marginal longitudinal nonparametric regression locality and efficiency of spline and kernel methods we consider nonparametric regression in a longitudinal marginal model of generalized estimating equation gee type with a time varying covariate in the situation where the number of observations per subject is finite and the number of subjects is large in such models the basic shape of the regression function is affected only by the covariate values and not otherwise by the ordering of the observations two methods of estimating the nonparametric function can be considered kernel methods and spline methods recently surprising evidence has emerged suggesting that for kernel methods previously proposed in the literature it is generally asymptotically preferable to ignore the correlation structure in our marginal model and instead assume that the data are independent that is working independence in the gee jargon as seen through equivalent kernel results in univariate independent data problems splines and kernels have similar behavior smoothing splines are equivalent to kernel regression with a s

local asymptotics for polynomial spline regression in this paper we develop a general theory of local asymptotics for least squares estimates over polynomial spline spaces in a regression problem the polynomial spline spaces we consider include univariate splines tensor product splines and bivariate or multivariate splines on triangulations we establish asymptotic normality of the estimate and study the magnitude of the bias due to spline approximation the asymptotic normality holds uniformly over the points where the regression function is to be estimated and uniformly over a broad class of design densities error distributions and regression functions the bias is controlled by the minimum l norm of the error when the target regression function is approximated by a function in the polynomial spline space that is used to define the estimate the control of bias relies on the stability in l norm of l 2 projections onto polynomial spline spaces asymptotic normality of least squares estimates over polynomial or trigonometric polynomial spaces is also treated by the general theory in addition a preliminary analysis of additive models is provided

model averaging based on leave subject out cross validation this paper develops a frequentist model averaging method based on the leave subject out cross validation this method is applicable not only to averaging longitudinal data models but also to averaging time series models which can have heteroscedastic errors the resulting model averaging estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors both simulation study and empirical example show the superiority of the proposed estimators over their competitors

quantitative characterization of spatiotemporal patterns abstract disorderness of spatiotemporal patterns which are obtained by discrete maps and partial differential equations is characterized quantitatively this characterization is very generic and can be used for almost all spatiotemporal patterns as examples the coupled map lattices that consist of the henon map and one of the nonlinear partial differential equations are studied

splines as local smoothers a smoothing spline is a nonparametric curve estimate that is defined as the solution to a minimization problem one problem with this representation is that it obscures the fact that a spline like most other nonparametric estimates is a local weighted average of the observed data this property has been used extensively to study the limiting properties of kernel estimates and it is advantageous to apply similar techniques to spline estimates although equivalent kernels have been identified for a smoothing spline these functions are either not accurate enough for asymptotic approximations or are restricted to equally spaced points this paper extends this previous work to understand a spline estimate s local properties it is shown that the absolute value of the spline weight function decreases exponentially away from its center this result is not asymptotic the only requirement is that the empirical distribution of the observation points be sufficiently close to a continuous distribution with a strictly positive density function these bounds are used to derive the asymptotic form for the bias and variance of a first order smoothing spline estimate the arguments leading to this result can be easily extended to higher order splines

periodicity in trajectories of chaotic systems in phase space abstract we have extracted various time correlations in trajectories of chaotic systems in phase space the time correlations in trajectories are calculated according to their local lyapunov exponents the time series is decomposed into the nonchotic component and the chaotic component the order q power spectrum is used to extract such various time correlations we have investigated the logistic map and the conservative standard map especially in the conservative standard map a trajectory is shown to have both periodic characteristics and chaotic characteristics

robust estimation in generalized partial linear models for clustered data in this article we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear models gplms for longitudinal data or clustered data in general we approximate the nonparametric function in the gplm by a regression spline and use bounded scores and leverage based weights in the estimating equation to achieve robustness against outliers we show that the regression spline approach avoids some of the intricacies associated with the profile kernel method and that robust estimation and inference can be carried out operationally as if a generalized linear model were used

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

spline smoothing the equivalent variable kernel method on considere une approche spline pour la regression non parametrique et l estimation de courbe on montre que dans un certain sens le lissage spline correspond approximativement au lissage par une methode du noyau avec une largeur de bande dependant de la densite locale des points du plan de regression

proper orthogonal decomposition method for analysis of nonlinear panel flutter with thermal effects in supersonic flow abstract the proper orthogonal decomposition pod method for analysis of nonlinear panel flutter subjected to supersonic flow is presented optimal pod modes are extracted from a chaotic galerkin mode responses the aeroelastic equations of motion are constructed using von karman plate theory first order piston theory and quasi steady thermal stress theory a simply supported plate with thermal loads from a uniformly distributed temperature is considered many types of panel behaviors including stable flat dynamically stable buckled limit cycle oscillation nonharmonic periodic motion quasi periodic motion and chaotic motion are observed our primary focus is on chaos and the route to chaos it is found that a sudden transition from the buckled state to chaos occurs time history phase portrait poincare map bifurcation diagram and lyapunov exponent are employed to study chaos the pod chaotic results obtained are compared with the traditional galerkin solutions it is shown that the pod method can obtain accurate chaotic solutions using fewer modes and less computational effort than the galerkin mode approach additionally the pod method converges faster in the analysis of chaotic transients effects of length to width ratios and thermal loads are presented it is found that a smaller width for fixed length will produce more stable flutter response while the thermal loads degrade the flutter boundary and result in a more complex evolution of dynamic motions the numerical simulations show that the robustness of the pod modes depends on the dynamic pressure but not on temperature

gibbs measures and power spectra for type i intermittent maps abstract gibbs measures of dynamical systems are investigated using the corresponding correlation function and power spectrum the method is shown to be equivalent to the concept of order q power spectra which has been developed previously a technique for the computation of these spectra is presented as an application we specially focus on the treatment of type i intermittent model maps and investigate their phase transition in the vicinity of the phase transition point the order q power spectra are shown to obey some typical scaling relation which is captured neither by the topological pressure nor by the ordinary power spectrum

point light source estimation from two images and its limits in this paper the performance of parameter estimation of a single static distant point light source from two video images is analyzed in terms of estimation theory the illumination parameters are the intensity and direction of the light source in the first part of this paper estimators from the literature are reviewed most recent estimators evaluate as input data two video images as well as the 3d shape and the 3d motion of the visible moving objects in the second part of the paper the performance of these recent methods is analyzed the input data to estimation as well as the inherent input data errors are described by a stochastic observation model based on this model the performance is analyzed regarding the cramer rao theoretical lower bound of estimation error variances the bound is derived for a variety of cases of scene illumination object motion and errors in input data for simplification purpose the bound is valid only for object motions with the rotation axis lying in the image plane the analysis shows in which cases which estimation accuracy can be expected with current methods finally a comparison of the bound with one of the recent estimators shows that recent estimators are suboptimal in case of errors in the 3d shape of the objects in future work the stochastic observation model presented in this paper can be used to improve illumination estimation

fluctuation of mean lyapunov exponent for turbulence abstract lyapunov exponent for the systems described by the complex ginzburg landau equation is studied through its statistics the probability distribution function for the finite time average lyapunov exponent is given its functional form is the same as the systems described by the kuramoto sivashinsky equation that expresses the weak turbulence it is predicted that many kinds of turbulence have the same characteristics concerning their statistics of lyapunov exponent

nonlinear dynamics and chaos in coupled shape memory oscillators shape memory and pseudoelastic effects are thermomechanical phenomena associated with martensitic phase transformations presented by shape memory alloys this contribution concerns with the dynamical response of coupled shape memory oscillators equations of motion are formulated by assuming a polynomial constitutive model to describe the restitution force of the oscillators and since they are associated with a five dimensional system the analysis is performed by splitting the state space in subspaces free and forced vibrations are analyzed showing different kinds of responses periodic quasi periodic chaos and hyperchaos are all possible in this system numerical investigations show interesting and complex behaviors dynamical jumps in free vibration and amplitude variation when temperature characteristics are changed are some examples this article also shown some characteristics related to chaos hyperchaos transition 2003 elsevier ltd all rights reserved

quantitative characterization of spatiotemporal chaos abstract in this paper one way to characterize spatiotemporal chaos is shown a coupled map lattice is used as a model for the spatiotemporal chaos the local expansion rate is defined for the coupled map lattice in the extension of the low dimensional temporal chaos it is shown that the local expansion rate is closely related to the spatiotemporal pattern of the spatiotemporal chaos the thermodynamic formalism is applied to the local expansion rate the thermodynamic functions describing fluctuations of the local expansion rate are shown the spatiotemporal pattern that fluctuates is shown at the same time it is shown clearly that the thermodynamic functions characterize the spatiotemporal chaos

a penalized spline approach to functional mixed effects model analysis summary in this work we propose penalized spline based methods for functional mixed effects models with varying coefficients we decompose longitudinal outcomes as a sum of several terms a population mean function covariates with time varying coefficients functional subject specific random effects and residual measurement error processes using penalized splines we propose nonparametric estimation of the population mean function varying coefficient random subject specific curves and the associated covariance function which represents between subject variation and the variance function of the residual measurement errors which represents within subject variation proposed methods offer flexible estimation of both the population level and subject level curves in addition decomposing variability of the outcomes as a between subject and a within subject source is useful in identifying the dominant variance component therefore optimally model a covariance function we use a likelihood based method to select multiple smoothing parameters furthermore we study the asymptotics of the baseline p spline estimator with longitudinal data we conduct simulation studies to investigate performance of the proposed methods the benefit of the between and within subject covariance decomposition is illustrated through an analysis of berkeley growth data where we identified clearly distinct patterns of the between and within subject covariance functions of children s heights we also apply the proposed methods to estimate the effect of anti hypertensive treatment from the framingham heart study data

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

self similar fluctuation and large deviation statistics in the shell model of turbulence both static and dynamic multiscalings of fluctuations of energy flux and energy dissipation rate in the gledzer ohkitani yamada goy shell model of turbulence are numerically investigated we compute the large deviation rate function of energy flux not only in the inertial range ir but also around the crossover between the inertial range and the dissipation range dr the rate function in ir exists to be concave which assures the applicability of the legendre transformation with the anomalous scaling exponents that have been investigated so far and turns out to be independent of the reynolds number on the contrary near the crossover scale an intermediate dissipation range imdr scaling is observed with the rate function in imdr which is accounted with the argument on dissipation scale fluctuation dominated by the energy flux fluctuation in the inertial range furthermore to study the difference between ir intermittency and dr intermittency we compute finite time averaged quantities of energy flux and energy dissipation rate and investigate their multiscaling behavior the difference observed in terms of their dynamic multiscaling is discussed

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

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

pattern dynamics in spatiotemporal chaos pattern selection diffusion of defect and pattern competition intermettency abstract a class of coupled map lattices is investigated as a model for the spatiotemporal chaos as the parameters are changed phase transitions among the patterns are observed pattern selection through the chaotic motion of domain is observed chaos is suppressed by the selection selection of the zigzag pattern is studied where localized defects which separate the two anti phase domains are found they change chaotically in time and move randomly in space the diffusion of defect is related with its chaotic motion collapse of zigzag pattern and the defect turbulence are studied in connection with the crisis in high dimensional dynamical systems pattern selection with longer wavelengths is found in the stronger coupling regime transition from pattern selection phase to fully developed turbulence occurs via the intermittency selective flicker like noise and the pareto distribution of lifetime of pattern are observed at the intermittency regime for the quantitative characterization of each phase pattern distributions pattern transition matrix static and dynamical entropies lifetime distribution of pattern spatiotemporal power spectra and lyapunov spectra are calculated phase transition from the pattern selection to fully developed turbulence is investigated with the use of these quantifiers where some order parameters and critical indeces are introduced

quantitative characterization of spatiotemporal chaos ii dynamic aspects and anomalous scaling abstract spatiotemporal chaos is characterized quantitatively the characterization of a special model for coupled map lattices has been carried out successfully yet the dynamic aspects of this model are discussed in the present paper anomalous scaling of the probability distribution function for the local lyapunov exponent is shown the characteristics of one model for spatiotemporal chaos are given statistically

on the thermodynamic approach towards time series analysis a scheme is presented which allows for the computation of the topological pressure and power spectra associated with equilibrium measures from a given time series its convergence properties are demonstrated on numerical data sets obtained from the lozi and the henon map numerical evidence for sharp peaks in the power spectrum of the non hyperbolic phase is given and supported by estimates using periodic orbit expansions

characterization of a system described by kuramoto sivashinsky equation with lyapunov exponent abstract the characteristics of a system described by kuramoto sivashinsky equation are obtained through the statistics of a mean lyapunov exponent this mean lyapunov exponent takes large values and fluctuates large when the system is disordered temporally and spatially this behavior of the spatially extended system is captured clearly by the probability distribution function for the time averaged one of the mean lyapunov exponent

fluctuation of mean lyapunov exponent for a coupled map lattice model abstract fluctuation of mean lyapunov exponent for the coupled map lattice of logistic map is studied theorem by gallavotti and cohen for many particle systems is applied to the coupled map lattice model it is shown that the fluctuation of mean lyapunov exponent for the model satisfies the extended form of the fluctuation theorem by them the concept of the mean lyapunov exponent introduced in this paper turns out to be realistic as well as the one for many particle systems as a result the relation between mean lyapunov exponent and entropy production rate is derived

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

estimation in a semiparametric model for longitudinal data with unspecified dependence structure this paper considers an extension of m estimators in semiparametric models for independent observations to the case of longitudinal data we approximate the nonparametric function by a regression spline and any m estimation algorithm for the usual linear models can then be used to obtain consistent estimators of the model and valid largesample inferences about the regression parameters without any specification of the error distribution and the covariance structure included as special cases are the analysis of the conditional mean and median functions for longitudinal data

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

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

sum of positive lyapunov exponents for kuramoto sivashinsky equation abstract the sum of positive lyapunov exponents expresses the entropy loss of the systems under study the sum of positive lyapunov exponents for kuramoto sivashinsky equation is studied its time series behaves like the on off intermittency they have laminar and burst parts alternately it is remarkable that the system in turbulent state loses its entropy intermittency like

chaotifing a linear hyperbolic system of partial differential equations by means of nonlinear boundary reflection abstract we introduced a hyperbolic linear system of partial differential equations with nonlinear boundary conditions and proved strictly that it is chaotic under some simple assumptions this can be understood as chaotifing a hyperbolic linear system of partial differential equations with nonlinear boundary conditions several examples of simulation are presented the numerical simulation fits the theoretical analysis well

on the asymptotics of penalized splines summavry we study the asymptotic behaviour of penalized spline estimators in the univariate case we use b splines and a penalty is placed on mth order differences of the coefficients the number of knots is assumed to converge to infinity as the sample size increases we show that penalized splines behave similarly to nadaraya watson kernel estimators with equivalent kernels depending upon m the equivalent kernels we obtain for penalized splines are the same as those found by silverman for smoothing splines the asymptotic distribution of the penalized spline estimator is gaussian and we give simple expressions for the asymptotic mean and variance provided that it is fast enough the rate at which the number of knots converges to infinity does not affect the asymptotic distribution the optimal rate of convergence of the penalty parameter is given penalized splines are not design adaptive

estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates this is the publisher s final pdf the published article is copyrighted by the institute of mathematical statistics and can be found at http www imstat org aos

a wavelet method for the characterization of spatiotemporal patterns this paper introduces a wavelet based method for the characterization of spatiotemporal patterns based on the wavelet multiresolution analysis two wavelet indices multiscale accumulative density mad and multiscale accumulative change mac are proposed for the characterization of the dynamics of the spatiotemporal patterns both indices are constructed by using orthogonal wavelet projection operators the mad is a measure of the spatial complexity of a pattern at a given time whereas the mac characterizes the spatial complexity of instantaneous change of the spatiotemporal patterns at a given time the ratio of the mad indices between the lowest and the highest scales reflects the order of coherence in a pattern the time series of both mad and mac provide the dynamical information of morphological pattern evolutions numerical experiments based on the cahn hilliard equation indicate that the proposed method is efficient for quantitatively characterizing the dynamics of the spatiotemporal patterns 2002 published by elsevier science b v

statistics of phase turbulence ii abstract the system described by the kuramoto sivashinsky equation skse is shown to have a short and a long time regimes the probability distribution function pdf for the absolute value of the solution is subjected to different scaling laws in the two time regimes the local expansion rate ler and its two time correlation function are calculated the time regime where the correlation for the ler remains is shorter than the one for the absolute value of the solution for the skse the fluctuation in the ler becomes small as the damping constant is increased the pdf for the ler is also given in this paper

quantitative characterization of spatiotemporal patterns ii abstract disorderness of spatiotemporal patterns which are obtained by nonlinear partial differential equations is characterized quantitatively the mean lyapunov exponent for a nonlinear partial differential equation is given the local lyapunov exponent which is a finite time average of the mean lyapunov exponent is shown to have close relation to the spatiotemporal patterns it is suggested that the systems which are described by nonlinear partial differential equations are characterized statistically through the probability distribution function of the local lyapunov exponent

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

fluctuation of mean lyapunov exponent for kuramoto sivashinsky equation abstract the statistical aspect of lyapunov exponent for kuramoto sivashinsky equation is studied fluctuation of mean lyapunov exponent is given by the probability distribution function of its time coarse grained quantity local lyapunov exponent the functional form of the probability distribution function is obtained its form is different from the one obtained from the large deviation statistics also the relation between the damping constant included in kuramoto sivashinsky equation and lyapunov exponent is obtained

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

consistent model selection for marginal generalized additive model for correlated data we consider the generalized additive model when responses from the same cluster are correlated incorporating correlation in the estimation of nonparametric components for the generalized additive model is important because it improves estimation efficiency and increases statistical power for model selection in our setting there is no specified likelihood function for the generalized additive model because the outcomes could be nonnormal and discrete which makes estimation and model selection very challenging problems we propose consistent estimation and model selection that incorporate the correlation structure we establish an asymptotic property with l2 norm consistency for the nonparametric components which achieves the optimal rate of convergence in addition the proposed model selection strategy is able to select the correct generalized additive model consistently that is with probability approaching to 1 the estimators for the zero function components converge to 0 almost surely we illus

a marginal approach to reduced rank penalized spline smoothing with application to multilevel functional data multilevel functional data are collected in many biomedical studies for example in a study of the effect of nimodipine on patients with subarachnoid hemorrhage sah patients underwent multiple 4 hr treatment cycles within each treatment cycle subjects vital signs were reported every 10 min these data have a natural multilevel structure with treatment cycles nested within subjects and measurements nested within cycles most literature on nonparametric analysis of such multilevel functional data focuses on conditional approaches using functional mixed effects models however parameters obtained from the conditional models do not have direct interpretations as population average effects when population effects are of interest we may employ marginal regression models in this work we propose marginal approaches to fit multilevel functional data through penalized spline generalized estimating equation penalized spline gee the procedure is effective for modeling multilevel correlated generalized

lyapunov exponent of partial differential equation abstract the method of calculating numerically the lyapunov exponent of partial differential equations is stated the mean lyapunov exponent and the local lyapunov exponent are introduced in order to characterize the systems described by the partial differential equations it is shown that the mean lyapunov exponent expresses clearly how disordered the spatial patterns are

local asymptotics for regression splines and confidence regions in this paper we study the local behavior of regression splines in particular explicit expressions for the asymptotic pointwise bias and variance of regression splines are obtained in addition asymptotic normality for regression splines is established leading to the construction of approximate confidence intervals and confidence bands for the regression function

ks entropy and mean lyapunov exponent for coupled map lattices abstract the statistics of kolmogorov sinai ks entropy for a coupled map lattice model are analyzed from the viewpoint of the thermodynamic formalism it is shown that the fluctuation of ks entropy for a coupled map lattice model satisfies the large deviation statistics also the probability density of lyapunov exponents pdle is studied and it is shown that the pdle gives the measure of the irregularity for the spatio temporal patterns mean lyapunov exponent is introduced and compared with ks entropy

acquiring 3 d models from sequences of contours this paper explores shape from contour for acquiring 3 d graphics models in this method a continuous sequence of images is taken as an object rotates a smooth convex shape can be estimated instantaneously from its contour and by the first derivative of contour movement trace of contour or contour distribution with time we also analyze shapes that do not satisfy the conditions of smoothness and visibility which are indispensable for modeling an object a region that does not expose as contour yields a nonsmoothness in the tracked contour movement we can thus detect such a region by contour distribution filtering and extract its accurate location by computing the left and right derivatives of the distribution this has not been studied previously these unknown regions are obtained for further investigation using other visual cues a general approach for building a geometrical object model using contours is then described the entire process from silhouettes to a 3 d model is based local computation this is promising for producing shapes in real time our direct goal is to establish 3 d graphics models of human faces for the growing needs of visual communications we have obtained some good results

3d surface estimation and model construction from specular motion in image sequences this work reconstructs a 3d graphics model of an object with specular surfaces by its rotation continuous images are taken to measure highlights on the smooth surfaces and their motion coplanar extended lights determine a plane of rays to produce a highlight stripe on the object 3d surfaces are then recovered from the moving stripe we investigate global motion characteristics of the highlights in the epipolar plane images so as to qualitatively identify surface types and control the modeling process under single and multiple plane of rays illuminations we give two quantitative approaches for surface and normal recovery which use highlight orientation in the image and highlight motion in the epipolar plane images the computations employ a first order differential equation and linear equations respectively

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

green kubo formula derived from large deviation statistics abstract numerical calculations for many physical systems including chaos and turbulence have been greatly developed in recent years we often investigate the characteristics of the time series for chaotic systems and study the essential laws underlying its time series we show the important characteristics which are sometimes not pointed out one of them is the green kubo formula which holds for the time series that satisfies the large deviation statistics extended version for the relation is shown in this paper and a simple example is given the relationship between the green kubo formula and the large deviation statistics is emphasized

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