrated for a linearized high order system that models unsteady motion of a two dimensional airfoil computation of the exact grammians would be impractical for such a large system for this problem very accurate reducedorder models are obtained that capture the required dynamics with just three states the new models exhibit far superiorperformancethanthosederived using a conventionalproperorthogonal decomposition although further development is necessary the concept also extends to nonlinear systems

the complex wishart distribution and the symmetric group let v be the space of r r hermitian matrices and let omega be the cone of the positive definite ones we say that the random variable s taking its values in overline omega has the complex wishart distribution gamma p sigma if mathbb e exp tr theta s det i r sigma theta p where sigma and sigma 1 theta are in omega and where p 1 2 r 1 or p r 1 in this paper we compute all moments of s and s 1 the techniques involve in particular the use of the irreducible characters of the symmetric group

local polynomial kernel regression for generalized linear models and quasi likelihood functions abstract we investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to generalized linear models and quasi likelihood contexts in the ordinary regression case local polynomial fitting has been seen to have several appealing features in terms of intuitive and mathematical simplicity one noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators these properties are shown to carry over to generalized linear model and quasi likelihood settings we also derive the asymptotic distributions of the proposed class of estimators that allow for straightforward interpretation and extensions of state of the art bandwidth selection methods

nonparametric additive regression for repeatedly measured data summary we develop an easily computed smooth backfitting algorithm for additive model fitting in repeated measures problems our methodology easily copes with various settings such as when some covariates are the same over repeated response measurements we allow for a working covariance matrix for the regression errors showing that our method is most efficient when the correct covariance matrix is used the component functions achieve the known asymptotic variance lower bound for the scalar argument case smooth backfitting also leads directly to design independent biases in the local linear case simulations show our estimator has smaller variance than the usual kernel estimator this is also illustrated by an example from nutritional epidemiology

smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables longitudinal samples i e datasets with repeated measurements over time are common in biomedical and epidemiological studies such as clinical trials and cohort observational studies an exploratory tool for the analyses of such data is the varying coefficient model y t xt t t t where y t and x t x 0 t x k t t are the response and covariates at time t t 0 t k t t are smooth coefficient curves of t and t is a mean zero stochastic process a special case that is of particular interest in many situations is data with time dependent response and time independent covariates we propose in this article a componentwise smoothing spline method for estimating 0 t k t nonparametrically based on the previous varying coefficient model and a longitudinal sample of t y t x with time independent covariates x x 0 x k t from n independent subjects a leave one subject out cross validation is suggested to choose the smoothing parameters asymptotic properties of our

statistical eigen inference from large wishart matrices we consider settings where the observations are drawn from a zero mean multivariate real or complex normal distribution with the population covariance matrix having eigenvalues of arbitrary multiplicity we assume that the eigenvectors of the population covariance matrix are unknown and focus on inferential procedures that are based on the sample eigenvalues alone i e eigen inference results found in the literature establish the asymptotic normality of the fluctuation in the trace of powers of the sample covariance matrix we develop concrete algorithms for analytically computing the limiting quantities and the covariance of the fluctuations we exploit the asymptotic normality of the trace of powers of the sample covariance matrix to develop eigenvalue based procedures for testing and estimation specifically we formulate a simple test of hypotheses for the population eigenvalues and a technique for estimating the population eigenvalues in settings where the cumulative distribution function of the nonrandom population eigenvalues has a staircase structure monte carlo simulations are used to demonstrate the superiority of the proposed methodologies over classical techniques and the robustness of the proposed techniques in high dimensional relatively small sample size settings the improved performance results from the fact that the proposed inference procedures are global in a sense that we describe and exploit global information thereby overcoming the inherent biases that cripple classical inference procedures which are local and rely on local information

the enriched space time finite element method est for simultaneous solution of fluid structure interaction the paper introduces a weighted residual based approach for the numerical investigation of the interaction of fluid flow and thin flexible structures the presented method enables one to treat strongly coupled systems involving large structural motion and deformation of multiple flow immersed solid objects the fluid flow is described by the incompressible navier stokes equations the current configuration of the thin structure of linear elastic material with non linear kinematics is mapped to the flow using the zero iso contour of an updated level set function the formulation of fluid structure and coupling conditions uniformly uses velocities as unknowns the integration of the weak form is performed on a space time finite element discretization of the domain interfacial constraints of the multi field problem are ensured by distributed lagrange multipliers the proposed formulation and discretization techniques lead to a monolithic algebraic system well suited for strongly coupled fluid structure systems embedding a thin structure into a flow results in non smooth fields for the fluid based on the concept of the extended finite element method the space time approximations of fluid pressure and velocity are properly enriched to capture weakly and strongly discontinuous solutions this leads to the present enriched space time est method numerical examples of fluid structure interaction show the eligibility of the developed numerical approach in order to describe the behavior of such coupled systems the test cases demonstrate the application of the proposed technique to problems where mesh moving strategies often fail copyright 2007 john wiley sons ltd

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

asymptotic normality for traces of polynomials in independent complex wishart matrices we derive a non asymptotic expression for the moments of traces of monomials in several independent complex wishart matrices extending some explicit formulas available in the literature we then deduce the explicit expression for the cumulants from the latter we read out the multivariate normal approximation to the traces of finite families of polynomials in independent complex wishart matrices

dimensional model reduction in non linear finite element dynamics of solids and structures a general approach to the dimensional reduction of non linear finite element models of solid dynamics is presented for the newmark implicit time discretization the computationally most expensive phase is the repeated solution of the system of linear equations for displacement increments to deal with this it is shown how the problem can be formulated in an approximation ritz basis of much smaller dimension similarly the explicit newmark algorithm can be also written in a reduced dimension basis and the computation time savings in that case follow from an increase in the stable time step length in addition the empirical eigenvectors are proposed as the basis in which to expand the incremental problem this basis achieves approximation optimality by using computational data for the response of the full model in time to construct a reduced basis which reproduces the full system in a statistical sense because of this global time viewpoint the basis need not be updated as with reduced bases computed from a linearization of the full finite element model if the dynamics of a finite element model is expressed in terms of a small number of basis vectors the asymptotic cost of the solution with the reduced model is lowered and optimal scalability of the computational algorithm with the size of the model is achieved at the same time numerical experiments indicate that by using reduced models substantial savings can be achieved even in the pre asymptotic range furthermore the algorithm parallelizes very efficiently the method we present is expected to become a useful tool in applications requiring a large number of repeated non linear solid dynamics simulations such as convergence studies design optimization and design of controllers of mechanical systems

projection based reduction of fluid structure interaction systems using monolithic space time modes abstract the focus of this work is the development of reduced models for engineering applications in complex bidirectional fluid structure interaction in the simultaneous solution procedure velocity variables are used for both fluid and solid and the whole set of model equations is discretized by a stabilized time discontinuous space time finite element method flexible structures are modeled using a three dimensional continuum approach in a total lagrangian setting considering large displacements and rotations in the flow domain the incompressible navier stokes equations describe the newtonian fluid a continuous finite element mesh is applied to the entire spatial domain and the discretized model equations are assembled in a single set of algebraic equations considering the two field problem as a whole the continuous fluid structure mesh with identical orders of approximation for both solid and fluid in space and time automatically yields conservation of mass momentum and energy at the fluid structure interface a mesh moving scheme is used to adapt the nodal coordinates of the fluid space time finite element mesh to the structural deformation the computational approach for strongly coupled fluid structure interaction is used to create suitable reduced models of generic nonlinear problems reduction is performed with monolithic projection based space time modes ensuring strong coupling of fluid and structure in the reduced model the contribution discusses results using proper orthogonal decomposition pod for determination of monolithic space time modes in the reduction of fluid structure systems

reduction method for finite element nonlinear dynamic analysis of shells doi 10 2514 1 j051003theprojectionoftheequationsofmotiononasuitablemodalbasiscandrasticallyreducethenumberofdegreesoffreedom of a nonlinear dynamic nite element analysis a reduction method based on enriching a set of vibrationmodeswithsecond ordermodescalculatedviaaperturbationtechniqueispresented thesesecond ordermodesarereadily calculated via the solution of corresponding linear problems the results indicate that the second ordermodes are displacement elds that are essential for an appropriate representation of the nonlinear behavior of thestructure problems exhibiting strong geometrical nonlinearities under relatively high dynamic loads aresuccessfully handled by forming the reduction basis with vibration modes and their corresponding second ordermodes calculated at two different static equilibrium con gurations

fluid structure interaction with large structural displacements the calculation of viscous flows inside deformable structures faces major difficulties when enforcing the kinematic compatibility at the fluid structure interface and updating the geometry of the domain this paper proposes to overcome these problems by considering the fluid and the structure as a unique continuous medium to be studied in a fixed reference configuration the resulting problem is then split into a fluid and a structural part through an additive decomposition of the space of kinematically admissible test functions this approach treats the structure in a fully lagrangian way and uses an associated arbitrary lagrangian eulerian ale formulation for the fluid such a strategy has three advantages which are detailed in the present paper it can be discretised in time by implicit stable energy conserving time integration schemes and solved by simple iterative uncoupled algorithms the fluid and the structural problems can be approximated by independent finite element spaces the most recent geometrically exact nonlinear shell models can be used for the structures the full strategy has been implemented into an industrial cfd code results obtained in the simulation of industrial hydraulic shock absorbers are presented at the end of the paper

semiparametric models for longitudinal data with application to cd4 cell numbers in hiv seroconverters summary the paper describes a semiparametric model for longitudinal data which is illustrated by its application to data on the time evolution of cd4 cell numbers in hiv seroconverters the essential ingredients of the model are a parametric linear model for covariate adjustment a nonparametric estimation of a smooth time trend serial correlation between measurements on an individual subject and random measurement error a back fitting algorithm is used in conjunction with a cross validation prescription to fit the model a notable feature in the application is that the onset of hiv infection is associated with a sudden drop in cd4 cells followed by a longer term slower decay the model is also used to estimate an individual s curve by combining his data with the population curve shrinkage toward the population mean trajectory is controlled in a natural way by the estimated covariance structure of the data

new local estimation procedure for a non parametric regression function for longitudinal data this paper develops a new estimation of nonparametric regression functions for clustered or longitudinal data we propose to use cholesky decomposition and profile least squares techniques to estimate the correlation structure and regression function simultaneously we further prove that the proposed estimator is as asymptotically efficient as if the covariance matrix were known a monte carlo simulation study is conducted to examine the finite sample performance of the proposed procedure and to compare the proposed procedure with the existing ones based on our empirical studies the newly proposed procedure works better than the naive local linear regression with working independence error structure and the efficiency gain can be achieved in moderate sized samples our numerical comparison also shows that the newly proposed procedure outperforms some existing ones a real data set application is also provided to illustrate the proposed estimation procedure

marginal nonparametric kernel regression accounting for within subject correlation there has been substantial recent interest in non and semiparametric methods for longitudinal or clustered data with dependence within clusters it has been shown rather inexplicably that when standard kernel smoothing methods are used in a natural way higher efficiency is obtained by assuming independence than by using the true correlation structure it is shown here that this result is a natural consequence of how standard kernel methods incorporate the within subject correlation in the asymptotic setting considered where the cluster sizes are fixed and the cluster number increases in this paper an alternative kernel smoothing method is proposed unlike the standard methods the smallest variance of the new estimator is achieved when the true correlation is assumed asymptotically the variance of the proposed method is uniformly smaller than that of the most efficient working independence approach a small simulation study shows that significant improvement is obtained for finite samples

partial linear regression models for clustered data this article considers the analysis of clustered data via partial linear regression models adopting the idea of modeling the within cluster correlation from the method of generalized estimating equations a least squares type estimate of the slope parameter is obtained through piecewise local polynomial approximation of the nonparametric component this slope estimate has several advantages a it attains n1 2 consistency without undersmoothing b it is efficient when correct within cluster correlation is used assuming multivariate normality of the error c the preceding properties hold regardless of whether or not the nonparametric component is of cluster level and d this estimation method naturally extends to deal with generalized partial linear models simulation studies and a real example are presented in support of the theory

data driven bandwidth selection in local polynomial fitting variable bandwidth and spatial adaptation when estimating a mean regression function and its derivatives locally weighted least squares regression has proven to be a very attractive technique the present paper focuses on the important issue of how to select the smoothing parameter or bandwidth in the case of estimating curves with a complicated structure a variable bandwidth is desirable furthermore the bandwidth should be indicated by the data themselves recent developments in nonparametric smoothing techniques inspired us to propose such a data driven bandwidth selection procedure which can be used to select both constant and variable bandwidths the idea is based on a residual squares criterion along with a good approximation of the bias and variance of the estimator the procedure can be applied to select bandwidths not only for estimating the regression curve but also for estimating its derivatives the resulting estimation procedure has the necessary flexibility for capturing complicated shapes of curves this is illustrated via a large variety of testing examples including examples with a large spatial variability the results are also compared with wavelet thresholding techniques and it seems that our results are at least comparable i e local polynomial regression using our data driven variable bandwidth has spatial adaptation properties that are similar to wavelets

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

a method for interpolating on manifolds structural dynamics reduced order models a rigorous method for interpolating a set of parameterized linear structural dynamics reduced order models roms is presented by design this method does not operate on the underlying set of parameterized full order models hence it is amenable to an online real time implementation it is based on mapping appropriately the rom data onto a tangent space to the manifold of symmetric positive definite matrices interpolating the mapped data in this space and mapping back the result to the aforementioned manifold algorithms for computing the forward and backward mappings are offered for the case where the roms are derived from a general galerkin projection method and the case where they are constructed from modal reduction the proposed interpolation method is illustrated with applications ranging from the fast dynamic characterization of a parameterized structural model to the fast evaluation of its response to a given input in all cases good accuracy is demonstrated at real time processing speeds copyright 2009 john wiley sons ltd

on the asymptotics of marginal regression splines with longitudinal data summary there have been studies on how the asymptotic efficiency of a nonparametric function estimator depends on the handling of the within cluster correlation when nonparametric regression models are used on longitudinal or cluster data in particular methods based on smoothing splines and local polynomial kernels exhibit different behaviour we show that the generalized estimation equations based on weighted least squares regression splines for the nonparametric function have an interesting property the asymptotic bias of the estimator does not depend on the working correlation matrix but the asymptotic variance and therefore the mean squared error is minimized when the true correlation structure is specified this property of the asymptotic bias distinguishes regression splines from smoothing splines

spline smoothing in a partly linear model on donne des estimations qui minimisent la somme des sommes residuelles des carres et une penalite de difficulte

bandwidth choice for nonparametric regression this paper is concerned with the problem of choosing a bandwidth parameter for nonparametric regression we analyze a tapered fourier series estimate and discuss the relationship of this estimate to a kernel estimate we first consider a method based on an unbiased estimate of mean square error and show that the bandwidth thus chosen is asymptotically optimal other methods are examined as well and are shown to be asymptotically equivalent a small simulation shows however that for small or moderate sample size the methods perform quite differently

empirical bias bandwidths for local polynomial nonparametric regression and density estimation abstract a data based local bandwidth selector is proposed for nonparametric regression by local fitting of polynomials the estimator called the empirical bias bandwidth selector ebbs is rather simple and easily allows multivariate predictor variables and estimation of any order derivative of the regression function ebbs minimizes an estimate of mean squared error consisting of a squared bias term plus a variance term the variance term used is exact not asymptotic though it involves the conditional variance of the response given the predictors that must be estimated the bias term is estimated empirically not from an asymptotic expression thus ebbs is similar to the double smoothing approach of hardle hall and marron and a local bandwidth selector of schucany but is developed here for a far wider class of estimation problems than what those authors considered ebbs is tested on simulated data and its performance seems quite satisfactory local polynomial smoothing of a histogram is a high

modeling liquid association in 2002 ker chau li introduced the liquid association measure to characterize three way interactions between genes and developed a computationally efficient estimator that can be used to screen gene expression microarray data for such interactions that study and others published since then have established the biological validity of the method and clearly demonstrated it to be a useful tool for the analysis of genomic data sets to build on this work we have sought a parametric family of multivariate distributions with the flexibility to model the full range of trivariate dependencies encompassed by liquid association such a model could situate liquid association within a formal inferential theory in this article we describe such a family of distributions a trivariate conditional normal model having gaussian univariate marginal distributions and in fact including the trivariate gaussian family as a special case perhaps the most interesting feature of the distribution is that the parameterization naturally parses the three way dependence structure into a number of distinct interpretable components one of these components is very closely aligned to liquid association and is developed as a measure we call modified liquid association we develop two methods for estimating this quantity and propose statistical tests for the existence of this type of dependence we evaluate these inferential methods in a set of simulations and illustrate their use in the analysis of publicly available experimental data

solution techniques for the fully discretized equations in computation of fluid structure interactions with the space time formulations we provide an overview of the solution techniques we have developed for the fully discretized equations encountered at every time step in computation of fluid structure interactions with the space time techniques these coupled nonlinear equations are generated from the finite element discretization of the governing equations for the fluid mechanics structural mechanics and the motion of the fluid mechanics mesh the fluid mechanics equations are discretized with the deforming spatial domain stabilized space time formulation the mesh motion is governed by the equations of elasticity with the smaller elements stiffened in the finite element formulation the coupled fully discretized equations are solved with the block iterative quasi direct and direct coupling methods we present numerical examples with incompressible flows and membrane and cable structures 2005 elsevier b v all rights reserved

variable bandwidth and local linear regression smoothers in this paper we introduce an appealing nonparametric method for estimating the mean regression function the proposed method combines the ideas of local linear smoothers and variable bandwidth hence it also inherits the advantages of both approaches we give expressions for the conditional mse and mise of the estimator minimization of the mise leads to an explicit formula for an optimal choice of the variable bandwidth moreover the merits of considering a variable bandwidth are discussed in addition we show that the estimator does not have boundary effects and hence does not require modifications at the boundary the performance of a corresponding plug in estimator is investigated simulations illustrate the proposed estimation method

reduced models for fluid structure interaction problems several so called reduced order formulations are reviewed for linear vibration analysis of bounded fluid structure systems for low modal density situations compressibility effects in the fluid for interior structural acoustic problems and free surface gravity effects for hydroelastic sloshing interaction problems in the case of incompressible liquids are examined reduced order models leading to symmetric matrix systems are then described using the static well posed behaviour of the irrotational fluid in this respect the fluid structure boundary value local equations expressed in terms of fluid scalar field variables for the fluid and displacement variables for the structure are regularized for zero frequency limit copyright 2004 john wiley sons ltd

second order freeness and fluctuations of random matrices ii unitary random matrices abstract we extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations we show how the concept of second order freeness which was introduced in part i allows one to understand global fluctuations of haar distributed unitary random matrices in particular independence between the unitary ensemble and another ensemble goes in the large n limit over into asymptotic second order freeness two important consequences of our general theory are i we obtain a natural generalization of a theorem of diaconis and shahshahani to the case of several independent unitary matrices ii we can show that global fluctuations in unitarily invariant multi matrix models are not universal

semiparametric estimation in general repeated measures problems summary the paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function special cases in our approach include marginal models for longitudinal or clustered data conditional logistic regression for matched case control studies multivariate measurement error models generalized linear mixed models with a semiparametric component and many others we propose profile kernel and backfitting estimation methods for these problems derive their asymptotic distributions and show that in likelihood problems the methods are semiparametric efficient although generally not true it transpires that with our methods profiling and backfitting are asymptotically equivalent we also consider pseudolikelihood methods where some nuisance parameters are estimated from a different algorithm the methods proposed are evaluated by using simulation studies and applied to the kenya haemoglobin data

space time proper generalized decompositions for the resolution of transient elastodynamic models in this paper we investigate ability of proper generalized decomposition pgd to solve transient elastodynamic models in space time domain classical methods use time integration schemes and an incremental resolution process we propose here to use standard time integration methods in a non incremental strategy as a result pgd gives a separated representation of the space time solution as a sum of tensorial products of space and time vectors that we interpret as space time modes recent time integration schemes are based on multi field formulations in this case separated representation can be constructed using state vectors in space and same vectors in time however we have experienced bad convergence order using this decomposition furthermore temporal approximation must be the same for all fields thus we propose an extension of classical separated representation for multi field problems this multi field pgd mf pgd uses space and time vectors that are different for each field calculation of decomposition is done using a monolithic approach in space and time potentially allowing the use of different approximations in space and time finally several simulations are performed with the transient elastodynamic problem with one dimension in space different approximations in time are investigated newmark scheme single field time discontinuous galerkin method and two fields time continuous and discontinuous galerkin methods

polynomial regression and estimating functions in the presence of multiplicative measurement error we consider the polynomial regression model in the presence of multiplicative measurement error in the predictor two general methods are considered with the methods differing in their assumptions about the distributions of the predictor and the measurement errors consistent parameter estimates and asymptotic standard errors are derived by using estimating equation theory diagnostics are presented for distinguishing additive and multiplicative measurement error data from a nutrition study are analysed by using the methods the results from a simulation study are presented and the performances of the methods are compared

multiplicative errors in variables models with applications to recent data released by the u s department of energy abstract in an errors in variables model the predicting variables are observed with errors traditionally the errors are assumed to be additive in this article i consider the case in which the error is multiplicative a situation that arises when analyzing some recent data released by the u s department of energy a consistent estimator is provided for regression coefficients by correcting the asymptotic bias of the least squares estimate it is shown that after being normalized by an estimate of its covariance is asymptotically normally distributed this can therefore be used to construct approximate tests and confidence sets for the results are essentially nonparametric

quasi likelihood estimation in semiparametric models abstract suppose the expected value of a response variable y may be written h x t where x and t are covariates each of which may be vector valued is an unknown parameter vector is an unknown smooth function and h is a known function in this article we outline a method for estimating the parameter of this type of semiparametric model using a quasi likelihood function algorithms for computing the estimates are given and the asymptotic distribution theory for the estimators is developed the generalization of this approach to the case in which y is a multivariate response is also considered the methodology is illustrated on two data sets and the results of a small monte carlo study are presented

covariate adjusted correlation analysis with application to fmr1 premutation female carrier data motivated by molecular data on female premutation carriers of the fragile x mental retardation 1 fmr1 gene we present a new method of covariate adjusted correlation analysis to examine the association of messenger rna mrna and number of cgg repeat expansion in the fmr1 gene the association between the molecular variables in female carriers needs to adjust for activation ratio actratio a measure which accounts for the protective effects of one normal x chromosome in females carriers however there are inherent uncertainties in the exact effects of actratio on the molecular measures of interest to account for these uncertainties we develop a flexible adjustment that accommodates both additive and multiplicative effects of actratio nonparametrically the proposed adjusted correlation uses local conditional correlations which are local method of moments estimators to estimate the pearson correlation between two variables adjusted for a third observable covariate the local method of moments estimators are averaged to arrive at the final covariate adjusted correlation estimator which is shown to be consistent we also develop a test to check the nonparametric joint additive and multiplicative adjustment form simulation studies illustrate the efficacy of the proposed method application to fmr1 premutation data on 165 female carriers indicates that the association between mrna and cgg repeat after adjusting for actratio is stronger finally the results provide independent support for a specific jointly additive and multiplicative adjustment form for actratio previously proposed in the literature

a monolithic approach to fluid structure interaction using space time finite elements abstract the paper presents a simultaneous solution procedure for fluid structure interaction problems the structural motion is described by geometrically nonlinear elastodynamics the fluid is modeled by the incompressible navier stokes equations the space time finite element method is applied to both continua leading to an almost uniform discretization in which velocity variables are used for fluid and structure in order to enforce momentum conservation and geometric continuity at the interface a weighted residual formulation of coupling conditions is introduced the discretized model equations for fluid structure and coupling conditions are formulated in a single equation system the nonlinear system and the fluid mesh movement are solved in a single iteration loop two dimensional examples of membrane flutter and vortex excited plate vibrations demonstrate the efficiency of the methodology

a space time galerkin least squares finite element formulation of the navier stokes equations for moving domain problems a space time galerkin least squares finite element formulation of the navier stokes equations is presented for the analysis of free surface flows moving spatial configurations and deforming fluid structure interfaces the variational equation is based on the time discontinuous galerkin method employing the physical entropy variables the space time elements are oriented in time to accommodate the spatial deformations if the elements are oriented along the particle paths the formulation is lagrangian and if they are fixed in time it is eulerian consequently this formulation is analogous to the arbitrary lagrangian eulerian ale technique a novel mesh rezoning strategy is presented to orient the elements in time and adapt the fluid mesh to the changing spatial configuration numerical results are presented to show the performance of the method

a computational framework for fluid structure interaction finite element formulation and applications abstract this work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies the fluid flow considered is governed by the incompressible navier stokes equations and modelled by employing stabilised low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the rigid body motion excited by the fluid flow is restricted by the elastic and damping properties of the supports for the temporal discretisation the discrete implicit generalised method is employed the resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearisation of the overall incremental problem the strong coupling is resolved and optimal convergence of the residuals is achieved several numerical examples are presented to demonstrate the robustness and efficiency of the methodology the examples clearly capture the phenomena of vortex induced oscillations and galloping

nonparametric function estimation for clustered data when the predictor is measured without with error abstract we consider local polynomial kernel regression with a single covariate for clustered data using estimating equations we assume that at most m observations are available on each cluster in the case of random regressors with no measurement error in the predictor we show that it is generally the best strategy to ignore entirely the correlation structure within each cluster and instead pretend that all observations are independent in the further special case of longitudinal data on individuals with fixed common observation times we show that equivalent to the pooled data approach is the strategy of fitting separate nonparametric regressions at each observation time and constructing an optimal weighted average we also consider what happens when the predictor is measured with error using the simex approach to correct for measurement error we construct an asymptotic theory for both the pooled and the weighted average estimators surprisingly for the same amount of smoothing the weighted a

transformations for smooth regression models with multiplicative errors we consider whether one should transform to estimate nonparametrically a regression curve sampled from data with a constant coefficient of variation i e with multiplicative errors kernel based smoothing methods are used to provide curve estimates from the data both in the original units and after transformation comparisons are based on the mean squared error mse or mean integrated squared error mise calculated in the original units even when the data are generated by the simplest multiplicative error model the asymptotically optimal mse or mise is surprisingly not always obtained by smoothing transformed data but in many cases by directly smoothing the original data which method is optimal depends on both the regression curve and the distribution of the errors data based procedures which could be useful in choosing between transforming and not transforming a particular data set are discussed the results are illustrated on simulated and real data