fully exponential laplace approximations for the joint modelling of survival and longitudinal data a common objective in longitudinal studies is the joint modelling of a longitudinal response with a time to event outcome random effects are typically used in the joint modelling framework to explain the interrelationships between these two processes however estimation in the presence of random effects involves intractable integrals requiring numerical integration we propose a new computational approach for fitting such models that is based on the laplace method for integrals that makes the consideration of high dimensional random effects structures feasible contrary to the standard laplace approximation our method requires much fewer repeated measurements per individual to produce reliable results

robust data driven inference for density weighted average derivatives this paper presents a novel data driven bandwidth selector compatible with the small bandwidth asymptotics developed in cattaneo crump and jansson 2009 for density weighted average derivatives the new bandwidth selector is of the plug in variety and is obtained based on a mean squared error expansion of the estimator of interest an extensive monte carlo experiment shows a remarkable improvement in performance when the bandwidth dependent robust inference procedures proposed by cattaneo crump and jansson 2009 are coupled with this new data driven bandwidth selector the resulting robust data driven confidence intervals compare favorably to the alternative procedures available in the literature the online supplemental material to this paper contains further results from the simulation study

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

efficient estimation of population level summaries in general semiparametric regression models this article considers a wide class of semiparametric regression models in which interest focuses on population level quantities that combine both the parametric and the nonparametric parts of the model special cases in this approach include generalized partially linear models generalized partially linear single index models structural measurement error models and many others for estimating the parametric part of the model efficiently profile likelihood kernel estimation methods are well established in the literature here our focus is on estimating general population level quantities that combine the parametric and nonparametric parts of the model e g population mean probabilities etc we place this problem in a general context provide a general kernel based methodology and derive the asymptotic distributions of estimates of these population level quantities showing that in many cases the estimates are semiparametric efficient for estimating the population mean with no missing data we s

regression analysis of interval censored survival data with covariates using log linear models we considered the regression analysis of the event time data with left right or interval censored observations we extended life table techniques for censored survival data using log linear models to incorporate interval censored failures the em algorithm was used to calculate maximum likelihood estimates for the parameters we assumed that the hazard function was a stepwise function over disjoint intervals of time thus the nonparametric model the parametric exponential model and the semiparametric cox proportional hazard model were easily implemented as special cases we adapted the restricted em algorithm to test hypotheses and to construct confidence intervals for the parameters these methods were applied in an analysis of the recurrence time for treated melanoma patients

donsker type theorems for nonparametric maximum likelihood estimators let mathcal p be a nonparametric probability model consisting of smooth probability densities and let hat p n be the corresponding maximum likelihood estimator based on n independent observations each distributed according to the law mathbb p with hat mathbb p n denoting the measure induced by the density hat p n define the stochastic process hat nu n f longmapsto sqrt n int fd hat mathbb p n mathbb p where f ranges over some function class mathcal f we give a general condition for donsker classes mathcal f implying that the stochastic process hat nu n is asymptotically equivalent to the empirical process in the space ell infty mathcal f of bounded functions on mathcal f this implies in particular that hat nu n converges in law in ell infty mathcal f to a mean zero gaussian process we verify the general condition for a large family of donsker classes mathcal f we give a number of applications convergence of the probability measure hat mathbb p n to mathbb p at rate sqrt n in certain metrics metrizing the topology of weak star convergence a unified treatment of convergence rates of the mle in a continuous scale of sobolev norms sqrt n efficient estimation of nonlinear functionals defined on mathcal p limit theorems at rate sqrt n for the maximum likelihood estimator of the convolution product mathbb p ast p

empirical evidence on the law of demand a sufficient condition for market demand to satisfy the law of demand is that the mean of all households income effect matrices be positive definite we show how this mean income effect matrix can be estimated from cross section data under metonymy an assumption about the distribution of households characteristics the estimation procedure uses the nonparametric method of average derivatives income effect matrices estimated this way from u k family expenditure data are in fact positive definite this result can be explained by a special form of heteroskedasticity in the data households demands are more dispersed at higher income levels

a semiparametric single index model with heterogeneous impacts on an unobserved variable this paper proposes a single index semiparametric model in which the unknown function has cross sectional unit specific weights the initial motivation comes from the search for a better measure of liquidity in stock trading which is captured by the unknown function here the model is estimated by semiparametric least squares developed by ichimura 1993 and ichimura and lee 1991 the proposed technique differs from theirs in at least two aspects first i show that the estimator has desirable asymptotic properties under less restrictive assumptions on data second the form of the unknown function is fixed however the coefficients are allowed to differ across the cross sectional units

a reduced constaint hp finite element method for shell problems we propose and analyze an hp finite element method for the nagdhi shell model based on rectangular elements we show that for the bending dominated case assuming sufficient smoothness on the solution the method is locking free in terms of both h and p as the thickness of the shell tends to zero our results are established under the assumption that the geometrical coefficients appearing in the model are piecewise polynomial functions

a locking free finite element method for naghdi shells abstract in this paper a locking free method using mixed finite elements is introduced to approximate the solution of naghdi shell problems with small parameter t the thickness of the shell the approach of arnold and brezzi 1997 is employed with some important changes instead of proving the discrete inf sup condition for arbitrary geometric coefficients which does not seem possible we prove a weaker stability condition for smooth enough geometrically dependent coefficients which is sufficient for deducing the optimal error estimate as long as h 2 t is uniformly bounded for extremely small t we can relax this condition either using a larger bubble space or stabilizing the problem by replacing t2 by t2 h4 in either case an optimal error estimate still holds

nonparametric benefit risk assessment using marker process in the presence of a terminal event abstractbenefit risk assessment is a crucial step in medical decision process in many biomedical studies both longitudinal marker measurements and time to a terminal event serve as important endpoints for benefit risk assessment the effect of an intervention or a treatment on the longitudinal marker process however can be in conflict with its effect on the time to the terminal event thus questions arise on how to evaluate treatment effects based on the two endpoints for the purpose of deciding on which treatment is most likely to benefit the patients in this article we present a unified framework for benefit risk assessment using the observed longitudinal markers and time to event data we propose a cumulative weighted marker process to synthesize information from the two endpoints and use its mean function at a prespecified time point as a benefit risk summary measure we consider nonparametric estimation of the summary measure under two scenarios i the longitudinal marker is measured inter

standard errors for em estimation log likelihood the well known sem algorithm uses the second approach we consider three additional algorithms one that uses the first approach and two that use the second we evaluate the complexity and precision of these three and the sem algorithm in seven examples the first is a single parameter example used to give insight the others are three examples in each of two areas of em application poisson mixture models and the estimation of covariance from incomplete data the examples show that there are algorithms that are much simpler and more accurate than the sem algorithm hopefully their simplicity will increase the availability of standard error estimates in em applications it is shown that as previously conjectured a symmetry diagnostic can accurately estimate errors arising from numerical differentiation some issues related to the speed of the em algorithm and algorithms that differentiate the em operator are identified

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

optimal bandwidth choice for density weighted averages abstract this paper characterizes the optimal bandwidth value for estimating density weighted averages statistics that arise in semiparametric estimation methods for index models and models of selected samples based on nonparametric kernel estimators the optimal bandwidth is derived by minimizing the leading terms of mean squared error of the density weighted average the optimal bandwidth formulation is developed by comparison to the optimal pointwise bandwidth of a naturally associated nonparametric estimation problem highlighting the role of sample size and the structure of nonparametric estimation bias the methods are illustrated by estimators of average density density weighted average derivatives and conditional covariances and bandwidth values are calculated for normal designs a simple plug in estimator for the optimal bandwidth is proposed finally the optimal bandwidth for estimating ratios of density weighted averages is derived showing that the earlier optimal formulae can be implemented directly using naturally defined residual values

quantile regression with censoring and endogeneity in this paper we develop a new censored quantile instrumental variable cqiv estimator and describe its properties and computation the cqiv estimator combines powell 1986 censored quantile regression cqr to deal with censoring with a control variable approach to incorporate endogenous regressors the cqiv estimator is obtained in two stages that are nonadditive in the unobservables the first stage estimates a nonadditive model with infinite dimensional parameters for the control variable such as a quantile or distribution regression model the second stage estimates a nonadditive censored quantile regression model for the response variable of interest including the estimated control variable to deal with endogeneity for computation we extend the algorithm for cqr developed by chernozhukov and hong 2002 to incorporate the estimation of the control variable we give generic regularity conditions for asymptotic normality of the cqiv estimator and for the validity of resampling methods to approximate its asymptotic distribution we verify these conditions for quantile and distribution regression estimation of the control variable our analysis covers two stage uncensored quantile regression with nonadditive first stage as an important special case we illustrate the computation and applicability of the cqiv estimator with a monte carlo numerical example and an empirical application on estimation of engel curves for alcohol

efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals this paper considers semiparametric efficient estimation ofconditional moment models with possibly nonsmooth residuals in unknown parametric components and unknown functions h of endogenous variables we show that 1 the penalized sieve minimum distance psmd estima tor can simultaneously achieve root n asymptotic normality ofand nonparametric optimal convergence rate of allowing for noncompact function parameter spaces 2 a simple weighted bootstrap procedure consistently estimates the limiting distribution of the psmd 3 the semi parametric efficiency bound formula of ai and chen 2003 remains valid for conditional models with nonsmooth residuals and the optimally weighted psmd estimator achieves the bound 4 the centered profiled optimally weighted psmd criterion is asymptotically chi square distributed we illustrate our theories using a partially linear quantile instrumental variables iv regression a monte carlo study and an empirical estimation of the shape invariant quantile iv engel curves

risk assessment for quantitative responses using a mixture model a problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment than others a mixture model has traditionally been proposed to describe the distribution of responses in treatment groups for such experiments using a mixture dose response model we derive an upper confidence limit on additional risk defined as the excess risk over the background risk due to an added dose our focus will be on experiments with continuous responses for which risk is the probability of an adverse effect defined as an event that is extremely rare in controls the asymptotic distribution of the likelihood ratio statistic is used to obtain the upper confidence limit on additional risk the method can also be used to derive a benchmark dose corresponding to a specified level of increased risk the em algorithm is utilized to find the maximum likelihood estimates of model parameters and an extension of the algorithm is proposed to derive the estimates when the model is subject to a specified level of added risk an example is used to demonstrate the results and it is shown that by using the mixture model a more accurate measure of added risk is obtained

antedependence models for nonstationary categorical longitudinal data with ignorable missingness likelihood based inference time index ordered random variables are said to be antedependent ad of order p1 p2 pn if the kth variable conditioned on the pk immediately preceding variables is independent of all further preceding variables inferential methods associated with ad models are well developed for continuous primarily normal longitudinal data but not for categorical longitudinal data in this article we develop likelihood based inferential procedures for unstructured ad models for categorical longitudinal data specifically we derive maximum likelihood estimators mles of model parameters penalized likelihood criteria and likelihood ratio tests for determining the order of antedependence and likelihood ratio tests for homogeneity across groups time invariance of transition probabilities and strict stationarity we give closed form expressions for mles and test statistics which allow for the possibility of empty cells and monotone missing data for all cases save strict stationarity for data with an arbitrary missingness pattern we derive an efficient restricted expectation maximization algorithm for obtaining mles we evaluate the performance of the tests by simulation we apply the methods to longitudinal studies of toenail infection severity measured on a binary scale and alzheimer s disease severity measured on an ordinal scale the analysis of the toenail infection severity data reveals interesting nonstationary behavior of the transition probabilities and indicates that an unstructured first order ad model is superior to stationary and other structured first order ad models that have previously been fit to these data the analysis of the alzheimer s severity data indicates that the antedependence is second order with time invariant transition probabilities suggesting the use of a second order autoregressive cumulative logit model

on use of the em algorithm for penalized likelihood estimation summary the em algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation this paper discusses properties of the em algorithm in such contexts concentrating on rates of conver gence and presents an alternative that is usually more practical and converges at least as quickly the em algorithm is a general approach to maximum likelihood estimation rather than a specific algorithm dempster et al 1977 discussed the method and derived basic properties demonstrating that a variety of procedures previously developed rather informally could be unified the common strand to problems where the approach is applicable is a notion of incomplete data this includes the conventional sense of missing data but is much broader than that the em algorithm demon strates its strength in situations where some hypothetical experiment yields data from which estimation is particularly convenient and economical the incomplete data actually at hand are regarded as observable functions of these complete data the resulting algorithms while usually slow to converge are often extremely simple and remain practical in large problems where no other approaches may be feasible dempster et al 1977 briefly refer to the use of the same approach to the problem of finding the posterior mode maximum a posteriori estimate in a bayesian estima

twicing kernels and a small bias property of semiparametric estimators the purpose of this note is to show how semiparametric estimators with a small bias property can be constructed the small bias property sbp of a semiparametric estimator is that its bias converges to zero faster than the pointwise and integrated bias of the nonparametric estimator on which it is based we show that semiparametric estimators based on twicing kernels have the sbp we also show that semiparametric estimators where nonparametric kernel estimation does not affect the asymptotic variance have the sbp in addition we discuss an interpretation of series and sieve estimators as idempotent transformations of the empirical distribution that helps explain the known result that they lead to the sbp in monte carlo experiments we find that estimators with the sbp have mean square error that is smaller and less sensitive to bandwidth than those that do not have the sbp

constrained maximum likelihood estimation of two level covariance structure model via em type algorithms in this paper the constrained maximum likelihood estimation of a two level covariance structure model with unbalanced designs is considered the two level model is reformulated as a single level model by treating the group level latent random vectors as hypothetical missing data then the popular em algorithm is extended to obtain the constrained maximum likelihood estimates for general nonlinear constraints the multiplier method is used at them step to find the constrained minimum of the conditional expectation an accelerated em gradient procedure is derived to handle linear constraints the empirical performance of the proposed em type algorithms is illustrated by some artifical and real examples

dual mixed p and hp finite elements for elastic membrane problems a complementary energy based dimensionally reduced plate model using a two field dual mixed variational principle of non symmetric stresses and rotations is derived both the membrane and bending equilibrium equations expressed in terms of non symmetric mid surface stress components are satisfied a priori introducing first order stress functions it is pointed out that i the membrane shear and bending energies of the plate written in terms of first order stress functions are decoupled ii although unmodified 3 d constitutive equations are applied the energy parts do not contain the 1 1 2 term for isotropic linearly elastic materials these facts mean that the finite element formulation based on the present plate model should be free from shear locking when the thickness tends to zero and free from incompressibility locking when the poisson ratio converges to 0 5 irrespective of low order h or higher order p elements are used curvilinear dual mixed hp finite elements with higher order stress approximation and continuous surface tractions are developed and presented for the membrane 2 d elasticity problem in this case the formulation requires the approximation of three independent variables two components of a first order stress function vector and a scalar rotation numerical performance of three quadrilateral dual mixed elements is presented and compared to displacement based hp finite elements when the poisson ratio converges to the incompressible limit of 0 5 the numerical results show that as expected the dual mixed elements developed in this paper are free from locking in the energy norm as well as in the stress computations for both h and p extensions copyright 2001 john wiley sons ltd

nonparametric estimators which can be plugged in we consider nonparametric estimation of an object such as a probability density or a regression function can such an estimator achieve the ratewise minimax rate of convergence on suitable function spaces while at the same time when plugged in estimate efficiently at a rate of n 1 2 with the best constant many functionals of the object for example can we have a density estimator whose definite integrals are efficient estimators of the cumulative distribution function we show that this is impossible for very large sets for example expectations of all functions bounded by m however we also show that it is possible for sets as large as indicators of all quadrants that is distribution functions we give appropriate constructions of such estimates

consistent estimation of limited dependent variable models despite misspecification of distribution abstract by exploiting conditions on the behavior of regressors estimators are developed which are consistent up to a factor of proportionality for the slope coefficients of the regression function of a imperfectly observed dependent variable limited dependent variables are a special case of interest the consistency is robust to misspecification of the distribution of the latent dependent variable the estimators are weighted pseudo maximum likelihood estimators which can be readily computed using popular methods and software

estimation of marginal effects in semiparametric selection models with binary outcomes this paper addresses the estimation of a semiparametric sample selection index model where both the selection rule and the outcome variable are binary since the marginal effects are often of primary interest and are difficult to recover in a semiparametric setting we focus on developing an estimator for the marginal effects this marginal effect estimator uses only observations where the selection probability is above a certain threshold a key innovation is that this high probability set is adaptive to the data we establish the large sample properties of the marginal effect estimator as well as those for an index estimator upon which it depends monte carlo studies show that these estimators perform well in finite samples

analytical and computational assessment of locking in the hp finite element method locking is the phenomenon by which the numerical approximation of parameter dependent problems deteriorates for values of the parameter close to a limiting value in this paper we give a definition of locking and develop precise computable and analytic ways to quantify it using the example of nearly incompressible elasticity we show by means of computational and theoretical results the difference between the h version and php version in combatting locking our results establish the superiority of high order elements both h p and hp when the standard variational form is used we also discuss other issues such as curved elements mixed methods and locking phenomena for problems over anisotropic materials and over thin domains

mixed spectral hp element formulation for nonlinear elasticity we present a mixed formulation for high order spectral hp element methods and investigate its stability in large strain analysis of nearly incompressible solids specifically we employ the displacement pressure formulation and use a pressure projection method along with general jacobi polynomial bases to derive the discrete equations we first study the convergence of the method for smooth and singular solutions of elastic and hyperelastic problems for various combinations of mixed elements subsequently we investigate numerically the validity of ellipticity and inf sup conditions for various test problems including cases with large deformation we find that the inf sup condition is satisfied even when the pressure interpolation order op is equal to the displacement order ou but to resolve the locking free behavior it is required that op ou 1 and this choice also gives the best convergence rate in large deformation analysis surprisingly the results are more stable for ou op ou k because the ellipticity in kernel is better satisfied with higher k as ou increases compared to the displacement only formulation the mixed formulation seems to have superior accuracy and it is overall more efficient especially for problems with high bulk modulus

hidden behavior prediction of complex systems under testing influence based on semiquantitative information and belief rule base compared with the observable behavior it is difficult to predict the hidden behavior of a complex system in the existing methods for predicting the hidden behavior a lot of testing data usually quantitative information are needed to be sampled however some complex engineering systems have the following characteristics 1 the systems cannot be tested periodically and the observable information is incomplete 2 the change process of hidden behavior may be affected by the test and 3 only part of quantitative information and qualitative knowledge i e semiquantitative information may be obtained these characteristics all related to the test are named as testing influence for simplicity although a model and a corresponding optimal algorithm for training the model parameters have been proposed to predict the hidden behavior on the basis of semiquantitative information and belief rule base brb the testing influence has not been considered in order to solve the above problems a new brb based model which can use the semiquantitative information is proposed under testing influence in this paper in the newly proposed forecasting model there are some parameters of which the initial values are usually assigned by experts and may not be accurate which can lead to the inaccurate prediction results as such an improved optimal algorithm for training the parameters of the forecasting model is further developed on the basis of the expectation maximization idea and the covariance matrix adaption evolution strategy cma es by using the semiquantitative information the proposed brb based model and the improved cma es algorithm can operate together in an integrated manner so as to improve the forecasting precision a case study is examined to demonstrate the ability and applicability of the newly proposed brb based forecasting model and the improved cma es algorithm

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

mixed hp finite element methods for problems in elasticity and stokes flow we consider the mixed formulation for the elasticity problem and the limiting stokes problem in bbb r d d 2 3 we derive a set of sufficient conditions under which families of mixed finite element spaces are simultaneously stable with respect to the mesh size h and subject to a maximum loss of o k frac d 1 2 with respect to the polynomial degree k we obtain asymptotic rates of convergence that are optimal up to o k epsilon in the displacement velocity and up to o k frac d 1 2 epsilon in the pressure with epsilon 0 arbitrary both rates being optimal with respect to h several choices of elements are discussed with reference to properties desirable in the context of the hp version

smoothing bias in density derivative estimation abstract this article discusses a generic feature of density estimation by local smoothing namely that estimated derivatives and location score vectors will display a systematic downward attenuation bias we study the behavior of kernel estimators indicating how the derivative bias arises and showing a simple result we then consider the estimation of score vectors negative log density derivatives which are motivated by the problem of estimating average derivatives and the adaptive estimation of regression models using fixed bandwidth limits we show how scores are proportionally downward biased for normal densities and argue from normal mixture densities that proportional bias can be a reasonable approximation we propose a simple diagnostic statistic for score bias

using em to obtain asymptotic variance covariance matrices the sem algorithm abstract the expectation maximization em algorithm is a popular and often remarkably simple method for maximum likelihood estimation in incomplete data problems one criticism of em in practice is that asymptotic variance covariance matrices for parameters e g standard errors are not automatic byproducts as they are when using some other methods such as newton raphson in this article we define and illustrate a procedure that obtains numerically stable asymptotic variance covariance matrices using only the code for computing the complete data variance covariance matrix the code for em itself and code for standard matrix operations the basic idea is to use the fact that the rate of convergence of em is governed by the fractions of missing information to find the increased variability due to missing information to add to the complete data variance covariance matrix we call this supplemented em algorithm the sem algorithm theory and particular examples reinforce the conclusion that the sem alg

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

the p and hp finite element method for problems on thin domains abstract the p and hp versions of the finite element method allow the user to change the polynomial degree to increase accuracy we survey these methods and show how this flexibility can be exploited to counter four difficulties that occur in the approximation of problems over thin domains such as plates beams and shells these difficulties are 1 control of modeling error 2 approximation of corner singularities 3 resolution of boundary layers and 4 control of locking our guidelines enable the efficient resolution of these difficulties when a p hp code is available

design principles and error analysis for reduced shear plate bending finite elements in this paper we consider the problem of designing plate bending elements which are free of shear locking this phenomenon is known to afflict several elements for the reissner mindlin plate model when the thickness d of the plate is small due to the inability of the approximating subspaces to satisfy the kirchhoff constraint to avoid locking a reduction operator is often applied to the stress to modify the variational formulation and reduce the effect of this constraint we investigate the conditions required on such reduction operators to ensure that the approximability and consistency errors are of the right order a set of sufficient conditions is presented under which optimal errors can be obtained these are derived directly without transforming the problem via a hemholtz decomposition or considering it as a mixed method our analysis explicitly takes into account boundary layers and their resolution and we prove via an asymptotic analysis that convergence of the finite element approximations will occur uniformly as d rightarrow 0 even on quasiuniform meshes the analysis is carried out in the case of a free boundary where the boundary layer is known to be strong we also propose and analyze a simple post processing scheme for the shear stress our general theory is used to analyze the well known mitc elements for the reissner mindlin plate as we show the theory makes it possible to analyze both straight and curved elements we also analyze some other elements

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

a gradient algorithm locally equivalent to the em algorithm in many problems of maximum likelihood estimation it is impossible to carry out either the e step or the m step of the em algorithm the present paper introduces a gradient algorithm that is closely related to the em algorithm this em gradient algorithm approximately solves the m step of the em algorithm by one iteration of newton s method since newton s method converges quickly the local properties of the em gradient algorithm are almost identical with those of the em algorithm any strict local maximum point of the observed likelihood locally attracts the em and em gradient algorithm at the same rate of convergence and near the maximum point the em gradient algorithm always produces an increase in the likelihood with proper modification the em gradient algorithm also exhibits global convergence properties that are similar to those of the em algorithm our proof of global convergence applies and improves existing theory for the em algorithm these theoretical points are reinforced by a discussion of three realistic examples illustrating how the em gradient algorithm can succeed where the em algorithm is intractable

kernel based semiparametric estimators small bandwidth asymptotics and bootstrap consistency this paper develops asymptotic approximations for kernel based semiparametric estimators under assumptions accommodating slower than usual rates of convergence of their nonparametric ingredients our first main result is a distributional approximation for semiparametric estimators that differs from existing approximations by accounting for a bias this bias is nonnegligible in general and therefore poses a challenge for inference our second main result shows that some but not all nonparametric bootstrap distributional approximations provide an automatic method of correcting for the bias our general theory is illustrated by means of examples and its main finite sample implications are corroborated in a simulation study

the problem of membrane locking in finite element analysis of cylindrical shells we analyse the problem of membrane locking in h p finite element models of a thin hemicylindrical shell roof loaded by a smoothly varying normal pressure distribution we show that in the standard finite element method locking occurs especially at low values ofp and when the finite element grid is not aligned with the axis of the cylinder a general strategy of avoiding locking by using modified bilinear forms is introduced and a special implementation of this strategy on aligned rectangular grids is considered

on methods of sieves and penalization we develop a general theory which provides a unified treatment for the asymptotic normality and efficiency of the maximum likelihood estimates mle s in parametric semiparametric and nonparametric models we find that the asymptotic behavior of substitution estimates for estimating smooth functionals are essentially governed by two indices the degree of smoothness of the functional and the local size of the underlying parameter space we show that when the local size of the parameter space is not very large the substitution standard nonsieve substitution sieve and substitution penalized mle s are asymptotically efficient in the fisher sense under certain stochastic equicontinuity conditions of the loglikelihood moreover when the convergence rate of the estimate is slow the degree of smoothness of the functional needs to compensate for the slowness of the rate in order to achieve efficiency when the size of the parameter space is very large the standard and penalized maximum likelihood procedures may be inefficient whereas the method of sieves may be able to overcome this difficulty this phenomenon is particularly manifested when the functional of interest is very smooth especially in the semiparametric case

the restricted em algorithm for maximum likelihood estimation under linear restrictions on the parameters abstract the em algorithm is one of the most powerful algorithms for obtaining maximum likelihood estimates for many incomplete data problems but when the parameters must satisfy a set of linear restrictions the em algorithm may be too complicated to apply directly in this article we propose maximum likelihood estimation procedures under a set of linear restrictions for situations in which the em algorithm could be used if there were no such restrictions on the parameters we develop a modification to the em algorithm which we call the restricted em algorithm incorporating the linear restrictions on the parameters this algorithm is easily updated by using the code for the complete data information matrix and the code for the usual em algorithm major applications of the restricted em algorithm are to construct likelihood ratio tests and profile likelihood confidence intervals we illustrate the procedure with two models a variance component model and a bivariate normal model

stabilized finite element formulations for shells in a bending dominated state we consider the design of finite element methods for the naghdi shell model in the case when the deformation is bending dominated two formulations based on stabilizing techniques are introduced and it is proved that they are stable hence free from locking the theoretical estimates are confirmed by numerical benchmark studies

estimating a class of triangular simultaneous equations models without exclusion restrictions this paper provides a control function estimator to adjust for endogeneity in the triangular simultaneous equations model where there are no available exclusion restrictions to generate suitable instruments our approach is to exploit the dependence of the errors on exogenous variables e g heteroscedasticity to adjust the conventional control function estimator the form of the error dependence on the exogenous variables is subject to restrictions but is not parametrically specified in addition to providing the estimator and deriving its large sample properties we present simulation evidence which indicates the estimator works well

analysis of a discontinuous galerkin method for the bending problem of koiter shell we present an analysis for a mixed finite element method for the bending problem of koiter shell we derive an error estimate showing that when the geometrical coefficients of the shell mid surface satisfy certain conditions the finite element method has the optimal order of accuracy which is uniform with respect to the shell thickness generally the error estimate shows how the accuracy is affected by the shell geometry and thickness it suggests that to achieve the optimal rate of convergence the triangulation should be properly refined in regions where the shell geometry changes dramatically the analysis is carried out for a balanced method in which the normal component of displacement is approximated by discontinuous piecewise cubic polynomials while the tangential components are approximated by discontinuous piecewise quadratic polynomials with some enrichments on elements affixed to the shell free boundary components of the membrane stress are approximated by continuous piecewise linear functions we also include a theory of balanced higher order elements and a theory of a simpler lower order method

on locking and robustness in the finite element method a numerical scheme for the approximation of a parameter dependent problem is said to exhibit locking if the accuracy of the approximations deteriorates as the parameter tends to a limiting value a robust numerical scheme for the problem is one that is essentially uniformly convergent for all values of the parameter precise mathematical definitions for these terms are developed their quantitative characterization is given and some general theorems involving locking and robustness are proven a model problem involving heat transfer is analyzed in detail using this mathematical framework and various related computational results are described applications to some different problems involving locking are presented

mixed hp fem on anisotropic meshes ii hanging nodes and tensor products of boundary layer meshes the divergence stability of mixed hp finite element methods for incompressible fluid flow is analyzed a discrete inf sup condition is proved for a general class of meshes the meshes may be refined anisotropically geometrically and may contain hanging nodes on geometric patches the inf sup constant is shown to be independent of the aspect ratio of the anisotropic elements and the dependence on the polynomial degree is analyzed numerical estimates of inf sup constants confirm the theoretical results

locking effects in the finite element approximation of plate models we analyze the robustness of various standard finite element schemes for a hierarchy of plate models and obtain asymptotic convergence estimates that are uniform in terms of the thickness d we identify h version schemes that show locking i e for which the asymptotic convergence rate deteriorates as d 0 and also show that the p version is free of locking in order to isolate locking erects from boundary layer erects which also arise as d 0 our analysis is carried out for the periodic case which is free of boundary layers we analyze in detail the lowest model of the hierarchy the well known reissner mindlin model and show that the locking and robustness of finite element schemes for higher models of the hierarchy are essentially identical to the riessner mindlin case