some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

central limit theorems for infinite series of queues and applications to simple exclusion we prove that a tagged particle in asymmetric simple exclusion satisfies a central limit theorem when properly rescaled to obtain this result we derive several results of positive or negative correlation for occupation times of a server in a series of queues which imply various central limit theorems

existence and comparison results for difference φ laplacian boundary value problems with lower and upper solutions in reverse order abstract this paper is devoted to the study of the existence and comparison results for nonlinear difference laplacian problems with mixed dirichlet neumann and periodic boundary value conditions we deduce existence of extremal solutions of periodic and neumann boundary value problems lying between a pair of lower and upper solutions given in reverse order we prove the optimality of some assumptions in

nonlinear boundary value problems for first order impulsive functional differential equations this paper is concerned with solutions of nonlinear boundary value problems for a class of first order functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid obviously we extend previous results

periodic boundary value problems for first order impulsive integro differential equations of mixed type this paper investigates the existence of minimal and maximal solutions of periodic boundary value problem for first order impulsive integro differential equations of mixed type by establishing a comparison result and using the method of upper and lower solutions and the monotone iterative technique

graphical model checking with correlated response data correlated response data arise often in biomedical studies the generalized estimation equation gee approach is widely used in regression analysis for such data however there are few methods available to check the adequacy of regression models in gee in this paper a graphical method is proposed based on cook and weisberg s marginal model plot a bootstrap method is applied to obtain the reference band to assess statistical uncertainties in comparing two marginal mean functions we also propose using the generalized additive model gam in a similar fashion the proposed two methods are easy to implement by taking advantage of existing smoothing and gam softwares for independent data the usefulness of the methodology is demonstrated through application to a correlated binary data set drawn from a clinical trial the lung health study

identification and nonparametric estimation of a transformed additively separable model let r x z be a function that along with its derivatives can be consistently estimated nonparametrically this paper discusses the identification and consistent estimation of the unknown functions h m g and f where r x z h m x z m x z g x f z and h is strictly monotonic an estimation algorithm is proposed for each of the model s unknown components when r x z represents a conditional mean function the resulting estimators use marginal integration to separate the components g and f our estimators are shown to have a limiting normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives their small sample performance is studied in a monte carlo experiment we apply our results to estimate generalized homothetic production functions for four industries in the chinese economy

analysis of repeated measurements using nonparametric smoothers and randomization tests the mixed model analysis of variance anova which is commonly applied to repeated measurements taken over time depends on specialized assumptions about the error distribution and fails to exploit information contained in the ordering of the data points over time this paper describes a procedure that overcomes these disadvantages while preserving familiar features of the mixed model anova group profiles are estimated by nonparametric smoothing of observed mean profiles group and time main effects and the group by time interaction effect are tested using randomization tests results of zerbe 1979 journal of the american statistical association 74 215 221 are used to construct f test approximations for the randomization tests of the group and group by time effects a new approximate f test for time effect is proposed a simulation study demonstrates that the approximations perform well and that smoothing increases the power of the tests for time main effect and group by time interaction the procedure is applied to data on hormone levels in cows

asymptotics of particle trajectories in infinite one dimensional systems with collisions we investigate the asymptotic behavior of the trajectories of a tagged particle tp in an infinite one dimensional system of point particles the particles move independently when not in contact the only interactions are harris type generalized elastic collisions which prevent crossings this is achieved by relabeling the independent trajectories when they cross when these trajectories are differentiable as in particles with velocities undergoing ornstein uhlenbeck processes collisions correspond to exchange of velocities we prove very generally that the suitably scaled tp trajectory converges weakly to a simple gaussian process this extends the results of spitzer for new tonian particles to very general non crossing processes the proof is based on the consideration of the simpler process which counts the crossings of the origin by the independent trajectories

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

first order impulsive ordinary differential equations with anti periodic and nonlinear boundary conditions the monotone iterative technique is a powerful method that have been used to approximate the extremal solutions of several problems 1 2 on the other hand impulsive differential equations are a basic tool to study some problems of biology medicine engineering and physics 3 in this paper we deal with the following nonlinear boundary value problem for first order differential equation with impulses at fixed points

tracer diffusion in lattice gases it has been proved that a tracer particle in a reversible lattice gas converges to brownian motion however only in a few particular cases has a strictly positive self diffusion coefficientd been established here we supply the missing piece and show thatd 0 in general the exceptions are one dimensional lattice gases with nearest neighbor jumps only for whichd 0 the proof establishes a variational formula ford which could be used to obtain realistic bounds

integral boundary value problems for first order integro differential equations with deviating arguments this paper deals with first order integro differential equations of mixed type with deviating arguments we investigate the existence of solutions of such problems with integral boundary conditions by establishing a comparison result and applying the monotone iterative technique to obtain corresponding results we also discuss first order differential inequalities with deviating arguments two examples demonstrate the application of our results

periodic boundary value problem for first order impulsive functional differential equations this paper discusses the periodic boundary value problem for a class of first order impulsive functional differential equations we establish several existence results under weaker hypotheses by using the leray schauder alternative the lower and upper solution method and the monotone iterative technique the corresponding results in the literature are improved or extended some examples are also given to illustrate the advantage of the results

more efficient local polynomial estimation in nonparametric regression with autocorrelated errors we propose a modification of local polynomial time series regression estimators that improves efficiency when the innovation process is autocorrelated the procedure is based on a pre whitening transformation of the dependent variable that must be estimated from the data we establish the asymptotic distribution of our estimator under weak dependence conditions we show that the proposed estimation procedure is more efficient than the conventional local polynomial method we also provide simulation evidence to suggest that gains can be achieved in moderate sized samples

self diffusion in simple models systems with long range jumps we review some exact results for the morion of a tagged particle in simple models then we study the density dependence of the sill diffusion coefficient d n in lattice systems with simple symmetric exclusion in which the particles can jump with equal rates to a set of n neighboring sites we obtain positive upper and lower bounds on f n n 1 d n d n 0 1 for is an element of 0 1 computer simulations for the square triangular and one dimensional lattices suggest that fn becomes effectively independent of n for n greater than or equal to 20

generalized boltzmann equation for lattice gas automata in this paper a theory is formulated that predicts velocity and spatial correlations between occupation numbers that occur in lattice gas automata violating semi detailed balance starting from a coupled bbgky hierarchy for then particle distribution functions cluster expansion techniques are used to derive approximate kinetic equations in zeroth approximation the standard nonlnear boltzmann equation is obtained the next approximation yields the ring kinetic equation similar to that for hard sphere systems describing the time evolution of pair correlations the ring equation is solved to determine the nonvanishing pair correlation functions in equilibrium for two models that violate semidetailed balance one is a model of interacting random walkers on a line the other one is a two dimensional fluid type model on a triangular lattice the numerical predictions agree very well with computer simulations

vector generalized additive models vector smoothing is used to extend the class of generalized additive models in a very natural way to include a class of multivariate regression models the resulting models are called vector generalized additive models the class of models for which the methodology gives generalized additive extensions includes the multiple logistic regression model for nominal responses the continuation ratio model and the proportional and non proportional odds models for ordinal responses and the bivariate probit and bivariate logistic models for correlated binary responses they may also be applied to generalized estimating equations

upper and lower solution methods for fully nonlinear boundary value problems abstract sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with nonlinear boundary conditions the conditions assume the existence of a strong upper solution lower solution pair a concept that is defined in the paper the differential equation has nonlinear dependence on all lower order derivatives of the unknown in particular appropriate nagumo conditions are obtained and employed

generalized estimating equations for correlated binary data using the odds ratio as a measure of association summary moment methods for analyzing repeated binary responses have been proposed by liang zeger 1986 and extended by prentice 1988 in their generalized estimating equations both liang zeger 1986 and prentice 1988 estimate the parameters associated with the expected value of an individual s vector of binary responses as well as the correlations between pairs of binary responses because the odds ratio has many desirable properties and some investigators may find the odds ratio is easier to interpret we discuss modelling the association between binary responses at pairs of times with the odds ratio we then modify the estimating equations of prentice to estimate the odds ratios in simulations the parameter estimates for the logistic regression model for the marginal probabilities appear slightly more efficient when using the odds ratio parameterization

existence and uniqueness of solutions of second order three point boundary value problems with upper and lower solutions in the reversed order abstract this paper studies the existence and uniqueness of solutions of second order three point boundary value problems with lower and upper solutions in the reversed order obtains the sufficient conditions for the existence and uniqueness of solutions by use of the monotone iterative method and gives the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution

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

nonparametric transfer function models in this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between input and output time series the transfer function is smooth with unknown functional forms and the noise is assumed to be a stationary autoregressive moving average arma process the nonparametric transfer function is estimated jointly with the arma parameters by modelling the correlation in the noise the transfer function can be estimated more efficiently the parsimonious arma structure improves the estimation efficiency in finite samples the asymptotic properties of the estimators are investigated the finite sample properties are illustrated through simulations and one empirical example

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

nonparametric fixed interval smoothing with vector splines a computationally efficient algorithm for nonparametric smoothing of vector signals with general measurement covariances is presented this algorithm provides an alternative to the optimal smoothing algorithms that hinge on possibly inaccurate parametric state space models automatic procedures that use the measurements to determine how much to smooth are developed and compared this adaptation allows the data to speak for itself without imposing a gauss markov model structure a nonparametric approach to covariance estimation for the case of independently identically distributed i i d measurement errors is presented monte carlo simulations demonstrate the performance of the algorithm

periodic boundary value problem for the second order impulsive functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problem for second order functional differential equations by using the method of lower and upper solutions coupled with monotone iterative technique

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

asymptotic confidence regions for kernel smoothing of a varying coefficient model with longitudinal data abstract we consider the estimation of the k 1 dimensional nonparametric component t of the varying coefficient model y t x t t t e t based on longitudinal observations yij x i tij tij i 1 n j 1 ni where tij is the jth observed design time point t of the ith subject and yij and x i tij are the real valued outcome and r k 1 valued covariate vectors of the ith subject at tij the subjects are independently selected but the repeated measurements within subject are possibly correlated asymptotic distributions are established for a kernel estimate of t that minimizes a local least squares criterion these asymptotic distributions are used to construct a class of approximate pointwise and simultaneous confidence regions for t applying these methods to an epidemiological study we show that our procedures are useful for predicting cd4 t helper lymphocytes cell changes among hiv human immunodeficiency virus infected persons the finite sample properties of o

boundary value problems involving upper and lower solutions in reverse order in this paper we discuss the existence of extreme solutions of the boundary value problem for a class of first order functional equations with a nonlinear boundary condition in the presence of a lower solution a and an upper solution b with email protected email protected we establish existence results of extreme solutions by using the method of upper and lower solutions and a monotone iterative technique

boundary value problems for a class of impulsive functional equations this paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions we study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times by the use of the monotone method some of the options included in this formulation are differential equations with maximum and integro differential equations in this paper we also prove that the lipschitzian character of the function which introduces the functional dependence in a differential equation is not a necessary condition for the development of the monotone iterative technique to obtain a solution and to approximate the extremal solutions to the equation in a given functional interval the corresponding results are established for the impulsive case the general formulation includes several types of functional dependence delay equations equations with maxima integro differential equations finally we consider the case of functional dependence which is given by nonincreasing and bounded functions

periodic boundary value problems for delay differential equations with impulses existence and approximation of solutions for an impulsive delay differential equation with periodic boundary value conditions are presented we use comparison principles and monotone iterative techniques

existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti periodic boundary conditions this paper describes the method of quasilinearization for first order nonlinear impulsive functional differential equations with anti periodic boundary conditions a monotone iterative technique coupled with lower and upper solutions is employed to obtain sequences of approximate solutions converging monotonically and quadratically to the unique solution of the problem at hand 2007 elsevier ltd all rights reserved

an application of isotonic longitudinal marginal regression to monitoring the healing process this paper discusses marginal regression for repeated ordinal measurements that are isotonic over time such data are often observed in longitudinal studies on healing processes where due to recovery the status of patients only improves or stays the same we show how this prior information can be used to construct appropriate and parsimoniously parametrized marginal models as a second aspect we also incorporate nonparametric fitting of covariate effects via a penalized quasi likelihood or gee approach we illustrate our methods by an application to injuries from sporting activities

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

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

design adaptive nonparametric regression abstract in this article we study the method of nonparametric regression based on a weighted local linear regression this method has advantages over other popular kernel methods moreover such a regression procedure has the ability of design adaptation it adapts to both random and fixed designs to both highly clustered and nearly uniform designs and even to both interior and boundary points it is shown that the local linear regression smoothers have high asymptotic efficiency i e can be 100 with a suitable choice of kernel and bandwidth among all possible linear smoothers including those produced by kernel orthogonal series and spline methods the finite sample property of the local linear regression smoother is illustrated via simulation studies nonparametric regression is frequently used to explore the association between covariates and responses there are many versions of kernel regression smoothers some estimators are not good for random designs such as in observational studies and

local polynomial estimation of nonparametric simultaneous equations models abstract we define a new procedure for consistent estimation of nonparametric simultaneous equations models under the conditional mean independence restriction of newey et al 1999 nonparametric estimation of triangular simultaneous equation models econometrica 67 565 603 it is based upon local polynomial regression and marginal integration techniques we establish the asymptotic distribution of our estimator under weak data dependence conditions simulation evidence suggests that our estimator may significantly outperform the estimators of pinkse 2000 nonparametric two step regression estimation when regressors and errors are dependent canadian journal of statistics 28 289 300 and newey and powell 2003 instrumental variable estimation of nonparametric models econometrica 71 1565 1578

marginal models for correlated binary responses with multiple classes and multiple levels of nesting a model for correlated binary data is presented marginal probabilities and odds ratios are allowed to have general regression structures that include multiple classes and multiple levels of nesting estimation is done through the generalized estimating equations approach of liang and zeger 1986 biometrika 73 13 22 they are contrasted with conditional models and recommendations for choosing between the two are given examples from genetic epidemiology are presented

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

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

some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions this paper investigates the existence and uniqueness of solutions for an impulsive mixed boundary value problem of nonlinear differential equations of fractional order email protected 1 2 our results are based on some standard fixed point theorems some examples are presented to illustrate the main results

central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions we prove a functional central limit theorem for additive functionals of stationary reversible ergodic markov chains under virtually no assumptions other than the necessary ones we use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk

existence of solutions for second order impulsive differential equations with deviating arguments abstract this paper deals with impulsive second order differential equations with deviating arguments we investigate the existence of solutions of such problems with nonlinear boundary conditions to obtain corresponding results we discuss also second order impulsive differential inequalities with deviating arguments

a likelihood based method for analysing longitudinal binary responses summary in this paper we discuss a likelihood based method for analysing correlated binary responses based on a multivariate model it is related to the pseudo maximum likelihood approach suggested recently by zhao prentice 1990 their parameterization results in a simple pairwise model in which the association between responses is modelled in terms of correlations while the present paper uses conditional log odds ratios with this approach higher order associations can be incorporated in a natural way one important advantage of this parameterization is that the maximum likelihood estimates of the marginal mean parameters are robust to misspecification of the time dependence we describe an iterative two stage procedure for obtaining the maximum likelihood estimates two examples are presented to illustrate this methodology

theta functions modular invariance and strings we use quillen s theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory in particular we show that the spin structure dependence of the chiral dirac determinant on a riemann surface is given by riemann s theta function we use this result to investigate the modular invariance of multiloop heterotic string amplitudes

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

nonparametric spline regression with autoregressive moving average errors summary we estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model unknown parameters are estimated by either maximum likelihood cross validation or generalized cross validation by expressing the problem in state space form we obtain 0 n algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross validation functions the finite sample properties of the function estimates are evaluated by an extensive simulation study and examples are given

semiparametric gmm estimation of spatial autoregressive models abstract we propose semiparametric gmm estimation of semiparametric spatial autoregressive sar models under weak moment conditions in comparison with the quasi maximum likelihood based semiparametric estimator of su and jin 2010 we allow for both heteroscedasticity and spatial dependence in the error terms we derive the limiting distributions of our estimators for both the parametric and nonparametric components in the model and demonstrate the estimator of the parametric component has the usual n asymptotics when the error term also follows an sar process we propose an estimator for the parameter in the sar error process and derive the joint asymptotic distribution for both spatial parameters consistent estimates for the asymptotic variance covariance matrices of both the parametric and nonparametric components are provided monte carlo simulations indicate that our estimators perform well in finite samples

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

nonparametric dynamic panel data models kernel estimation and specification testing abstract motivated by the first differencing method for linear panel data models we propose a class of iterative local polynomial estimators for nonparametric dynamic panel data models with or without exogenous regressors the estimators utilize the additive structure of the first differenced model the fact that the two additive components have the same functional form and the unknown function of interest is implicitly defined as a solution of a fredholm integral equation of the second kind we establish the uniform consistency and asymptotic normality of the estimators we also propose a consistent test for the correct specification of linearity in typical dynamic panel data models based on the l 2 distance of our nonparametric estimates and the parametric estimates under the linear restriction we derive the asymptotic distributions of the test statistic under the null hypothesis and a sequence of pitman local alternatives and prove its consistency against global alternatives simulations suggest that the proposed estimators and tests perform well for finite samples we apply our new method to study the relationships among economic growth the initial economic condition and capital accumulation and find a significant nonlinear relation between economic growth and the initial economic condition

detecting dependencies in smooth regression models summary a class of simple estimators for the correlation of the errors in nonparametric regression models is proposed for the fixed design case these estimators are based on squared differences of various spans of the data and are consistent so long as the regression function is lipschitz continuous the limiting distribution is established and applied to derive asymptotic global and local tests for different null hypotheses of uncorrelatedness the finite sample behaviour of estimators and tests is investigated in a monte carlo study a more general class of estimators using generalized difference schemes is also introduced

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

modeling longitudinal data with ordinal response by varying coefficients the paper presents a smooth regression model for ordinal data with longitudinal dependence structure a marginal model with cumulative logit link mccullagh 1980 is applied to cope for the ordinal scale and the main and covariate effects in the model are allowed to vary with time local fitting is pursued and asymptotic properties of the estimates are discussed a data example demonstrates the exploratory flavor of the smooth model in a second step the longitudinal dependence of the observations is considered cumulative log odds ratios are fitted locally which provides insight how the dependence of the ordinal observations changes with time

estimating semiparametric arch models by kernel smoothing methods we investigate a class of semiparametric arch models that includes as a special case the partially nonparametric pnp model introduced by engle and ng 1993 and which allows for both flexible dynamics and flexible function form with regard to the news impact function we show that the functional part of the model satisfies a type ii linear integral equation and give simple conditions under which there is a unique solution we propose an estimation method that is based on kernel smoothing and profiled likelihood we establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model we also discuss efficiency of both the parametric part and the nonparametric part we investigate the performance of our procedures on simulated data and on a sample of s p500 index returns we find evidence of asymmetric news impact functions consistent with the parametric analysis

extremal solutions for third order nonlinear problems with upper and lower solutions in reversed order abstract this paper deals with the existence of extremal solutions for the third order nonlinear boundary value problem u t f t u t t a b u a a u a b u b c in the presence of a pair of lower and upper solutions in reversed order here r r is an increasing homeomorphism f a b r r is a carathedory function and a b c r the proof follows from monotone iterative techniques which are based on suitable anti maximum principles for adequate operators to deduce such results we study some related problems coupled with boundary value conditions of the form p 0 u a q 0 u a a p 1 u b q 1 u b b u a c and u a a u a b u b c

estimation of semivarying coefficient time series models with arma errors serial correlation in the residuals of time series models can cause bias in both model estimation and prediction however models with such serially correlated residuals are difficult to estimate especially when the regression function is nonlinear existing estimation methods require strong assumption for the relation between the residuals and the regressors which excludes the commonly used autoregressive models in time series analysis by extending the whittle likelihood estimation this paper investigates in details a semi parametric autoregressive model with arma sequence of residuals asymptotic normality of the estimators is established and a model selection procedure is proposed numerical examples are employed to illustrate the performance of the proposed estimation method and the necessity of incorporating the serial correlation in the residuals

kernel smoothing of data with correlated errors abstract kernel smoothing is a common method of estimating the mean function in the nonparametric regression model y f x e where f x is a smooth deterministic mean function and e is an error process with mean zero in this article the mean squared error of kernel estimators is computed for processes with correlated errors and the estimators are shown to be consistent when the sequence of error processes converges to a mixing sequence the standard techniques for bandwidth selection such as cross validation and generalized cross validation are shown to perform very badly when the errors are correlated standard selection techniques are shown to favor undersmoothing when the correlations are predominantly positive and oversmoothing when negative the selection criteria can however be adjusted to correct for the effect of correlation in simulations the standard selection criteria are shown to behave as predicted the corrected criteria are shown to be very effective when the correlation functi

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

the monotone method for neumann functional differential equations with upper and lower solutions in the reverse order abstract in this paper we show that the monotone technique produces two monotone sequences that converge uniformly to extremal solutions of second order functional differential equations and laplacian equations with neumann boundary value conditions moreover we obtain existence results assuming upper and lower solutions in the reverse order

extremal solutions for the first order impulsive functional differential equations with upper and lower solutions in reversed order this paper studies the existence of solutions of first order impulsive functional differential equations with lower and upper solutions in the reversed order obtains the sufficient conditions for the existence of solutions by establishing a new comparison principle and using the monotone iterative technique a concrete example is presented and solved to illustrate the obtained results

variable selection and model averaging in semiparametric overdispersed generalized linear models we express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use bayesian variable selection to determine which predictors enter the model and whether they enter linearly or flexibly when the variance term is null we obtain a generalized additive model which becomes a generalized linear model if the predictors enter the mean linearly the model is estimated using markov chain monte carlo simulation and the methodology is illustrated using real and simulated data sets

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

diffusion of color in the simple exclusion process we prove a diffusion scaling limit for the macroscopic densities of colored particles performing the simply excluded random walk and relate this to the limiting behavior of a test particle in equilibrium

boundary value problems for systems of nonlinear integro differential equations with deviating arguments by establishing a comparison result and using the method of upper and lower solutions and the monotone iterative technique we investigate the systems of nonlinear mixed integro differential equations with deviating arguments and mixed boundary value conditions sufficient conditions are established for the existence of extremal system of solutions of the given problem

periodic boundary value problems for the first order impulsive functional differential equations this paper is concerned with the existence of extreme solutions of the periodic boundary value problems for a class of first order functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid meanwhile we extend previous results

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

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

periodic boundary value problem for the first order impulsive functional differential equations this paper is concerned with the existence of extreme solutions of the periodic boundary value problem for a class of first order impulsive functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid meanwhile we extend previous results