on optimum hamiltonians for state transformations for a prescribed pair of quantum states i and f we establish an elementary derivation of the optimum hamiltonian under constraints on its eigenvalues that generates the unitary transformation i f in the shortest duration the derivation is geometric in character and does not rely on variational calculus

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

generalized partially linear single index models abstract the typical generalized linear model for a regression of a response y on predictors x z has conditional mean function based on a linear combination of x z we generalize these models to have a nonparametric component replacing the linear combination t 0x t 0z by 0 t 0x t 0z where 0 is an unknown function we call these generalized partially linear single index models gplsim the models include the single index models which have 0 0 using local linear methods we propose estimates of the unknown parameters 0 0 and the unknown function 0 and obtain their asymptotic distributions examples illustrate the models and the proposed estimation methodology

a profile likelihood approach for longitudinal data analysis summary inappropriate choice of working correlation structure in generalized estimating equations gee could lead to inefficient parameter estimation while impractical normality assumption in likelihood approach would limit its applicability in longitudinal data analysis in this article we propose a profile likelihood method for estimating parameters in longitudinal data analysis via maximizing the estimated likelihood the proposed method yields consistent and efficient estimates without specifications of the working correlation structure nor the underlying error distribution both theoretical and simulation results confirm the satisfactory performance of the proposed method we illustrate our methodology with a diastolic blood pressure data set

time optimal synthesis for left invariant control systems on series so 3 consider the control system sigma given by dot x x f ug where x in so 3 u leq 1 and f g in so 3 define two perpendicular left invariant vector fields normalized so that f cos al and g sin al al in 0 pi 4 in this paper we provide an upper bound and a lower bound for n alpha the maximum number of switchings for time optimal trajectories of sigma more precisely we show that n s al leq n al leq n s al 4 where n s al is a suitable integer function of al such that n s al stackrel lower2pt hbox smash sim mbox tiny al to 0 pi 4 alpha the result is obtained by studying the time optimal synthesis of a projected control problem on rr p 2 where the projection is defined by an appropriate hopf fibration finally we study the projected control problem on the unit sphere s 2 it exhibits interesting features which will be partly rigorously derived and partially described by numerical simulations

quadratic inference functions for varying coefficient models with longitudinal data nonparametric smoothing methods are used to model longitudinal data but the challenge remains to incorporate correlation into nonparametric estimation procedures in this article we propose an efficient estimation procedure for varying coefficient models for longitudinal data the proposed procedure can easily take into account correlation within subjects and deal directly with both continuous and discrete response longitudinal data under the framework of generalized linear models the proposed approach yields a more efficient estimator than the generalized estimation equation approach when the working correlation is misspecified for varying coefficient models it is often of interest to test whether coefficient functions are time varying or time invariant we propose a unified and efficient nonparametric hypothesis testing procedure and further demonstrate that the resulting test statistics have an asymptotic chi squared distribution in addition the goodness of fit test is applied to test whether the model assumption is satisfied the corresponding test is also useful for choosing basis functions and the number of knots for regression spline models in conjunction with the model selection criterion we evaluate the finite sample performance of the proposed procedures with monte carlo simulation studies the proposed methodology is illustrated by the analysis of an acquired immune deficiency syndrome aids data set

efficient statistical inference procedures for partially nonlinear models and their applications motivated by an analysis of a real data set in ecology we consider a class of partially nonlinear models where both a nonparametric component and a parametric component are present we develop two new estimation procedures to estimate the parameters in the parametric component consistency and asymptotic normality of the resulting estimators are established we further propose an estimation procedure and a generalized f test procedure for the nonparametric component in the partially nonlinear models asymptotic properties of the newly proposed estimation procedure and the test statistic are derived finite sample performance of the proposed inference procedures are assessed by monte carlo simulation studies an application in ecology is used to illustrate the proposed methods

a smooth simultaneous confidence corridor for the mean of sparse functional data functional data analysis fda has become an important area of statistics research in the recent decade yet a smooth simultaneous confidence corridor scc does not exist in the literature for the mean function of sparse functional data scc is a powerful tool for making statistical inference on an entire unknown function nonetheless classic hungarian embedding techniques for establishing asymptotic correctness of scc completely fail for sparse functional data we propose a local linear scc and a shoal of confidence intervals sci for the mean function of sparse functional data and establish that it is asymptotically equivalent to the scc of independent regression data using new results from gaussian process extreme value theory the scc procedure is examined in simulations for its superior theoretical accuracy and performance and used to analyze growth curve data confirming findings with quantified high significance levels supplementary materials for this article are available online

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

bayesian inference in semiparametric mixed models for longitudinal data we consider bayesian inference in semiparametric mixed models spmms for longitudinal data spmms are a class of models that use a nonparametric function to model a time effect a parametric function to model other covariate effects and parametric or nonparametric random effects to account for the within subject correlation we model the nonparametric function using a bayesian formulation of a cubic smoothing spline and the random effect distribution using a normal distribution and alternatively a nonparametric dirichlet process dp prior when the random effect distribution is assumed to be normal we propose a uniform shrinkage prior usp for the variance components and the smoothing parameter when the random effect distribution is modeled nonparametrically we use a dp prior with a normal base measure and propose a usp for the hyperparameters of the dp base measure we argue that the commonly assumed dp prior implies a nonzero mean of the random effect distribution even when a base measure with mean zero is specified this implies weak identifiability for the fixed effects and can therefore lead to biased estimators and poor inference for the regression coefficients and the spline estimator of the nonparametric function we propose an adjustment using a postprocessing technique we show that under mild conditions the posterior is proper under the proposed usp a flat prior for the fixed effect parameters and an improper prior for the residual variance we illustrate the proposed approach using a longitudinal hormone dataset and carry out extensive simulation studies to compare its finite sample performance with existing methods

semiparametric regression for clustered data we consider estimation in a semiparametric partially generalised linear model for clustered data using estimating equations a marginal model is assumed where the mean of the outcome variable depends on some covariates parametrically and a cluster level covariate nonparametrically a profile kernel method allowing for working correlation matrices is developed we show that the nonparametric part of the model can be estimated using standard nonparametric methods including smoothing parameter estimation and the parametric part of the model can be estimated in a profile fashion the asymptotic distributions of the parameter estimators are derived and the optimal estimators of both the nonparametric and parametric parts are shown to be obtained when the working correlation matrix equals the actual correlation matrix the asymptotic covariance matrix of the parameter estimator is consistently estimated by the sandwich estimator we show that the semiparametric efficient score takes on a simple form and our profile kernel method is semiparametric efficient the results for the case where the nonparametric part of the model is an observation level covariate are noted to be dramatically different

time optimal cnot between indirectly coupled qubits in a linear ising chain we give analytical solutions for the time optimal synthesis of entangling gates between indirectly coupled qubits 1 and 3 in a linear spin chain of three qubits subject to an ising hamiltonian interaction with a symmetric coupling j plus a local magnetic field acting on the intermediate qubit the energy available is fixed but we relax the standard assumption of instantaneous unitary operations acting on single qubits the time required for performing an entangling gate which is equivalent modulo local unitary operations to the cnot 1 3 between the indirectly coupled qubits 1 and 3 is i e faster than a previous estimate based on a similar hamiltonian and the assumption of local unitaries with zero time cost furthermore performing a simple walsh hadamard rotation in the hilbert space of qubit 3 shows that the time optimal synthesis of the cnot 1 3 which acts as the identity when the control qubit 1 is in the state 0 while if the control qubit is in the state 1 the target qubit 3 is flipped as also requires the same time t

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

generalized quasi likelihood ratio tests for semiparametric analysis of covariance models in longitudinal data abstractwe model generalized longitudinal data from multiple treatment groups by a class of semiparametric analysis of covariance models which take into account the parametric effects of time dependent covariates and the nonparametric time effects in these models the treatment effects are represented by nonparametric functions of time and we propose a generalized quasi likelihood ratio test procedure to test if these functions are identical our estimation procedure is based on profile estimating equations combined with local linear smoothers we find that the much celebrated wilks phenomenon which is well established for independent data still holds for longitudinal data if a working independence correlation structure is assumed in the test statistic however this property does not hold in general especially when the working variance function is misspecified our empirical study also shows that incorporating correlation into the test statistic does not necessarily improve the power of the test the

the quantum brachistochrone problem for non hermitian hamiltonians recently bender brody jones and meister found that in the quantum brachistochrone problem the passage time needed for the evolution of certain initial states into specified final states can be made arbitrarily small when the time evolution operator is taken to be non hermitian but pt symmetric here we demonstrate that such phenomena can also be obtained for non hermitian hamiltonians for which pt symmetry is completely broken i e dissipative systems we observe that the effect of a tunable passage time can be achieved by projecting between orthogonal eigenstates by means of a time evolution operator associated with a non hermitian hamiltonian it is not essential that this hamiltonian is pt symmetric

estimating equations for parameters in means and covariances of multivariate discrete and continuous responses generalized estimating equations are introduced in an ad hoc fashion for the covariance matrix of a multivariate response these equations are to be solved jointly with score equations from a generalized linear model for mean parameters a class of quadratic exponential models is used to develop joint estimating equations for mean and covariance parameters in a more systematic fashion and proposals for the use of such equations are developed comments on the relative merits of the ad hoc and model based approaches to estimation are given and a regression illustration with a bivariate response is provided

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

regression analysis of sparse asynchronous longitudinal data we consider estimation of regression models for sparse asynchronous longitudinal observations where time dependent responses and covariates are observed intermittently within subjects unlike with synchronous data where the response and covariates are observed at the same time point with asynchronous data the observation times are mismatched simple kernel weighted estimating equations are proposed for generalized linear models with either time invariant or time dependent coefficients under smoothness assumptions for the covariate processes which are similar to those for synchronous data for models with either time invariant or time dependent coefficients the estimators are consistent and asymptotically normal but converge at slower rates than those achieved with synchronous data simulation studies evidence that the methods perform well with realistic sample sizes and may be superior to a naive application of methods for synchronous data based on an ad hoc last value carried forward approach the practical utility of the methods is illustrated on data from a study on human immunodeficiency virus

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

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

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

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

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

analysis of longitudinal data with semiparametric estimation of covariance function improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data both involve estimation of the covariance function yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points a class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed a kernel estimator for estimating the nonparametric variance function is developed two methods for estimating parameters in the correlation structure a quasi likelihood approach and a minimum generalized variance method are proposed a semiparametric varying coefficient partially linear model for longitudinal data is introduced and an estimation procedure for model coefficients using a profile weighted least squares approach is proposed sampling properties of the proposed estimation procedures are studied and asy

partly functional temporal process regression with semiparametric profile estimating functions summary marginal mean models of temporal processes in event time data analysis are gaining more attention for their milder assumptions than the traditional intensity models recent work on fully functional temporal process regression tpr offers great flexibility by allowing all the regression coefficients to be nonparametrically time varying the existing esti mation procedure however prevents successive goodness of fit test for covariate coefficients in comparing a sequence of nested models this article proposes a partly functional tpr model in the line of marginal mean models some covari ate effects are time independent while others are completely unspecified in time this class of models is very rich includ ing the fully functional model and the semiparametric model as special cases to estimate the parameters we propose semiparametric profile estimating equations which are solved via an iterative algorithm starting at a consistent estimate from a fully functional model in the existing work no smoothing is needed in contrast to other varying coefficient meth ods the weak convergence of the resultant estimators are developed using the empirical process theory successive tests of time varying effects and backward model selection procedure can then be carried out the practical usefulness of the methodology is demonstrated through a simulation study and a real example of recurrent exacerbation among cystic fibrosis patients

additive partial linear models with measurement errors we consider statistical inference for additive partial linear models when the linear covariate is measured with error we propose attenuation to correction and simex estimators of the parameter of interest it is shown that the first resulting estimator is asymptotically normal and requires no undersmoothing this is an advantage of our estimator over existing backfitting based estimators for semiparametric additive models which require undersmoothing of the nonparametric component in order for the estimator of the parametric component be root n consistent this feature stems from a decrease of the bias of the resulting estimator which is appropriately derived using a profile procedure a similar characteristic in semiparametric partially linear models was obtained by wang et al 2005 we also discuss the asymptotics of the proposed simex approach finite sample performance of the proposed estimators is assessed by simulation experiments the proposed methods are applied to a dataset from a semen study

understanding nonparametric estimation for clustered data summary in this note we give an alternative formulation of the nonparametric estimators of wang 2003 with the identity link this results in a closed form of the estimator that has computational advantages and gives insight into the rationale behind the estimator

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

efficient semiparametric regression for longitudinal data with nonparametric covariance estimation summary for longitudinal data when the within subject covariance is misspecified the semiparametric regression estimator may be inefficient we propose a method that combines the efficient semiparametric estimator with nonparametric covariance estimation and is robust against misspecification of covariance models we show that kernel covariance estimation provides uniformly consistent estimators for the within subject covariance matrices and the semiparametric profile estimator with substituted nonparametric covariance is still semiparametrically efficient the finite sample performance of the proposed estimator is illustrated by simulation in an application to cd4 count data from an aids clinical trial we extend the proposed method to a functional analysis of the covariance model

the effect of estimating weights in weighted least squares abstract in weighted least squares it is typical that the weights are unknown and must be estimated most packages provide standard errors assuming that the weights are known this is fine for sufficiently large sample sizes but what about for small to moderate sample sizes the investigation of this article into the effect of estimating weights proceeds under the assumption typical in practice that one has a parametric model for the variance function in this context generalized least squares consists of a an initial estimate of the regression parameter b a method for estimating the variance function and c the number of iterations in reweighted least squares by means of expansions for the covariance it is shown that each of a c can matter in problems of small to moderate size a few conclusions may be of practical interest first estimated standard errors assuming that the weights are known can be too small in practice the investigation indicates that a simple bootstrap operation resul

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

efficient semiparametric marginal estimation for longitudinal clustered data we consider marginal generalized semiparametric partially linear models for clustered data lin and carroll derived the semiparametric efficient score function for this problem in the multivariate gaussian case but they were unable to construct a semiparametric efficient estimator that actually achieved the semiparametric information bound here we propose such an estimator and generalize the work to marginal generalized partially linear models we investigate asymptotic relative efficiencies of the estimators that ignore the within cluster correlation structure either in nonparametric curve estimation or throughout we evaluate the finite sample performance of these estimators through simulations and illustrate it using a longitudinal cd4 cell count dataset both theoretical and numerical results indicate that properly taking into account the within subject correlation among the responses can substantially improve efficiency

exact solutions of the isoholonomic problem and the optimal control problem in holonomic quantum computation the isoholonomic problem in a homogeneous bundle is formulated and solved exactly the problem takes a form of a boundary value problem of a variational equation the solution is applied to the optimal control problem in holonomic quantum computer we provide a prescription to construct an optimal controller for an arbitrary unitary gate and apply it to a k dimensional unitary gate which operates on an n dimensional hilbert space with n 2k our construction is applied to several important unitary gates such as the hadamard gate the cnot gate and the two qubit discrete fourier transformation gate controllers for these gates are explicitly constructed

additive extensions to generalized estimating equation methods the methods underlying vector generalized additive models are extended to provide additive extensions to the generalized estimating equations approaches to multivariate regression problems of liang and zeger and the subsequent literature the methods are illustrated by two examples using correlated binary data concerning the presence or absence of several plant species at the same geographical site and chest pain in male workers from a workforce study with minor modification the extensions are shown to apply to longitudinal data

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

anova for longitudinal data with missing values we carry out anova comparisons of multiple treatments for longitudinal studies with missing values the treatment effects are modeled semiparametrically via a partially linear regression which is flexible in quantifying the time effects of treatments the empirical likelihood is employed to formulate model robust nonparametric anova tests for treatment effects with respect to covariates the nonparametric time effect functions and interactions between covariates and time the proposed tests can be readily modified for a variety of data and model combinations that encompasses parametric semiparametric and nonparametric regression models cross sectional and longitudinal data and with or without missing values

on repeated measures analysis with misspecified covariance structure in recent years various sophisticated methods have been developed for the analysis of repeated measures or longitudinal data the more traditional approach based on a normal likelihood function has been shown to be unsatisfactory in the sense of yielding asymptotically biased estimates when the covariance structure is misspecified more recent methodology based on generalized linear models and quasi likelihood estimation has gained widespread acceptance as generalized estimating equations however this also has theoretical problems in this paper a suggestion is made for improving the asymptotic behaviour of estimators by using the older approach implemented via gaussian estimation the resulting estimating equations include the quasi score function as one component so the methodology proposed can be viewed as a combination of gaussian estimation and generalized estimating equations which has a firmer asymptotic basis than either alone has

penalized spline models for functional principal component analysis summary we propose an iterative estimation procedure for performing functional principal component analysis the procedure aims at functional or longitudinal data where the repeated measurements from the same subject are correlated an increasingly popular smoothing approach penalized spline regression is used to represent the mean function this allows straightforward incorporation of covariates and simple implementation of approximate inference procedures for coefficients for the handling of the within subject correlation we develop an iterative procedure which reduces the dependence between the repeated measurements that are made for the same subject the resulting data after iteration are theoretically shown to be asymptotically equivalent in probability to a set of independent data this suggests that the general theory of penalized spline regression that has been developed for independent data can also be applied to functional data the effectiveness of the proposed procedure is demonstrated via a simulation study and an application to yeast cell cycle gene expression data

time optimal quantum evolution of mixed states we present a general formalism based on the variational principle for finding the time optimal quantum evolution of mixed states governed by a master equation when the hamiltonian and the lindblad operators are subject to certain constraints the problem may be reduced to solving first a fundamental equation which can be written down once the constraints are specified for the hamiltonian and then solving the constraints and the master equation for the lindblad and the density operators as an application of our formalism we study a simple one qubit model where the optimal lindblad operators can be simulated by a tunable coupling with an ancillary qubit

informative estimation and selection of correlation structure for longitudinal data identifying an informative correlation structure is important in improving estimation efficiency for longitudinal data we approximate the empirical estimator of the correlation matrix by groups of known basis matrices that represent different correlation structures and transform the correlation structure selection problem to a covariate selection problem to address both the complexity and the informativeness of the correlation matrix we minimize an objective function that consists of two parts the difference between the empirical information and a model approximation of the correlation matrix and a penalty that penalizes models with too many basis matrices the unique feature of the proposed estimation and selection of correlation structure is that it does not require the specification of the likelihood function and therefore it is applicable for discrete longitudinal data we carry out the proposed method through a groupwise penalty strategy which is able to identify more complex structures the

semiparametric estimation of covariance matrixes for longitudinal data estimation of longitudinal data covariance structure poses significant challenges because the data usually are collected at irregular time points a viable semiparametric model for covariance matrixes has been proposed that allows one to estimate the variance function nonparametrically and to estimate the correlation function parametrically by aggregating information from irregular and sparse data points within each subject but the asymptotic properties of the quasi maximum likelihood estimator qmle of parameters in the covariance model are largely unknown we address this problem in the context of more general models for the conditional mean function including parametric nonparametric or semiparametric we also consider the possibility of rough mean regression function and introduce the difference based method to reduce biases in the context of varying coefficient partially linear mean regression models this provides a more robust estimator of the covariance function under a wider range of situati

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

generalized partially linear models for incomplete longitudinal data in the presence of population level information in observational studies interest often lies in estimation of the population level relationship between the explanatory variables and dependent variables and the estimation is often done using longitudinal data longitudinal data often feature sampling error and bias due to non random drop out however inclusion of population level information can increase estimation efficiency in this paper we consider a generalized partially linear model for incomplete longitudinal data in the presence of the population level information a pseudo empirical likelihood based method is introduced to incorporate population level information and non random drop out bias is corrected by using a weighted generalized estimating equations method a three step estimation procedure is proposed which makes the computation easier several methods that are often used in practice are compared in simulation studies which demonstrate that our proposed method can correct the non random drop out bias and increase the estimation efficiency especially for small sample size or when the missing proportion is high we apply this method to an alzheimer s disease study

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

weak and strong uniform consistency of kernel regression estimates we study the estimation of a regression function by the kernel method under mild conditions on the window the bandwidth and the underlying distribution of the bivariate observations x i y i we obtain the weak and strong uniform convergence rates on a bounded interval these results parallel those of silverman 1978 on density estimation and extend those of schuster and yakowitz 1979 and collomb 1979 on regression estimation

semiparametric mean covariance regression analysis for longitudinal data efficient estimation of the regression coefficients in longitudinal data analysis requires a correct specification of the covariance structure existing approaches usually focus on modeling the mean with specification of certain covariance structures which may lead to inefficient or biased estimators of parameters in the mean if misspecification occurs in this article we propose a data driven approach based on semiparametric regression models for the mean and the covariance simultaneously motivated by the modified cholesky decomposition a regression spline based approach using generalized estimating equations is developed to estimate the parameters in the mean and the covariance the resulting estimators for the regression coefficients in both the mean and the covariance are shown to be consistent and asymptotically normally distributed in addition the nonparametric functions in these two structures are estimated at their optimal rate of convergence simulation studies and a real data analysis show

equivalent kernels of smoothing splines in nonparametric regression for clustered longitudinal data correlation we show that a smoothing spline estimator is asymptotically equivalent to a recently proposed seemingly unrelated kernel estimator of wang 2003 for any working covariance matrix we show that both estimators can be obtained iteratively by applying conventional kernel or spline smoothing to pseudo observations this result allows us to study the asymptotic properties of the smoothing spline estimator by deriving its asymptotic bias and variance we show that smoothing splines are consistent for an arbitrary working covariance and have the smallest variance when assuming the true covariance we further show that both the seemingly unrelated kernel estimator and the smoothing spline estimator are nonlocal unless working independence is assumed but have asymptotically negligible bias their finite sample performance is compared through simulations our results justify the use of efficient non local estimators such as smoothing splines for clustered longitudinal data

exploring families of quantum controls for generating unitary transformations a numerical method is presented for exploring the intertwined roles of the control field structure and the final time t in determining the unitary evolution operator u t 0 for finite level quantum control systems the algorithm can a identify controls achieving a target unitary operator w at time t up to machine precision and b identify a continuous family of controls producing the same operator w over a continuous interval of final times the high degree of precision is obtained in part by exploiting the geometry of the unitary group in particular geodesics of the unitary group are followed both for tracking to a target transformation and for error management

a joint modelling approach for longitudinal studies in longitudinal studies it is of fundamental importance to understand the dynamics in the mean function variance function and correlations of the repeated or clustered measurements for modelling the covariance structure cholesky type decomposition based approaches have been demonstrated to be effective however parsimonious approaches for directly revealing the correlation structure between longitudinal measurements remain less well explored and existing joint modelling approaches may encounter difficulty in interpreting the covariation structure we propose a novel joint mean variance correlation modelling approach for longitudinal studies by applying hyperspherical co ordinates we obtain an unconstrained parameterization for the correlation matrix that automatically guarantees its positive definiteness and we develop a regression approach to model the correlation matrix of the longitudinal measurements by exploiting the parameterization the modelling framework proposed is parsimonious interpretable and flexible for analysing longitudinal data extensive data examples and simulations support the effectiveness of the approach proposed

efficient semiparametric mean association estimation for longitudinal binary responses semiparametric methods for longitudinal data with association within subjects have recently received considerable attention however existing methods for semiparametric longitudinal binary regression modeling i mainly concern mean structures with association parameters treated as nuisance ii generally require a correct specification of the covariance structure for misspecified covariance structure may lead to inefficient mean parameter estimates and iii usually run into computation and estimation problems when the time points are irregularly and possibly subject specific in this article we propose a semiparametric logistic regression model which simultaneously takes into account both the mean and response association structures via conditional log odds ratio for multivariate longitudinal binary outcomes our main interest lies in efficient estimation of both the marginal and association parameters the estimators of the parameters are obtained via the profile kernel approach we evaluate the proposed methodology through simulation studies and apply it to a real dataset both theoretical and empirical results demonstrate that the proposed method yields highly efficient estimators and performs satisfactorily copyright 2012 john wiley sons ltd

a semiparametric model for cluster data in the analysis of cluster data the regression coefficients are frequently assumed to be the same across all clusters this hampers the ability to study the varying impacts of factors on each cluster in this paper a semiparametric model is introduced to account for varying impacts of factors over clusters by using cluster level covariates it achieves the parsimony of parametrization and allows the explorations of nonlinear interactions the random effect in the semiparametric model accounts also for within cluster correlation local linear based estimation procedure is proposed for estimating functional coefficients residual variance and within cluster correlation matrix the asymptotic properties of the proposed estimators are established and the method for constructing simultaneous confidence bands are proposed and studied in addition relevant hypothesis testing problems are addressed simulation studies are carried out to demonstrate the methodological power of the proposed methods in the finite sample the proposed model and methods are used to analyse the second birth interval in bangladesh leading to some interesting findings

robust variable selection in semiparametric mean covariance regression for longitudinal data analysis this paper considers robust semiparametric smooth threshold generalized estimating equations for the analysis of longitudinal data based on the modified cholesky decomposition and b spline approximations the proposed method can automatically eliminate inactive predictors by setting the corresponding parameters to be zero and simultaneously estimate the mean regression coefficients generalized autoregressive coefficients and innovation variances in order to overcome the outliers in either the response or and the covariate domain we use a bounded score function and leverage based weights to achieve better robustness moreover the proposed estimators have desired large sample properties including consistency and oracle property finally monte carlo simulation studies are conducted to investigate the robustness and efficiency of the proposed method under different contaminations

shortest paths help solve geometric optimization problems in planar regions the goal of this paper is to show that the concept of the shortest path inside a polygonal region contributes to the design of efficient algorithms for certain geometric optimization problems involving simple polygons computing optimum separators maximum area or perimeter inscribed triangles a minimum area circumscribed concave quadrilateral or a maximum area contained triangle the structure for the algorithms presented is as follows a decompose the initial problem into a low degree polynomial number of optimization problems b solve each individual subproblem in constant time using standard methods of calculus basic methods of numerical analysis or linear programming these same optimization techniques can be applied to splinegons curved polygons first a decomposition technique for curved polygons is developed this technique is substituted for triangulation in creating equally efficient curved versions of the algorithms for the shortest path tree ray shooting and two point shortest path

gee analysis of clustered binary data with diverging number of covariates clustered binary data with a large number of covariates have become increasingly common in many scientific disciplines this paper develops an asymptotic theory for generalized estimating equations gee analysis of clustered binary data when the number of covariates grows to infinity with the number of clusters in this large n diverging p framework we provide appropriate regularity conditions and establish the existence consistency and asymptotic normality of the gee estimator furthermore we prove that the sandwich variance formula remains valid even when the working correlation matrix is misspecified the use of the sandwich variance formula leads to an asymptotically valid confidence interval and wald test for an estimable linear combination of the unknown parameters the accuracy of the asymptotic approximation is examined via numerical simulations we also discuss the diverging p asymptotic theory for general gee the results in this paper extend the recent elegant work of xie and yang ann statist 31 2003 310 347 and balan and schiopu kratina ann statist 32 2005 522 541 in the fixed p setting

nonparametric estimation and testing of fixed effects panel data models in this paper we consider the problem of estimating nonparametric panel data models with fixed effects we introduce an iterative nonparametric kernel estimator we also extend the estimation method to the case of a semiparametric partially linear fixed effects model to determine whether a parametric semiparametric or nonparametric model is appropriate we propose test statistics to test between the three alternatives in practice we further propose a test statistic for testing the null hypothesis of random effects against fixed effects in a nonparametric panel data regression model simulations are used to examine the finite sample performance of the proposed estimators and the test statistics

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

empirical dynamics for longitudinal data we demonstrate that the processes underlying on line auction price bids and many other longitudinal data can be represented by an empirical first order stochastic ordinary differential equation with time varying coefficients and a smooth drift process this equation may be empirically obtained from longitudinal observations for a sample of subjects and does not presuppose specific knowledge of the underlying processes for the nonparametric estimation of the components of the differential equation it suffices to have available sparsely observed longitudinal measurements which may be noisy and are generated by underlying smooth random trajectories for each subject or experimental unit in the sample the drift process that drives the equation determines how closely individual process trajectories follow a deterministic approximation of the differential equation we provide estimates for trajectories and especially the variance function of the drift process at each fixed time point the proposed empirical dynamic model implies a decomposition of the derivative of the process underlying the longitudinal data into a component explained by a linear component determined by a varying coefficient function dynamic equation and an orthogonal complement that corresponds to the drift process an enhanced perturbation result enables us to obtain improved asymptotic convergence rates for eigenfunction derivative estimation and consistency for the varying coefficient function and the components of the drift process we illustrate the differential equation with an application to the dynamics of on line auction data