on hearing the shape of a general multi connected vibrating membrane in r2 with piecewise smooth positive functions in the robin boundary conditions the asymptotic expansion of the trace of the heat kernel q t email protected j 1 exp email protected j as t 0 has been derived for a variety of domains where l j are the eigenvalues of the negative laplace email protected email protected i 1 email protected email protected x i 2in the x 1 x 2 plane the dependence of q t on the connectivity of domains and the boundary conditions are analyzed particular attention is given for a general multiply connected bounded domain in r 2 together with a finite number of piecewise robin boundary conditions where the coefficients in the boundary conditions are piecewise smooth positive functions some applications of an ideal gas enclosed in the general multiply connected domain are given

new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis semiparametric regression models are very useful for longitudinal data analysis the complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis in this article two new approaches are proposed for estimating the regression coefficients in a semiparametric model the asymptotic normality of the resulting estimators is established an innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models the proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters rates of convergence of the resulting estimators are established with a proper choice of regularization parameters and penalty functions the proposed variable selection procedures are shown to perform as well as an oracle estimator a robust standard error formula is derived usi

two step estimation of functional linear models with applications to longitudinal data functional linear models are useful in longitudinal data analysis they include many classical and recently proposed statistical models for longitudinal data and other functional data recently smoothing spline and kernel methods have been proposed for estimating their coefficient functions nonparametrically but these methods are either intensive in computation or inefficient in performance to overcome these drawbacks in this paper a simple and powerful two step alternative is proposed in particular the implementation of the proposed approach via local polynomial smoothing is discussed methods for estimating standard deviations of estimated coefficient functions are also proposed some asymptotic results for the local polynomial estimators are established two longitudinal data sets one of which involves time dependent covariates are used to demonstrate the approach proposed simulation studies show that our two step approach improves the kernel method proposed by hoover and co workers in several aspects such as accuracy computational time and visual appeal of the estimators

asymptotic results for maximum likelihood estimators in joint analysis of repeated measurements and survival time maximum likelihood estimation has been extensively used in the joint analysis of repeated measurements and survival time however there is a lack of theoretical justification of the asymptotic properties for the maximum likelihood estimators this paper intends to fill this gap specifically we prove the consistency of the maximum likelihood estimators and derive their asymptotic distributions the maximum likelihood estimators are shown to be semiparametrically efficient

temporal process regression summary we consider regression for response and covariates which are temporal processes observed over intervals a functional generalised linear model is proposed which includes extensions of standard models in multi state survival analysis simple nonparametric esti mators of time indexed parameters are developed using working independence estimating equations and are shown to be uniformly consistent and to converge weakly to gaussian processes the procedure does not require smoothing or a markov assumption unlike approaches based on transition intensities the usual definition of optimal estimating equations for parametric models is then generalised to the functional model and the optimum is identified in a class of functional generalised estimating equations simulations demonstrate large efficiency gains relative to working independence at times where censoring is heavy the estimators are the basis for new tests of the covariate effects and for the estimation of models in which greater structure is imposed on the parameters providing novel goodness of fit tests the methodology s practical utility is illustrated in a data analysis

can one hear the shape of a drum revisited in a landmark paper mark kac in 1966 amer math monthly 73 pp 1 23 showed that geometric properties of regions in r 2 can be obtained by studying the asymptotic properties of the spectrum of the laplacian he also conjectured that the shape of a region might be completely determined by the spectrum we describe recent developments in this field and discuss the status of the kac conjecture as well as similar conjectures for operators other than the laplacian

the wave equation approach for solving inverse eigenvalue problems of a multi connected region in r3 with robin conditions the asymptotic expansion for t of the trace of the wave kernel email protected t email protected u 1exp email protected 1 2 u where m u u 1 are the eigenvalues of the negative laplacian email protected email protected 3 b 1 x b 2 in the x 1 x 2 x 3 space where i 1 and

semiparametric modeling of repeated measurements under outcome dependent follow up in regression analysis of repeated measurements that are taken at subject specific times the availability of the outcome data may be related to the past outcome and to other measured variables that are not in the intended regression model in this paper we propose a natural extension of the semiparametric regression procedure of lin and ying j am stat assoc 2001 96 103 126 by building a class of inverse intensity rate ratio weighted estimators that accommodate such outcome dependent follow up the estimators have a closed form are radicaln consistent asymptotically normal and do not require estimation of any infinite dimensional parameters we give several simulations to demonstrate the estimator s performance and show a sensitivity study under follow up with various degrees of dependence on outcome related variables we illustrate our approach using data from a randomized health services research study with noncompliance to scheduled visits

structural matrix algebras and their lattices of invariant subspaces abstract a structural matrix algebra r of n n matrices over a field f has a distributive lattice lat r of invariant subspaces fn this and related known results are reproven here in a fresh way further we investigate what happens when r still operates on fn but is isomorphic to a structural matrix algebra of m m matrices m n then m r contains a certain distributive sublattice but needs not itself be distributive if m is not too small a shadow of distributivity is retained in the form of 2 distributivity and subdirect reducibility of lat r

joint partially linear model for longitudinal data with informative drop outs in biomedical research a steep rise or decline in longitudinal biomarkers may indicate latent disease progression which may subsequently cause patients to drop out of the study ignoring the informative drop out can cause bias in estimation of the longitudinal model in such cases a full parametric specification may be insufficient to capture the complicated pattern of the longitudinal biomarkers for these types of longitudinal data with the issue of informative drop outs we develop a joint partially linear model with an aim to find the trajectory of the longitudinal biomarker specifically an arbitrary function of time along with linear fixed and random covariate effects is proposed in the model for the biomarker while a flexible semiparametric transformation model is used to describe the drop out mechanism advantages of this semiparametric joint modeling approach are the following 1 it provides an easier interpretation compared to standard nonparametric regression models and 2 it is a natural way to control for common observable and unobservable prognostic factors that may affect both the longitudinal trajectory and the drop out process we describe a sieve maximum likelihood estimation procedure using the em algorithm where the akaike information criterion aic and bayesian information criterion bic are considered to select the number of knots we show that the proposed estimators achieve desirable asymptotic properties through empirical process theory the proposed methods are evaluated by simulation studies and applied to prostate cancer data

on the θ function of a riemannian manifold with boundary let be a compact riemannian manifold of dimension n with smooth boundary let 1 2 be the eigenvalues of the laplace beltrami operator with the boundary condition n 0 the associated function t n 1 exp n t has an asymptotic expansion of the form 4 t n 2 t a 0 a 1 t 1 2 a 2 t a 3 t 3 2 a 4 t 2 the values of a 0 a 1 are well known

theory of a curved planar waveguide with robin boundary conditions a model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative robin boundary condition is analyzed theoretically within the framework of the linear schrodinger equation and is applied to the study of the processes in the bent magnetic multilayers superconducting films and metallic ferrite filled waveguides in particular subband thresholds of the straight and curved parts of the film are calculated and analyzed as a function of the robin parameter 1 lambda with lambda being an extrapolation length entering robin boundary condition for the arbitrary robin coefficients which are equal on the opposite interfaces of the strip and for all bend parameters the lowest mode energy of the continuously curved duct is always smaller than its straight counterpart accordingly the bound state below the fundamental propagation threshold of the straight arms always exists as a result of the bend in terms of the superconductivity language it means an increased critical temperature of the curved film compared to its straight counterpart localized level dependence on the parameters of the curve is investigated with its energy decreasing with increasing bend angle and decreasing bend radius conditions of the bound state existence for the different robin parameters on the opposite edges are analyzed too in particular it is shown that the bound state below the first transverse threshold of the straight arm always exists if the inner extrapolation length is not larger than the outer one in the opposite case there is a range of the bend parameters where the curved film cannot trap the wave and form the localized mode for example for the fixed bend radius the bound state emerges from the continuum at some nonzero bend angle that depends on the difference of the two lengths lambda at the opposite interfaces various transport properties of the film such as interference blockade of the current flow at some special energies is also discussed with the special attention being paid to the transformation from the dirichlet to the neumann case as the extrapolation length lambda sweeps the positive axis

empirical likelihood semiparametric regression analysis for longitudinal data a semiparametric regression model for longitudinal data is considered the empirical likelihood method is used to estimate the regression coefficients and the baseline function and to construct confidence regions and intervals it is proved that the maximum empirical likelihood estimator of the regression coefficients achieves asymptotic efficiency and the estimator of the baseline function attains asymptotic normality when a bias correction is made two calibrated empirical likelihood approaches to inference for the baseline function are developed we propose a groupwise empirical likelihood procedure to handle the inter series dependence for the longitudinal semiparametric regression model and employ bias correction to construct the empirical likelihood ratio functions for the parameters of interest this leads us to prove a nonparametric version of wilks theorem compared with methods based on normal approximations the empirical likelihood does not require consistent estimators for the asymptotic variance and bias a simulation compares the empirical likelihood and normal based methods in terms of coverage accuracies and average areas lengths of confidence regions intervals

higher dimensional inverse problem of the wave equation for a general multi connected bounded domain with a finite number of smooth mixed boundary conditions the spectral function m t j 1 exp it m j 1 2 where m j j 1 are the eigenvalues of the negative laplacian d 3 u 1 3 x u 2 in the x 1 x 2 x 3 space is studied for small t for a variety of bounded domains where

modeling partly conditional means with longitudinal data abstract we propose a general modeling approach to longitudinal data that is a hybrid of the marginal regression models of zeger and liang and of the classical transition models such as used in time series analyses rather than conditioning at time t only on covariate values as is typical with the marginal approach or on the entire history of the process up to t as is typical with the transition model approach we suggest models that condition on a subset of the process history estimation proceeds using generalized estimating equation methodology but with the restriction that the working covariance matrix is diagonal the proposed regression models share common features with cox regression models for failure time data in that they are composed of a nuisance baseline function of time and a simple parametric function of the covariates two illustrative examples are presented

some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates abstract recurrent event time data are common in medical research examples include infections in aids patients and seizures in epilepsy patients in this context as well as in the more usual context of a single failure time variable time dependent covariates are frequently of interest we suggest some rate functions that might be displayed when analyzing recurrent failure time data or when the effect of a categorical time dependent covariate is of interest estimators of these functions are provided along with two sample test statistics a new approach to regression modeling of these data is suggested and contrasted with existing methods our methods do not require that an explicit model be formulated for the probabilistic association between failure times within an individual this is in line with the currently popular generalized estimating equation approach to longitudinal data if the nature of such associations is known or is of particular interest then alternative methods may be appropriate

eigenvalues of the laplacian for the third boundary values problem an extension to higher dimensions soit r a r b 0 0 2 une coque spherique on suppose connu exactement le spectre de valeurs propres 0 1 2 3 j quand j pour le probleme 3 u 0 dans u r 1 u r a 0 u r 2 u r b 0 ou 1 et 2 sont des constantes positives on determine la geometrie de et les impedances 1 et 2

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

convergence rate of sieve estimates in this paper we develop a general theory for the convergence rate of sieve estimates maximum likelihood estimates mle s and related estimates obtained by optimizing certain empirical criteria in general parameter spaces in many cases especially when the parameter space is infinite dimensional maximization over the whole parameter space is undesirable in such cases one has to perform maximization over an approximating space sieve of the original parameter space and allow the size of the approximating space to grow as the sample size increases this method is called the method of sieves in the case of the maximum likelihood estimation an mle based on a sieve is called a sieve mle we found that the convergence rate of a sieve estimate is governed by a the local expected values variances and l 2 entropy of the criterion differences and b the approximation error of the sieve a robust nonparametric regression problem a mixture problem and a nonparametric regression problem are discussed as illustrations of the theory we also found that when the underlying space is too large the estimate based on optimizing over the whole parameter space may not achieve the best possible rates of convergence whereas the sieve estimate typically does not suffer from this difficulty

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

semiparametric and nonparametric regression analysis of longitudinal data this article deals with the regression analysis of repeated measurements taken at irregular and possibly subject specific time points the proposed semiparametric and nonparametric models postulate that the marginal distribution for the repeatedly measured response variable y at time t is related to the vector of possibly time varying covariates x through the equations e y t x t 0 t 0x t and e y t x t 0 t 0 t x t where 0 t is an arbitrary function of t 0 is a vector of constant regression coefficients and 0 t is a vector of time varying regression coefficients the stochastic structure of the process y is completely unspecified we develop a class of least squares type estimators for 0 which is proven to be n consistent and asymptotically normal with simple variance estimators furthermore we develop a closed form estimator for a cumulative function of 0 t which is shown to be n consistent and on proper normalization converges weakly to a zero mean gaussian pr

semiparametric regression for clustered data using generalized estimating equations we consider estimation in a semiparametric generalized linear model for clustered data using estimating equations our results apply to the case where the number of observations per cluster is finite whereas the number of clusters is large the mean of the outcome variable is of the form g xt t where g is a link function x and t are covariates is an unknown parameter vector and t is an unknown smooth function kernel estimating equations proposed previously in the literature are used to estimate the infinite dimensional nonparametric function t and a profile based estimating equation is used to estimate the finite dimensional parameter vector we show that for clustered data this conventional profile kernel method often fails to yield a n consistent estimator of along with appropriate inference unless working independence is assumed or t is artificially undersmoothed in which case asymptotic inference is possible to gain insight into these results we derive the se

can one hear the dimension of a fractal we consider the spectrum of the laplacian in a bounded open domain of n with a rough boundary i e with possibly non integer dimension and we discuss a conjecture by m v berry generalizing weyl s conjecture then using ideas mark kac developed in his famous study of the drum we give upper and lower bounds for the second term of the expansion of the partition function the main thesis of the paper is to show that the relevant measure of the roughness of the boundary should be based on minkowski dimensions and on minkowski measures rather than on haussdorff ones

outcome vector dependent sampling with longitudinal continuous response data stratified sampling based on summary statistics the analysis of longitudinal trajectories usually focuses on evaluation of explanatory factors that are either associated with rates of change or with overall mean levels of a continuous outcome variable in this manuscript we introduce valid design and analysis methods that permit outcome dependent sampling of longitudinal data for scenarios where all outcome data currently exist but a targeted sub study is being planned in order to collect additional key exposure information on a limited number of subjects we propose a stratified sampling based on specific summaries of individual longitudinal trajectories and we detail an ascertainment corrected maximum likelihood approach for estimation using the resulting biased sample of subjects in addition we demonstrate that the efficiency of an outcome based sampling design relative to use of a simple random sample depends highly on the choice of outcome summary statistic used to direct sampling and we show a natural link between the goals of the longitudinal regression model and corresponding desirable designs using data from the childhood asthma management program where genetic information required retrospective ascertainment we study a range of designs that examine lung function profiles over four years of follow up for children classified according to their genotype for the il 13 cytokine

a latent class mixture model for incomplete longitudinal gaussian data in the analyses of incomplete longitudinal clinical trial data there has been a shift away from simple methods that are valid only if the data are missing completely at random to more principled ignorable analyses which are valid under the less restrictive missing at random assumption the availability of the necessary standard statistical software nowadays allows for such analyses in practice while the possibility of data missing not at random mnar cannot be ruled out it is argued that analyses valid under mnar are not well suited for the primary analysis in clinical trials rather than either forgetting about or blindly shifting to an mnar framework the optimal place for mnar analyses is within a sensitivity analysis context one such route for sensitivity analysis is to consider next to selection models pattern mixture models or shared parameter models the latter can also be extended to a latent class mixture model the approach taken in this article the performance of the so obtained flexible model is assessed through simulations and the model is applied to data from a depression trial

hearing the shape of a general convex domain abstract the spectral function t j 1 exp t j where j j 1 are the eigenvalues of the laplace operator i 1 2 x i 2 in the x 1 x 2 plane is studied for a general convex domain together with an impedance condition on a part of its boundary and another impedance condition on the remaining part of that boundary

a theory of finite closure spaces based on implications abstract although many notions familiar from topology and matroid theory make sense for arbitrary closure spaces we claim that implicational bases are most worthwhile studying they are applied in the theory of relational data bases and in formal concept analysis further applications in combinatorics and algebra are foreseeable the main theorem describes the structure of minimum respectively optimal implicational bases of any finite closure space it has strong corollaries for specific closure spaces e g having a geometric respectively modular respectively lower distributive lattice of closed sets

an inverse problem for a general annular bounded domain in r2 with mixed boundary conditions and its physical applications this paper deals with the very interesting problem about the influence of the boundary conditions on the distribution of the eigenvalues of the negative laplacian in r 2 the asymptotic expansion of the trace of the heat kernel q t u 1 exp t m n where m n n 1 are the eigenvalues of the negative laplacian d 2 k 1 2 x k 2 in the x 1 x 2 plane is studied for short time t of a general annular bounded domain w in r 2 together with its smooth inner boundary w 1 and its smooth outer boundary w 2 where a finite number of dirichlet neumann and robin boundary conditions on the piecewise smooth components c i i 1 m of w 1 and on the piecewise smooth components c i i m 1 n of w 2 such that w 1 i 1 m c i and w 2 i m 1 n c i are considered in this paper one may extract information on the geometry of w by analyzing the asymptotic expansions of q t for short time t some applications of q t for an ideal gas enclosed in w are given thermodynamic quantities of an ideal gas enclosed in w are examined we use an asymptotic expansion for high temperatures to obtain the partition function of an ideal gas showing the leading corrections to the internal energy due to a finite container we show that the ideal gas cannot feel the shape of its container although it can feel some geometrical properties of it

bayesian semiparametric regression for longitudinal binary processes with missing data longitudinal studies with binary repeated measures are widespread in biomedical research marginal regression approaches for balanced binary data are well developed whereas for binary process data where measurement times are irregular and may differ by individuals likelihood based methods for marginal regression analysis are less well developed in this article we develop a bayesian regression model for analyzing longitudinal binary process data with emphasis on dealing with missingness we focus on the settings where data are missing at random mar which require a correctly specified joint distribution for the repeated measures in order to draw valid likelihood based inference about the marginal mean to provide maximum flexibility the proposed model specifies both the marginal mean and serial dependence structures using nonparametric smooth functions serial dependence is allowed to depend on the time lag between adjacent outcomes as well as other relevant covariates inference is fully bayesian using simulations we show that adequate modeling of the serial dependence structure is necessary for valid inference of the marginal mean when the binary process data are mar longitudinal viral load data from the hiv epidemiology research study are analyzed for illustration

robust inference for univariate proportional hazards frailty regression models we consider a class of semiparametric regression models which are one parameter extensions of the cox j roy statist soc ser b 34 1972 187 220 model for right censored univariate failure times these models assume that the hazard given the covariates and a random frailty unique to each individual has the proportional hazards form multiplied by the frailty the frailty is assumed to have mean 1 within a known one parameter family of distributions inference is based on a nonparametric likelihood the behavior of the likelihood maximizer is studied under general conditions where the fitted model may be misspecified the joint estimator of the regression and frailty parameters as well as the baseline hazard is shown to be uniformly consistent for the pseudo value maximizing the asymptotic limit of the likelihood appropriately standardized the estimator converges weakly to a gaussian process when the model is correctly specified the procedure is semiparametric efficient achieving the semiparametric information bound for all parameter components it is also proved that the bootstrap gives valid inferences for all parameters even under misspecification we demonstrate analytically the importance of the robust inference in several examples in a randomized clinical trial a valid test of the treatment effect is possible when other prognostic factors and the frailty distribution are both misspecified under certain conditions on the covariates the ratios of the regression parameters are still identifiable the practical utility of the procedure is illustrated on a non hodgkin s lymphoma dataset

asymptotics for nonparametric and semiparametric fixed effects panel models abstract in this paper we investigate the problem of estimating nonparametric and semiparametric panel data models with fixed effects we focus on establishing the asymptotic results for estimators using smooth backfitting methods we consider two estimators for the smooth unknown function in nonparametric panel regressions one is a local linear estimator constructed similar as the one in mammen et al 2009 which was proposed for the additive nonparametric panel model the other is the local profile likelihood based estimator proposed by henderson et al 2008 hcl hereafter we build the link and compare the difference between these two estimators which are constructed under different sets of conditions we put both of these estimators in the smooth backfitting algorithm framework discussed in mammen et al 1999 following the recently developed theories on backfitting kernel estimates in mammen et al 2009 we establish the asymptotic normality of these estimators and hence verify the conjectures made by hcl and complement their paper further we consider a partially linear fixed effects panel data model with the nonparametric component estimated using the methods discussed in the first part of the paper we give the asymptotic result for the estimators of finite dimensional parameters which shows that the first step plug in estimators will not affect the asymptotic variance in the second step estimation

semiparametric regression for repeated outcomes with nonignorable nonresponse abstract we consider inference about the parameter indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values that is nonresponse is nonignorable we propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal can for estimating when the response probabilities can be parametrically modeled and a can estimator exists the proposed estimators do not require full specification of a parametric likelihood and their computation does not require numerical integration our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse we show that our class essentially consists of all can estimators of we also show that the asymptotic variance of the optimal estimator in our

on hearing the shape of rectilinear regions from complete knowledge of the eigenvalues of the negative laplacian on a bounded domain one may extract information on the geometry and the boundary conditions by analyzing the asymptotic expansion of a spectral function explicit calculations are performed for an equilateral triangular domain with dirichlet or neumann boundary conditions yielding in particular the corner angle terms in three dimensions some applications to eigenvalue problems for an equilateral triangular prism are dealt with including the solid vertex terms

estimation in partially linear models with missing covariates the partially linear model y xt z has been studied extensively when data are completely observed in this article we consider the case where the covariate x is sometimes missing with missingness probability depending on y z new methods are developed for estimating and our methods are shown to outperform asymptotically methods based only on the complete data asymptotic efficiency is discussed and the semiparametric efficient score function is derived justification of the use of the nonparametric bootstrap in this context is sketched the proposed estimators are extended to a working independence analysis of longitudinal clustered data and applied to analyze an aids clinical trial dataset the results of a simulation experiment are also given to illustrate our approach

a semiparametric additive regression model for longitudinal data in previous work we have studied a nonparametric additive time varying regression model for longitudinal data recorded at irregular intervals the model allows the influence of each covariate to vary separately with time for small datasets however only a limited number of covariates may be handled in this way in this paper we introduce a semiparametric regression model for longitudinal data the influence of some of the covariates varies nonparametrically with time while the effect of the remaining covariates are constant no smoothing is necessary in the estimation of the parametric terms of the model asymptotics are derived using martingale techniques for the cumulative regression functions which are much easier to estimate and study than the regression functions themselves the approach is applied to longitudinal data from the copenhagen study group for liver diseases schlichting et al 1983

analysis of infant growth curves using multivariate adaptive splines summary in this paper we study the effect of cocaine use by a pregnant woman on the growth of her infant after birth using a data set from a retrospective study we found that cocaine use was a marginally significant contributor to the infant growth as measured by bodyweight prom a statistical point of view the data represent a common though complex structure that has received little attention in the statistical literature to analyze these data we adopt and further enhance an approach developed recently called masal multivariate adaptive splines for the analysis of longitudinal data in addition to the fitting of growth curves we demonstrate particularly how to explore and estimate the underlying covariance structures for the longitudinal data that were collected from a rather irregular schedule

an inverse problem of the wave equation for a general doubly connected region in r2 with a finite number of piecewise smooth robin boundary conditions the spectral distribution m t w 1 exp ite w 1 2 where e w w 1 are the eigenvalues of the negative laplacian d k 1 2 x k 2in the x 1 x 2 plane is studied for a variety of domains where 0

nonparametric smoothing estimates of time varying coefficient models with longitudinal data this paper considers nonparametric estimation in a varying coefficient model with repeated measurements y ij x ij t ij for i 1 n and j 1 n i where x ij x ij x ijk t and y ij x ij t ij denote the jth outcome covariate and time design points respectively of the ith subject the model considered here is y ij x ij t t ij e i t ij where t 0 t k t t for k 0 are smooth nonparametric functions of interest and e i t is a zero mean stochastic process the measurements are assumed to be independent for different subjects but can be correlated at different time points within each subject two nonparametric estimators of t namely a smoothing spline and a locally weighted polynomial are derived for such repeatedly measured data a crossvalidation criterion is proposed for the selection of the corresponding smoothing parameters asymptotic properties such as consistency rates of convergence and asymptotic mean squared errors are established for kernel estimators a special case of the local polynomials these asymptotic results give useful insights into the reliability of our general estimation methods an example of predicting the growth of children born to hiv infected mothers based on gender hiv status and maternal vitamin a levels shows that this model and the corresponding nonparametric estimators are useful in epidemiological studies

semiparametric regression analysis of longitudinal data with informative observation times statistical analysis of longitudinal data has been discussed by many authors and a number of methods have been proposed most of the research have focused on situations where observation times are independent of or carry no information about the response variable and therefore rely on conditional inference procedures given the observation times this article considers a different situation where the independence assumption may not hold that is the observation times may carry information about the response variable for inference estimating equation approaches are proposed and both large sample and final sample properties of the proposed methods are established the methodology is applied to a bladder cancer study that motivated this investigation

kernel regression estimation using repeated measurements data abstract the estimation of growth curves has been studied extensively in parametric situations here we consider the nonparametric estimation of an average growth curve suppose that there are observations from several experimental units each following the regression model y xi f xj e j 1 n where e1 e n are correlated zero mean errors and 0 x1 xn 1 are fixed constants we study some of the properties of a kernel estimator of f x asymptotic and finite sample results concerning the mean squared error of the estimator are obtained in particular the influence of correlation on the bandwidth minimizing mean squared error is discussed a data based method for selecting the bandwidth is illustrated in a data analysis most previous research on kernel regression estimators has involved uncorrelated errors we investigate how dependence of the errors changes the behavior of a kernel estimator our theorems concerning the asymptotic mean squared error show that the estimator cannot be consistent un

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

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

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

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

an inverse eigenvalue problem for a general convex domain the underlying problem is to deduce the precise shape of a membrane from the complete knowledge of the eigenvalues i for the lapace operator a cf a ax in the x1x2 plane let d g r be a simply connected bounded domain with a smooth boundary ad let us suppose that the a are the eigenvalues of the impedance problem au k o in d

an inverse problem for a general vibrating annular membrane in r3 with its physical applications further results this paper deals with the very interesting problem about the influence of the boundary conditions on the distribution of the eigenvalues of the negative laplacian in r 3 the trace of the heat semigroup q t email protected v 1 exp email protected v where m v v 1 are the eigenvalues of the negative laplacian email protected email protected b 1 email protected x b 2 in the x 1 x 2 x 3 space is studied for short time t for a general vibrating annular membrane w in r 3 together with its smooth inner bounding surface s 1 and its smooth outer bounding surface s 2 where a finite number of dirichlet neumann and robin boundary conditions on the piecewise smooth components s i i 1 m of s 1 and on the piecewise smooth components s i i m 1 n of s 2 is considered such that s email protected i 1 ms i and s email protected i m 1 ns i in this paper one may extract information on the geometry of w by analyzing the asymptotic expansions of q t for short time t some applications of q t for an ideal gas enclosed in the general vibrating annular membrane w are given we show that the asymptotic expansion of q t for short time t plays an important role in investigating the influence of the annular region w on the thermodynamic quantities of an ideal gas some applications of q t for an ideal gas enclosed in a compact n dimensional riemannian manifold are also given we show that the ideal gas cannot feel the shape of its container although it can feel some geometrical properties of it

varying coefficient models and basis function approximations for the analysis of repeated measurements summary a global smoothing procedure is developed using basis function approximations for estimating the parameters of a varying coefficient model with repeated measurements inference procedures based on a resampling subject bootstrap are proposed to construct confidence regions and to perform hypothesis testing conditional biases and variances of our estimators and their asymptotic consistency are developed explicitly finite sample properties of our procedures are investigated through a simulation study application of the proposed approach is demonstrated through an example in epidemiology in contrast to the existing methods this approach applies whether or not the covariates are timeinvariant and does not require binning of the data when observations are sparse at distinct observation times

higher dimensional inverse problem for a multi connected bounded domain with piecewise smooth robin boundary conditions and its physical applications the asymptotic expansions of the trace of the heat kernel q t email protected j 1 exp email protected j for short time t have been derived for a variety of bounded domains where l j j 1 are the eigenvalues of the negative laplace operator email protected email protected i 1 3 x i 2 in the x 1 x 2 x 3 space the dependence of q t on the connectivity of bounded domains and the boundary conditions is analyzed particular attention is given for an arbitrary multiply connected bounded domain w in r 3 together with piecewise smooth robin boundary conditions where the coefficients in these conditions are assumed to be piecewise smooth positive functions some applications of an ideal gas enclosed in the multiply connected bounded domain w are given we show that the ideal gas cannot feel the shape of its container although it can feel some geometrical properties of it

an inverse eigenvalue problem of the wave equation for a multi connected region in r2 together with three different types of boundary conditions the trace of the wave kernel m t email protected w 1exp ite 1 2 w where e w w 1 are the eigenvalues of the negative laplacian email protected email protected 2 k 1 email protected x k 2 in the x 1 x 2 plane is studied for a variety of bounded domains where

an inverse problem for the three dimensional multi connected vibrating membrane with robin boundary conditions this paper deals with the very interesting problem about the influence of the boundary conditions on the distribution of the eigenvalues of the negative laplacian in r 3 the trace of the heat semigroup q t n 1exp t m n where m n n 1 are the eigenvalues of the negative laplacian 2 3 b 1 x b 2 in the x 1 x 2 x 3 space is studied for a general multiply connected bounded domain w in r 3 surrounded by simply connected bounded domains w j with smooth bounding surfaces s j j 1 n where a finite number of piecewise smooth robin boundary conditions on the piecewise smooth components s i i 1 k j 1 k j of the bounding surfaces s j are considered such that s j k j i 1 k j 1s i where k 0 0 some applications of q t for an ideal gas enclosed in the multiply connected bounded container w with robin boundary conditions are given we show that the asymptotic expansion of q t for short time t plays an important role in investigating the influence of the finite container w on the thermodynamic quantities of an ideal gas

regression analysis of panel count data with covariate dependent observation and censoring times panel count data often occur in a long term study where the primary end point is the time to a specific event and each subject may experience multiple recurrences of this event furthermore suppose that it is not feasible to keep subjects under observation continuously and the numbers of recurrences for each subject are only recorded at several distinct time points over the study period moreover the set of observation times may vary from subject to subject in this paper regression methods which are derived under simple semiparametric models are proposed for the analysis of such longitudinal count data especially we consider the situation when both observation and censoring times may depend on covariates the new procedures are illustrated with data from a well known cancer study

the wave equation approach to an inverse problem for a general multi connected domain in r2 with mixed boundary conditions the spectral function email protected t email protected j 1 exp email protected j 1 2 where m j j 1 are the eigenvalues of the negative laplacian email protected email protected u 1 email protected x u 2 in r 2 is studied for small t for a variety of domains where

nonparametric maximum likelihood estimation by the method of sieves maximum likelihood estimation often fails when the parameter takes values in an infinite dimensional space for example the maximum likelihood method cannot be applied to the completely nonparametric estimation of a density function from an operatorname iid sample the maximum of the likelihood is not attained by any density in this example as in many other examples the parameter space positive functions with area one is too big but the likelihood method can often be salvaged if we first maximize over a constrained subspace of the parameter space and then relax the constraint as the sample size grows this is grenander s method of sieves application of the method sometimes leads to new estimators for familiar problems or to a new motivation for an already well studied technique we will establish some general consistency results for the method and then we will focus on three applications

incidence algebras that are uniquely determined by their zero nonzero matrix pattern abstract to what extent is the isomorphism type of an incidence algebra determined by the zero nonzero pattern of a matrix representation we settle the question in a natural framework where the matrices are subdivided into four blocks the lower left is zero the diagonal blocks are fixed and the upper right is variable

an optimal selection of regression variables summary an asymptotically optimal selection of regression variables is proposed the key assumption is that the number of control variables is infinite or increases with the sample size it is also shown that mallows s qp akaike s fpe and aic methods are all asymptotically equivalent to this method

hearing the shape of a general doubly connected domain in r3 with impedance boundary conditions the basic problem in this paper is that of determining the geometry of a general doubly connected domain in r3 together with an impedance condition on its inner bounding surface and another impedance condition on its outer bounding surface from the complete knowledge of the eigenvalues j j 1 for the three dimensional laplacian using the asymptotic expansion of the spectral function t j 1 exp t j for small positive t

inferences for a semiparametric model with panel data summary in a longitudinal study suppose that for each subject repeated measurements of the response variable and covariates are collected at a set of distinct irregularly spaced time points we consider a semiparametric model which relates the mean of the response variable at each time point proportionally to a function of a time dependent covariate vector to analyse such panel data inference procedures for regression parameters are proposed without involving any nonparametric function estimation for the nuisance mean function a dataset from a recent aids clinical trial is used to illustate the new proposal

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

semiparametric regression for the mean and rate functions of recurrent events the counting process with the cox type intensity function has been commonly used to analyse recurrent event data this model essentially assumes that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process recently pepe and cai and lawless and co workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the poisson type assumption in this paper we provide a rigorous justification of such robust procedures through modern empirical process theory furthermore we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean rate model the advantages of the robust procedures are demonstrated through simulation studies an illustration with multiple infection data taken from a clinical study on chronic granulomatous disease is also provided

semiparametric stochastic mixed models for longitudinal data abstract we consider inference for a semiparametric stochastic mixed model for longitudinal data this model uses parametric fixed effects to represent the covariate effects and an arbitrary smooth function to model the time effect and accounts for the within subject correlation using random effects and a stationary or nonstationary stochastic process we derive maximum penalized likelihood estimators of the regression coefficients and the nonparametric function the resulting estimator of the nonparametric function is a smoothing spline we propose and compare frequentist inference and bayesian inference on these model components we use restricted maximum likelihood to estimate the smoothing parameter and the variance components simultaneously we show that estimation of all model components of interest can proceed by fitting a modified linear mixed model we illustrate the proposed method by analyzing a hormone dataset and evaluate its performance through simulations

modeling longitudinal data with nonignorable dropouts using a latent dropout class model summary in longitudinal studies with dropout pattern mixture models form an attractive modeling framework to account for nonignorable missing data however pattern mixture models assume that the components of the mixture distribution are entirely determined by the dropout times that is two subjects with the same dropout time have the same distribution for their response with probability one as that is unlikely to be the case this assumption made lead to classification error in addition if there are certain dropout patterns with very few subjects which often occurs when the number of observation times is relatively large pattern specific parameters may be weakly identified or require identifying restrictions we propose an alternative approach which is a latent class model the dropout time is assumed to be related to the unobserved latent class membership where the number of classes is less than the number of observed patterns a regression model for the response is specified conditional on the latent variable this is a type of shared parameter model where the shared parameter is discrete parameter estimates are obtained using the method of maximum likelihood averaging the estimates of the conditional parameters over the distribution of the latent variable yields estimates of the marginal regression parameters the methodology is illustrated using longitudinal data on depression from a study of hiv in women

simultaneous inference of linear models with time varying coefficients summary the paper considers construction of simultaneous confidence tubes for time varying regression coefficients in functional linear models using a gaussian approximation result for non stationary multiple time series we show that the constructed simultaneous confidence tubes have asymptotically correct nominal coverage probabilities our results are applied to the problem of testing whether the regression coefficients are of certain parametric forms which is a fundamental problem in the inference of functional linear models as an application we analyse an environmental data set and study the association between levels of pollutants and hospital admissions