semiparametric nonlinear mixed effects models and their applications nonlinear mixed effects models nlmms and self modeling nonlinear regression semor models are often used to fit repeated measures data they use a common function shared by all subjects to model variation within each subject and some fixed and or random parameters to model variation between subjects the parametric nlmm may be too restrictive and the semiparametric semor model ignores correlations within each subject in this article we propose a class of semiparametric nonlinear mixed effects models snmms that extend nlmms semor models and many other existing models in a natural way a snmm assumes that the mean function depends on some parameters and nonparametric functions the parameters provide an interpretable data summary the nonparametric functions provide flexibility to allow the data to decide some unknown or uncertain components such as the shape of the mean response over time a second stage model with fixed and random effects is used to model the parameters smoothing splines are us

smoothing splines for longitudinal data in a longitudinal data model with fixed and random effects polynomials are used to model the fixed effects and smoothing polynomial splines are used to model the within subject random effect curves the splines are generated by modelling the data for each subject as observations of an integrated random walk with observational error the initial conditions for each subject s deviation from the fixed effect curve are assumed to have zero mean and arbitrary covariance matrix which is estimated by maximum likelihood producing an empirical bayes estimate this is in contrast to modelling a single curve using a diffuse prior an example is presented using unbalanced longitudinal data from a pilot study in breast cancer patients

low rank scale invariant tensor product smooths for generalized additive mixed models summary a general method for constructing low rank tensor product smooths for use as components of generalized additive models or generalized additive mixed models is presented a penalized regression approach is adopted in which tensor product smooths of several variables are constructed from smooths of each variable separately these marginal smooths being represented using a low rank basis with an associated quadratic wiggliness penalty the smooths offer several advantages i they have one wiggliness penalty per covariate and are hence invariant to linear rescaling of covariates making them useful when there is no natural way to scale covariates relative to each other ii they have a useful tuneable range of smoothness unlike single penalty tensor product smooths that are scale invariant iii the relatively low rank of the smooths means that they are computationally efficient iv the penalties on the smooths are easily interpretable in terms of function shape v the smooths can be generated completely automatically from any marginal smoothing bases and associated quadratic penalties giving the modeler considerable flexibility to choose the basis penalty combination most appropriate to each modeling task and vi the smooths can easily be written as components of a standard linear or generalized linear mixed model allowing them to be used as components of the rich family of such models implemented in standard software and to take advantage of the efficient and stable computational methods that have been developed for such models a small simulation study shows that the methods can compare favorably with recently developed smoothing spline anova methods

smoothing spline anova frailty model for recurrent event data summary gap time hazard estimation is of particular interest in recurrent event data this article proposes a fully nonparametric approach for estimating the gap time hazard smoothing spline analysis of variance anova decompositions are used to model the log gap time hazard as a joint function of gap time and covariates and general frailty is introduced to account for between subject heterogeneity and within subject correlation we estimate the nonparametric gap time hazard function and parameters in the frailty distribution using a combination of the newton raphson procedure the stochastic approximation algorithm saa and the markov chain monte carlo mcmc method the convergence of the algorithm is guaranteed by decreasing the step size of parameter update and or increasing the mcmc sample size along iterations model selection procedure is also developed to identify negligible components in a functional anova decomposition of the log gap time hazard we evaluate the proposed methods with simulation studies and illustrate its use through the analysis of bladder tumor data

stable and efficient multiple smoothing parameter estimation for generalized additive models representation of generalized additive models gam s using penalized regression splines allows gam s to be employed in a straightforward manner using penalized regression methods not only is inference facilitated by this approach but it is also possible to integrate model selection in the form of smoothing parameter selection into model fitting in a computationally efficient manner using well founded criteria such as generalized cross validation the current fitting and smoothing parameter selection methods for such models are usually effective but do not provide the level of numerical stability to which users of linear regression packages for example are accustomed in particular the existing methods cannot deal adequately with numerical rank deficiency of the gam fitting problem and it is not straightforward to produce methods that can do so given that the degree of rank deficiency can be smoothing parameter dependent in addition models with the potential flexibility of gam s can also present

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

the application of bifurcation method to a higher order kdv equation abstract bifurcation method of dynamical systems is employed to investigate bifurcation of solitary waves in the higher order kdv equation u t au n u x u xxx 0 where n 1 and a r numbers of solitary waves are given for each parameter condition under some parameter conditions explicit solitary wave solutions are obtained specially some new solitary wave solutions are found for kdv or mkdv equation

fuzzy smooth preproximity spaces abstract the concept of a fuzzy smooth preproximity space is introduced and studied also some particular constructions of fuzzy smooth preproximity are given a natural link is established between this concept and the concept of fuzzy pretopological spaces and fuzzy preuniform spaces

smoothing spline anova for multivariate bernoulli observations with application to ophthalmology data we combine a smoothing spline analysis of variance ss anova model and a log linear model to build a partly flexible model for multivariate bernoulli data the joint distribution conditioning on the predictor variables is estimated the log odds ratio is used to measure the association between outcome variables a numerical scheme based on the block one step successive over relaxation sor newton ralphson algorithm is proposed to obtain an approximate solution for the variational problem we extend the generalized approximate cross validation gacv and the randomized gacv for choosing smoothing parameters to the case of multivariate bernoulli responses the randomized version is fast and stable to compute and is used to adaptively select smoothing parameters in each block onestep sor iteration approximate bayesian confidence intervals are obtained for the flexible estimates of the conditional logit functions simulation studies are conducted to check the performance of the proposed method using the com

using local correlation in kernel based smoothers for dependent data nous considerons le probleme general de lisser des donnees correlees afin d obtenir une estimation non parametrique d une fonction quand un nombre aleatoire mais borne de mesures est disponible pour chaque sujet nous proposons une simple extension du lissage par regression polynomiale qui conserve les proprietes asymptotiques du modele de travail d independance tout en reduisant le biais conditionnel et la variance pour des tailles d echantillons courantes comme le montrent des calculs exacts dans certains modeles particuliers nous illustrons notre methode par le lissage de donnees longitudinales de declin fonctionnel chez 100 patients atteints de la maladie de huntington on montre que la classe des polynomes locaux d estimation par noyaux precedemment consideres dans la litterature utilise la structure de correlation de maniere apparemment non optimale ce qui explique pourquoi quelques tentatives anterieures d incorporer la correlation sont asymptotiquement inferieures a l hypothese de travail d independance

fuzzy proximities and totally bounded fuzzy uniformities after the classical papers of zadeh 181 and chang 3 many concepts of general topology have been extended to fuzzy set theory in this paper we are interested to develop the study of fuzzy uniformities fuzzy proximities and of the connexions between such structures fuzzy uniformities have been introduced by lowen in 9 and with slight modifications in lo and by hutton in 5 the two approaches are quite different however the one proposed by hutton seems to suit much better to fuzzy set theory also because it allows to generalize a lot of results in the most proper way therefore in this paper we shall deal with hutton fuzzy uniformities the concept of fuzzy proximity used up to now see e g 7 8 15 1 is quite unsatisfactory indeed its fuzzyness is rather poor since these fuzzy proximities are in a canonical l 1 correspondence with the usual proximities see remark 2 6 moreover the open sets of the induced topologies are crisp and though every lowen fuzzy uniformity induces a fuzzy proximity this correspondence cannot work well since the two structures do not give the same fuzzy topology for these reasons we propose a new definition of fuzzy proximity it differs from the old one only in axiom p5 in short we could say that we privilege complementation with respect to intersection an agreement between the two operations being problematic in fuzzy set theory we point out that as a consequence a fuzzy set may be far from itself however this fact ought not to amaze anyone since it may happen just for pale sets which in a certain sense resemble the empty set nevertheless this modification enables us to associate a topology in a completely different way moreover every fuzzy uniformity induces a fuzzy proximity and vice versa we succeed to construct a fuzzy uniformity starting with a given fuzzy proximity and the induced topologies do not change at any step this implies that the topologies which admit a fuzzy proximity are exactly the completely regular ones moreover we prove that there exists a l l correspondence between fuzzy proximity spaces and a

explicit exact solutions for new general two dimensional kdv type and two dimensional kdv burgers type equations with nonlinear terms of any order in this paper we have improved the tanh method by means of a proper transformation and a general ansatz applying the improved method and direct assumption method with symbolic computation we consider two kinds of equations general two dimensional kdv type equations with nonlinear terms

bayesian hierarchical spatially correlated functional data analysis with application to colon carcinogenesis in this article we present new methods to analyze data from an experiment using rodent models to investigate the role of p27 an important cell cycle mediator in early colon carcinogenesis the responses modeled here are essentially functions nested within a two stage hierarchy standard functional data analysis literature focuses on a single stage of hierarchy and conditionally independent functions with near white noise however in our experiment there is substantial biological motivation for the existence of spatial correlation among the functions which arise from the locations of biological structures called colonic crypts this possible functional correlation is a phenomenon we term crypt signaling thus as a point of general methodology we require an analysis that allows for functions to be correlated at the deepest level of the hierarchy our approach is fully bayesian and uses markov chain monte carlo methods for inference and estimation analysis of this data set gives new insights into the structure of p27 expression in early colon carcinogenesis and suggests the existence of significant crypt signaling our methodology uses regression splines and because of the hierarchical nature of the data dimension reduction of the covariance matrix of the spline coefficients is important we suggest simple methods for overcoming this problem

functional mixed effects models in this article a new class of functional models in which smoothing splines are used to model fixed effects as well as random effects is introduced the linear mixed effects models are extended to nonparametric mixed effects models by introducing functional random effects which are modeled as realizations of zero mean stochastic processes the fixed functional effects and the random functional effects are modeled in the same functional space which guarantee the population average and subject specific curves have the same smoothness property these models inherit the flexibility of the linear mixed effects models in handling complex designs and correlation structures can include continuous covariates as well as dummy factors in both the fixed or random design matrices and include the nested curves models as special cases two estimation procedures are proposed the first estimation procedure exploits the connection between linear mixed effects models and smoothing splines and can be fitted using existing software the second procedure is a sequential estimation procedure using kalman filtering this algorithm avoids inversion of large dimensional matrices and therefore can be applied to large data sets a generalized maximum likelihood gml ratio test is proposed for inference and model selection an application to comparison of cortisol profiles is used as an illustration

fuzzy proximity spaces redefined abstract we use the concept l quasi coincident in fuzzy set theory to redefine l fuzzy proximity space and we study the following problems proximity of l fuzzy normal spaces l fuzzy filters proximity neighborhoods and the l fuzzy topology induced by the l fuzzy proximity

a flexible model for human circadian rhythms many hormones and other physiological processes vary in a circadian pattern although a sine cosine function can be used to model these patterns this functional form is not appropriate when there is asymmetry between the peak and nadir phases in this paper we describe a semiparametric periodic spline function that can be fit to circadian rhythms the model includes both phase and amplitude so that the time and the magnitude of the peak or nadir can be estimated we also describe tests of fit for components in the model data from an experiment to study immunological responses in humans are used to demonstrate the methods

wavelet based functional mixed models increasingly scientific studies yield functional data in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid we present new methodology that generalizes the linear mixed model to the functional mixed model framework with model fitting done by using a bayesian wavelet based approach this method is flexible allowing functions of arbitrary form and the full range of fixed effects structures and between curve covariance structures that are available in the mixed model framework it yields nonparametric estimates of the fixed and random effects functions as well as the various between curve and within curve covariance matrices the functional fixed effects are adaptively regularized as a result of the non linear shrinkage prior that is imposed on the fixed effects wavelet coefficients and the random effect functions experience a form of adaptive regularization because of the separately estimated variance components for each wavelet coefficient because we have posterior samples for all model quantities we can perform pointwise or joint bayesian inference or prediction on the quantities of the model the adaptiveness of the method makes it especially appropriate for modelling irregular functional data that are characterized by numerous local features like peaks

l fuzzy smirnov compactifications in this paper we get the pointwise characterization of the l fuzzy topology induced by an l fuzzy proximity space and study some important properties of l fuzzy proximity induced spaces also we discuss the n compactness separated relations and separation axioms of l fuzzy proximity spaces on the base of the method of induced spaces and above conclusions we establish the l fuzzy smirnov compactification and construct an example for l fuzzy smirnov compactifications

mixed effects smoothing spline analysis of variance we propose a general family of nonparametric mixed effects models smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function the random effects are generic and are modelled parametrically by assuming that the covariance function depends on a parsimonious set of parameters these parameters and the smoothing parameter are estimated simultaneously by the generalized maximum likelihood method we derive a connection between a nonparametric mixed effects model and a linear mixed effects model this connection suggests a way of fitting a nonparametric mixed effects model by using existing programs the classical two way mixed models and growth curve models are used as examples to demonstrate how to use smoothing spline analysis of variance decompositions to build nonparametric mixed effects models similarly to the classical analysis of variance components of these nonparametric mixed effects models can be interpreted as main effects and interactions the penalized likelihood estimates of the fixed effects in a two way mixed model are extensions of james stein shrinkage estimates to correlated observations in an example three nested nonparametric mixed effects models are fitted to a longitudinal data set

smoothing spline models with correlated random errors abstract spline smoothing techniques are commonly used to estimate the mean function in a nonparametric regression model their performances depend greatly on the choice of smoothing parameters many methods of selecting smoothing parameters such as generalized maximum likelihood gml generalized cross validation gcv and unbiased risk ubr have been developed under the assumption of independent observations they tend to underestimate smoothing parameters when data are correlated in this article i assume that observations are correlated and that the correlation matrix depends on a parsimonious set of parameters i extend the gml gcv and ubr methods to estimate the smoothing parameters and the correlation parameters simultaneously i also relate a smoothing spline model to three mixed effects models these relationships show that the smoothing spline estimates evaluated at design points are best linear unbiased prediction blup estimates and that the gml estimates of the smoothing parameters an

some new and general solutions to the compound kdv burgers system with nonlinear terms of any order abstract in this letter a new riccati equation expansion method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations the main idea of this method is to take full advantage of the solutions of the riccati equation to construct exact travelling wave solutions of nonlinear partial differential equations as a result some more generalized solutions which contain triangular periodic solutions exp function solutions and the soliton like solutions are obtained

on induced fuzzy topological spaces the concept of induced fuzzy topological spaces was introduced by weiss 11 subsequently lowen 2 31 defined two mappings o and i which established the relationship between fuzzy topological spaces and topological spaces and proved some deeper results on induced fuzzy topological spaces since then several other authors continued the investigation of such spaces in this paper we will use the decomposition theorem for fuzzy sets to simplify the proofs of some theorems due to lowen and discuss the closure and interior operators separability ci c and separation properties of induced fuzzy topological spaces

domain wall solutions of kdv like equations with higher order nonlinearity the author considers certain nonlinear partial differential equations which are korteweg de vries kdv like equations with higher order nonlinearity it is shown that these have kink domain wall solutions for particular values of the coefficients of the nonlinear terms the solutions are compared with the standard known solution of the lambda phi 2n field theories some conservation laws for these systems of equations are also given

testing for cubic smoothing splines under dependent data in most research on smoothing splines the focus has been on estimation while inference especially hypothesis testing has received less attention by defining design matrices for fixed and random effects and the structure of the covariance matrices of random errors in an appropriate way the cubic smoothing spline admits a mixed model formulation which places this nonparametric smoother firmly in a parametric setting thus nonlinear curves can be included with random effects and random coefficients the smoothing parameter is the ratio of the random coefficient and error variances and tests for linear regression reduce to tests for zero random coefficient variances we propose an exact f test for the situation and investigate its performance in a real pine stem data set and by simulation experiments under certain conditions the suggested methods can also be applied when the data are dependent

a distribution free test of constant mean in linear mixed effects models we propose a distribution free procedure an analogy of the dip test in non parametric regression to test whether the means of responses are constant over time in repeated measures data unlike the existing tests the proposed procedure requires very minimal assumptions to the distributions of both random effects and errors we study the asymptotic reference distribution of the test statistic analytically and propose a permutation procedure to approximate the finite sample reference distribution the size and power of the proposed test are illustrated and compared with competitors through several simulation studies we find that it performs well for data of small sizes regardless of model specification finally we apply our test to a data example to compare the effect of fatigue in two different methods used for cardiopulmonary resuscitation

exact travelling wave solutions of the dissipative coupled korteweg de vries equation this paper employs the theory of planar dynamical systems and undetermined coefficient method to study travelling wave solutions of the dissipative coupled korteweg de vries equation the possible kink profile solitary wave solutions and approximate damped oscillatory solutions of the equation are obtained by using undetermined coefficient method error estimates indicate that the approximate solutions are meaningful

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

extension of the stein estimating procedure through the use of estimating functions abstract this article extends the stein method through the use of estimating functions godambe 1960 to address the simultaneous estimation of k population parameters 1 k in a mixed model setting the procedure generalizes the stein method by a allowing us to deal effectively with complications such as inequality of population variances that may arise in non gaussian mixed models b being appropriate for estimating i in populations of varying sizes and in particular populations of small sizes and c applying to situations where it cannot be assumed that the i s have unbiased estimators or even estimators of finite moment the focus of the article is on the quadratic variance function exponential family morris 1983b estimators for the parameters of the mixed model are developed in a regression model setting in which the i s are allowed to vary with a vector of covariates an application to incidence rates for the iceland breast cancer incidence data is presented for illustra

smoothing spline analysis of variance models a new tool for the analysis of cyclic biomechanical data cyclic biomechanical data are commonplace in orthopedic rehabilitation and sports research where the goal is to understand and compare biomechanical differences between experimental conditions and or subject populations a common approach to analyzing cyclic biomechanical data involves averaging the biomechanical signals across cycle replications and then comparing mean differences at specific points of the cycle this pointwise analysis approach ignores the functional nature of the data which can hinder one s ability to find subtle differences between experimental conditions and or subject populations to overcome this limitation we propose using mixed effects smoothing spline analysis of variance ssanova to analyze differences in cyclic biomechanical data the ssanova framework makes it possible to decompose the estimated function into the portion that is common across groups i e the average cycle ac and the portion that differs across groups i e the contrast cycle cc by partitioning the signal in such a manner we can obtain estimates of the cc differences ccds which are the functions directly describing group differences in the cyclic biomechanical data using both simulated and experimental data we illustrate the benefits of using ssanova models to analyze differences in noisy biomechanical gait signals collected from multiple locations joints of subjects participating in different experimental conditions using bayesian confidence intervals the ssanova results can be used in clinical and research settings to reliably quantify biomechanical differences between experimental conditions and or subject populations

the analysis of longitudinal data using mixed model l splines l splines are a large family of smoothing splines defined in terms of a linear differential operator this article develops l splines within the context of linear mixed models and uses the resulting mixed model l spline to analyze longitudinal data from a grassland experiment in the spirit of time series analysis a periodic mixed model l spline is developed which partitions data into a smooth periodic component plus smooth long term trend

semiparametric regression for periodic longitudinal hormone data from multiple menstrual cycles summary we consider semiparametric regression for periodic longitudinal data parametric fixed effects are used to model the covariate effects and a periodic nonparametric smooth function is used to model the time effect the within subject correlation is modeled using subject specific random effects and a random stochastic process with a periodic variance function we use maximum penalized likelihood to estimate the regression coefficients and the periodic nonparametric time function whose estimator is shown to be a periodic cubic smoothing spline we use restricted maximum likelihood to simultaneously estimate the smoothing parameter and the variance components we show that all model parameters can be easily obtained by fitting a linear mixed model a common problem in the analysis of longitudinal data is to compare the time profiles of two groups e g between treatment and placebo we develop a scaled chi squared test for the equality of two nonparametric time functions the proposed model and the test are illustrated by analyzing hormone data collected during two consecutive menstrual cycles and their performance is evaluated through simulations

inference for smooth curves in longitudinal data with application to an aids clinical trial we discuss a longitudinal study where data for many subjects are collected at irregular intervals the study is a randomized trial of hiv infected subjects and the response variable of interest is serum neopterin the mean of the outcome variable taken over patients in each treatment group is assumed to follow a smooth curve piecewise cubic polynomials with a moderate number of knots are used to model the curves a general parametric form is assumed for the covariance structure maximum penalized likelihood estimation is used to smooth the over parameterized curves statistical inference for the mean curves including confidence bands and hypothesis tests is discussed two approaches one using a bayesian interpretation of the penalized likelihood and the other based on the asymptotic distribution of the maximum penalized likelihood estimates are discussed and contrasted the properties of the confidence bands obtained from these two approaches are evaluated by examining their coverage rates in a simulation study

optimal smoothing in nonparametric mixed effect models mixed effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures in this article we study an approach to the nonparametric estimation of mixed effect models we consider models with parametric random effects and flexible fixed effects and employ the penalized least squares method to estimate the models the issue to be addressed is the selection of smoothing parameters through the generalized cross validation method which is shown to yield optimal smoothing for both real and latent random effects simulation studies are conducted to investigate the empirical performance of generalized cross validation in the context real data examples are presented to demonstrate the applications of the methodology

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

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

simple fitting of subject specific curves for longitudinal data we present a simple semiparametric model for fitting subject specific curves for longitudinal data individual curves are modelled as penalized splines with random coefficients this model has a mixed model representation and it is easily implemented in standard statistical software we conduct an analysis of the long term effect of radiation therapy on the height of children suffering from acute lymphoblastic leukaemia using penalized splines in the framework of semiparametric mixed effects models the analysis revealed significant differences between therapies and showed that the growth rate of girls in the study cannot be fully explained by the group average curve and that individual curves are necessary to reflect the individual response to treatment we also show how to implement these models in s plus and r in the appendix

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

variable selection for semiparametric mixed models in longitudinal studies we propose a double penalized likelihood approach for simultaneous model selection and estimation in semiparametric mixed models for longitudinal data two types of penalties are jointly imposed on the ordinary log likelihood the roughness penalty on the nonparametric baseline function and a nonconcave shrinkage penalty on linear coefficients to achieve model sparsity compared to existing estimation equation based approaches our procedure provides valid inference for data with missing at random and will be more efficient if the specified model is correct another advantage of the new procedure is its easy computation for both regression components and variance parameters we show that the double penalized problem can be conveniently reformulated into a linear mixed model framework so that existing software can be directly used to implement our method for the purpose of model inference we derive both frequentist and bayesian variance estimation for estimated parametric and nonparametric components simulation is used to evaluate and compare the performance of our method to the existing ones we then apply the new method to a real data set from a lactation study

a bayesian model for sparse functional data we propose a method for analyzing data which consist of curves on multiple individuals i e longitudinal or functional data we use a bayesian model where curves are expressed as linear combinations of b splines with random coefficients the curves are estimated as posterior means obtained via markov chain monte carlo mcmc methods which automatically select the local level of smoothing the method is applicable to situations where curves are sampled sparsely and or at irregular time points we construct posterior credible intervals for the mean curve and for the individual curves this methodology provides unified efficient and flexible means for smoothing functional data

reduced rank mixed effects models for spatially correlated hierarchical functional data hierarchical functional data are widely seen in complex studies where subunits are nested within units which in turn are nested within treatment groups we propose a general framework of functional mixed effects model for such data within unit and within subunit variations are modeled through two separate sets of principal components the subunit level functions are allowed to be correlated penalized splines are used to model both the mean functions and the principal components functions where roughness penalties are used to regularize the spline fit an expectation maximization em algorithm is developed to fit the model while the specific covariance structure of the model is utilized for computational efficiency to avoid storage and inversion of large matrices our dimension reduction with principal components provides an effective solution to the difficult tasks of modeling the covariance kernel of a random function and modeling the correlation between functions the proposed methodology is illus

uniformity and proximity of l fuzzy topological spaces abstract in 3 4 a k katsaras defined fuzzy proximity spaces and studied some of their properties in 5 we used the concept l quasi coincident in fuzzy set theory and fuzzy topology to redefine l fuzzy proximity space in such a way that it takes fuzzy proximity space as a special case also some pathologic properties were avoided for example proposition 2 1 in 4 in 5 we proved also some results analogous to those that hold for ordinary proximity spaces in this paper we continue the study of l fuzzy proximity spaces we shall prove that the partially ordered set x of all l fuzzy proximities on x is a complete lattice theorem 2 5 and we shall discuss the relationship between l fuzzy uniform spaces and l fuzzy proximity spaces theorem 3 4 4 1

fsem functional structural equation models for twin functional data the aim of this article is to develop a novel class of functional structural equation models fsems for dissecting functional genetic and environmental effects on twin functional data while chara

smoothing spline anova for exponential families with application to the wisconsin epidemiological study of diabetic retinopathy the 1994 neyman memorial lecture let y i i 1 n be independent observations with the density of y i of the form h y i f i exp y i f i b f i c y i where b and c are given functions and b is twice continuously differentiable and bounded away from 0 let i t f t i where t t 1 t d t 1 t d t the t are measurable spaces of rather general form and f is an unknown function on t with some assumed smoothness properties given y i t i i 1 n it is desired to estimate f t for t in some region of interest contained in t we develop the fitting of smoothing spline anova models to this data of the form f t c f t f t t the components of the decomposition satisfy side conditions which generalize the usual side conditions for parametric anova the estimate of f is obtained as the minimizer in an appropriate function space of l y f j f j f where l y f is the negative log likelihood of y y 1 y n given f the j j are quadratic penalty functionals and the anova decomposition is terminated in some manner there are five major parts required to turn this program into a practical data analysis tool 1 methods for deciding which terms in the anova decomposition to include model selection 2 methods for choosing good values of the smoothing parameters 3 methods for making confidence statements concerning the estimate 4 numerical algorithms for the calculations and finally 5 public software in this paper we carry out this program relying on earlier work and filling in important gaps the overall scheme is applied to bernoulli data from the wisconsin epidemiologic study of diabetic retinopathy to model the risk of progression of diabetic retinopathy as a function of glycosylated hemoglobin duration of diabetes and body mass index it is believed that the results have wide practical application to the analysis of data from large epidemiologic studies

high dimensional odes coupled with mixed effects modeling techniques for dynamic gene regulatory network identification gene regulation is a complicated process the interaction of many genes and their products forms an intricate biological network identification of this dynamic network will help us understand the biological processes in a systematic way however the construction of a dynamic network is very challenging for a high dimensional system in this article we propose to use a set of ordinary differential equations ode coupled with dimensional reduction by clustering and mixed effects modeling techniques to model the dynamic gene regulatory network grn the ode models allow us to quantify both positive and negative gene regulation as well as feedback effects of genes in a functional module on the dynamic expression changes of genes in another functional module which results in a directed graph network a five step procedure clustering smoothing regulation identification parameter estimates refining and function enrichment analysis csief is developed to identify the ode based dynamic grn in the prop

inference in generalized additive mixed modelsby using smoothing splines generalized additive mixed models are proposed for overdispersed and correlated data which arise frequently in studies involving clustered hierarchical and spatial designs this class of models allows flexible functional dependence of an outcome variable on covariates by using nonparametric regression while accounting for correlation between observations by using random effects we estimate nonparametric functions by using smoothing splines and jointly estimate smoothing parameters and variance components by using marginal quasi likelihood because numerical integration is often required by maximizing the objective functions double penalized quasi likelihood is proposed to make approximate inference frequentist and bayesian inferences are compared a key feature of the method proposed is that it allows us to make systematic inference on all model components within a unified parametric mixed model framework and can be easily implemented by fitting a working generalized linear mixed model by using existing statistical software a bias correction procedure is also proposed to improve the performance of double penalized quasi likelihood for sparse data we illustrate the method with an application to infectious disease data and we evaluate its performance through simulation

some asymptotic results on generalized penalized spline smoothing the paper discusses asymptotic properties of penalized spline smoothing if the spline basis increases with the sample size the proof is provided in a generalized smoothing model allowing for non normal responses the results are extended in two ways first assuming the spline coefficients to be a priori normally distributed links the smoothing framework to generalized linear mixed models we consider the asymptotic rates such that the laplace approximation is justified and the resulting fits in the mixed model correspond to penalized spline estimates secondly we make use of a fully bayesian viewpoint by imposing an a priori distribution on all parameters and coefficients we argue that with the postulated rates at which the spline basis dimension increases with the sample size the posterior distribution of the spline coefficients is approximately normal the validity of this result is investigated in finite samples by comparing markov chain monte carlo results with their asymptotic approximation in a simulation study

order homomorphisms on fuzzes abstract in this paper basic properties of the concept of order homomorphisms on fuzzes 4 which is a proper generalization of the concept of fuzz functions 1 are studied conditions for fuzz functions to be functions of zadeh s type are obtained moreover the concepts of continuous closed and open order homomorphisms are introduced and studied

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

traveling waves to a burgers korteweg de vries type equation with higher order nonlinearities abstract in this paper first we survey some recent advances in the study of traveling wave solutions to the burgers korteweg de vries equation and some comments are given then we study a burgers korteweg de vries type equation with higher order nonlinearities a qualitative analysis to a two dimensional autonomous system which is equivalent to the burgers kdv type equation is presented and indicates that under certain conditions the burgers korteweg de vries type equation has neither nontrivial bell profile solitary waves nor periodic waves finally a solitary wave solution is obtained by means of the first integral method which is based on the ring theory of commutative algebra

a signal extraction approach to modeling hormone time series with pulses and a changing baseline abstract hormones serve as regulating signals for many biological processes in recent years it was determined that many hormones are secreted in a pulsatile manner and that the pulsatile secretion pattern in addition to the absolute concentration level is important in regulating biological processes consequently it is necessary to characterize the latent secretion patterns from measurements of concentration levels the characterization is complicated by the presence of a biological circadian rhythm when hormone concentrations are plotted over time the resultant time series usually exhibits occasional short rises superimposed on a slowly changing baseline this is a result of a mixture of pulsatile secretions and a circadian rhythm in this article we present a signal extraction approach to model simultaneously a slowly changing component and a pulsatile component of a time series a smoothing spline is used to model the baseline and a multiprocess dynamic linear model is used to model the pulsati

local polynomial mixed effects models for longitudinal data we consider a nonparametric mixed effects model yi tij tij vi tij i tij j 1 2 ni i 1 2 n for longitudinal data we propose combining local polynomial kernel regression and linear mixed effects lme model techniques to estimate both fixedeffects population curve t and random effects curves vi t the resulting estimator called the local polynomial lme llme estimator takes the local correlation structure of the longitudinal data into account naturally we also propose new bandwidth selection strategies for estimating t and vi t simulation studies show that our estimator for t is superior to the existing estimators in the sense of mean squared errors the asymptotic bias variance mean squared errors and asymptotic normality are established for the llme estimators of t when ni is bounded and n tends to infinity our llme estimator converges in a standard nonparametric rate and the asymptotic bias and variance are essentially the same as those of the kernel generalized esti

inference in smoothing spline analysis of variance summary smoothing spline analysis of variance decomposes a multivariate function into additive components this decomposition not only provides an efficient way to model a multivariate function but also leads to meaningful inference by testing whether a certain component equals 0 no formal procedure is yet available to test such a hypothesis we propose an asymptotic method based on the likelihood ratio to test whether a functional component is 0 this test allows us to choose an optimal model and to compare groups of curves we first develop the general theory by exploiting the connection between mixed effects models and smoothing splines we then apply this to compare two groups of curves and to select an optimal model in a two dimensional problem a small simulation is used to assess the finite sample performance of the likelihood ratio test