a relaxed cutting plane method for semi infinite semi definite programming in this paper we develop two discretization algorithms with a cutting plane scheme for solving combined semi infinite and semi definite programming problems i e a general algorithm when the parameter set is a compact set and a typical algorithm when the parameter set is a box set in the m dimensional space we prove that the accumulation point of the sequence points generated by the two algorithms is an optimal solution of the combined semi infinite and semi definite programming problem under suitable assumption conditions two examples are given to illustrate the effectiveness of the typical algorithm

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

theory and simulation of time fractional fluid diffusion in porous media we simulate a fluid flow in inhomogeneous anisotropic porous media using a time fractional diffusion equation and the staggered fourier pseudospectral method to compute the spatial derivatives a fractional derivative of the order of 0 2 replaces the first order time derivative in the classical diffusion equation it implies a time dependent permeability tensor having a power law time dependence which describes memory effects and accounts for anomalous diffusion we provide a complete analysis of the physics based on plane waves the concepts of phase group and energy velocities are analyzed to describe the location of the diffusion front and the attenuation and quality factors are obtained to quantify the amplitude decay we also obtain the frequencydomain green function the time derivative is computed with the gr unwald letnikov summation which is a finite difference generalization of the standard finite difference operator to derivatives of fractional order the results match the analytical solution obtained from the green function an example of the pressure field generated by a fluid injection in a heterogeneous sandstone illustrates the performance of the algorithm for different values of t he calculation requires storing the whole pressure field in the computer memory since anomalous diffusion recalls the past

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

recovering optimal basic variables in karmarkar s polynomial algorithm for linear programming primal slack ellipsoids are described which contain all of the optimal primal feasible solutions in a standard form variant of karmarkar s projective algorithm for linear programming lp using these ellipsoids we show how to identify optimal basic variables using few additional arithmetic operations and also simultaneously reduce the size of the lp problem during the course of the algorithm some preliminary computational experiments are given which compare different stopping criteria

generalized langevin equation with a three parameter mittag leffler noise abstract the relaxation functions for a given generalized langevin equation in the presence of a three parameter mittag leffler noise are studied analytically the results are represented by three parameter mittag leffler functions exact results for the velocity and displacement correlation functions of a diffusing particle are obtained by using the laplace transform method the asymptotic behavior of the particle in the short and long time limits are found by using the tauberian theorems it is shown that for large times the particle motion is subdiffusive for 1 and superdiffusive for many previously obtained results are recovered due to the many parameters contained in the noise term the model considered in this work may be used to improve the description of data and to model anomalous diffusive processes in complex media

conical projection algorithms for linear programming the linear programming problem is manipulated to be stated as a non linear programming problem in which karmarkar s logarithmic potential function is minimized in the positive cone generated by the original feasible set the resulting problem is then solved by a master algorithm that iteratively rescales the problem and calls an internal unconstrained non linear programming algorithm several different procedures for the internal algorithm are proposed giving priority either to the reduction of the potential function or of the actual cost we show that karmarkar s algorithm is equivalent to this method in the special case in which the internal algorithm is reduced to a single steepest descent iteration all variants of the new algorithm have the same complexity as karmarkar s method but the amount of computation is reduced by the fact that only one projection matrix must be calculated for each call of the internal algorithm

nonparametric regression in the presence of measurement error summary in many regression applications the independent variable is measured with error when this happens conventional parametric and nonparametric regression techniques are no longer valid we consider two diverent approaches to nonparametric regression the first uses the simex simulation extrapolation method and makes no assumption about the distribution of the unobserved error prone predictor for this approach we derive an asymptotic theory for kernel regression which has some surprising implications penalised regression splines are also considered for fixed number of known knots the second approach assumes that the error prone predictor has a distribution of a mixture of normals with an unknown number of components and uses regression splines simulations illustrate the results

nonparametric additive regression for repeatedly measured data summary we develop an easily computed smooth backfitting algorithm for additive model fitting in repeated measures problems our methodology easily copes with various settings such as when some covariates are the same over repeated response measurements we allow for a working covariance matrix for the regression errors showing that our method is most efficient when the correct covariance matrix is used the component functions achieve the known asymptotic variance lower bound for the scalar argument case smooth backfitting also leads directly to design independent biases in the local linear case simulations show our estimator has smaller variance than the usual kernel estimator this is also illustrated by an example from nutritional epidemiology

thermal wave model of bioheat transfer with modified riemann liouville fractional derivative in this paper a new fractional thermal wave model of the bioheat transfer ftwmbt caused by spatial heating is built using taylor s series expansion of modified riemann liouville fractional derivatives a one dimensional analytical solution of the ftwmbt in a finite medium is obtained the ftwmbt in the case 1 interpolates the standard thermal wave model of bioheat transfer and the well known pennes bioheat equation 0 finally numerical results are presented graphically for various values of different parameters this study demonstrates that fractional models can provide a unified approach to examine the heat transfer in biological tissue

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

constraint reduction for linear programs with many inequality constraints consider solving a linear program in standard form where the constraint matrix a is m times n with n gg m gg 1 such problems arise for example as the result of finely discretizing a semi infinite program the cost per iteration of typical primal dual interior point methods on such problems is o m 2n we propose to reduce that cost by replacing the normal equation matrix ad 2a t where d is a diagonal matrix with a reduced version of same dimension a qd q 2a q t where q is an index set including the indices of m most nearly active or most violated dual constraints at the current iterate with m geq m a prescribed integer this can result in a speedup of close to n q at each iteration promising numerical results are reported for constraint reduced versions of a dual feasible affine scaling algorithm and of mehrotra s predictor corrector method s mehrotra it siam j optim 2 1992 pp 575 601 in particular while it could be expected that neglecting a large portion of the constraints especially at early iterations may result in a significant deterioration of the search direction it appears that the total number of iterations typically remains essentially constant as the size of the reduced constraint set is decreased down to some threshold in some cases this threshold is a small fraction of the total set in the case of the affine scaling algorithm global convergence and local quadratic convergence are proved

the fractional finite hankel transform and its applications in fractal space in the present work a generalized finite hankel transform is derived which is useful in solving equations in fractal dimension df and involving a fractal diffusion coefficient d0r the corresponding inversion formula is established and some properties are given then the transform is successfully used to solve a class of time fractional diffusion equations in fractional spatial dimension with an absorbent term and schrodinger equation in fractional dimensional space green s functions and exact wave function of the above problems are found

an implementation of karmarkar s algorithm for linear programming this paper describes the implementation of power series dual affine scaling variants of karmarkar s algorithm for linear programming based on a continuous version of karmarkar s algorithm two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested linear programs are expressed in an inequality form which allows for the inexact computation of the algorithm s direction of improvement resulting in a significant computational advantage implementation issues particular to this family of algorithms such as treatment of dense columns are discussed the code is tested on several standard linear programming problems and compares favorably with the simplex codeminos 4 0

a joint model for survival and longitudinal data measured with error the relationship between a longitudinal covariate and a failure time process can be assessed using the cox proportional hazards regression model we consider the problem of estimating the parameters in the cox model when the longitudinal covariate is measured infrequently and with measurement error we assume a repeated measures random effects model for the covariate process estimates of the parameters are obtained by maximizing the joint likelihood for the covariate process and the failure time process this approach uses the available information optimally because we use both the covariate and survival data simultaneously parameters are estimated using the expectation maximization algorithm we argue that such a method is superior to naive methods where one maximizes the partial likelihood of the cox model using the observed covariate values it also improves on two stage methods where in the first stage empirical bayes estimates of the covariate process are computed and then used as time dependent covariates in a second stage to find the parameters in the cox model that maximize the partial likelihood

new local estimation procedure for a non parametric regression function for longitudinal data this paper develops a new estimation of nonparametric regression functions for clustered or longitudinal data we propose to use cholesky decomposition and profile least squares techniques to estimate the correlation structure and regression function simultaneously we further prove that the proposed estimator is as asymptotically efficient as if the covariance matrix were known a monte carlo simulation study is conducted to examine the finite sample performance of the proposed procedure and to compare the proposed procedure with the existing ones based on our empirical studies the newly proposed procedure works better than the naive local linear regression with working independence error structure and the efficiency gain can be achieved in moderate sized samples our numerical comparison also shows that the newly proposed procedure outperforms some existing ones a real data set application is also provided to illustrate the proposed estimation procedure

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

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

transformations to additivity in measurement error models in many problems one wants to model the relationship between a response y and a covariate x sometimes it is difficult expensive or even impossible to observe x directly but one can instead observe a substitute variable w that is easier to obtain by far the most common model for the relationship between the actual covariate of interest x and the substitute w is w x u where the variable u represents measurement error this assumption of additive measurement error may be unreasonable for certain data sets we propose a new model namely h w h x u where h is a monotone transformation function selected from some family h of monotone functions the idea of the new model is that in the correct scale measurement error is additive we propose two possible transformation families h one is based on selecting a transformation that makes the within sample mean and standard deviation of replicated w s uncorrelated the second is based on selecting the transformation so that the errors u s fit a prespecified distribution transformation families used are the parametric power transformations and a cubic spline family several data examples are presented to illustrate the methods

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

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

the time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems abstract in this paper a time fractional fourier law is obtained from fractional calculus according to the fractional fourier law a fractional heat conduction equation with a time fractional derivative in the general orthogonal curvilinear coordinate system is built the fractional heat conduction equations in other orthogonal coordinate systems are readily obtainable as special cases in addition we obtain the solution of the fractional heat conduction equation in the cylindrical coordinate system in terms of the generalized h function using integral transformation methods the fractional heat conduction equation in the case 0 1 interpolates the standard heat conduction equation 1 and the localized heat conduction equation 0 finally numerical results are presented graphically for various values of order of fractional derivative

linear programs for constraint satisfaction problems abstract a novel representation is described that models some important np hard problems such as the propositional satisfiability problem sat the traveling salesperson problem tsp the quadratic assignment problem qap and the minimal set covering problem mscp by means of only two types of constraints choice constraints and exclusion constraints in its main section the paper presents an approach for solving an m cnf sat problem conjunctive normal form satisfaction n variables p clauses clause length m by integer programming the approach is unconventional because 2n distinct 0 1 variables are used for each clause of the m cnf sat problem the constraint matrix a forces that for every clause exactly one 0 1 variable is set equal to 1 choice constraint and no two 0 1 variables representing a literal and its complement are both set equal to 1 exclusion constraints the particular m cnf sat instance is coded in a cost vector which serves for maximization of the number of satisfied clauses the paper presents a modification of the simplex for solving the obtained integer program a main theorem of the paper is that this algorithm always finds a 0 1 integer solution a solution of the integer program corresponds to a solution of the m cnf sat and vice versa the results of significant experimental tests are reported and the procedure is compared to other approaches the same modelling technique is then used for the traveling salesperson problem for the minimal set covering and for the quadratic assignment problem it is shown that a uniform approach is thus useful

nonparametric inference for local extrema with application to oligonucleotide microarray data in yeast genome identifying local extrema of expression profiles is one primary objective in some cdna microarray experiments to study the replication dynamics of the yeast genome for example local peaks of hybridization intensity profiles correspond to putative replication origins we propose a nonparametric kernel smoothing nks technique to detect local hybridization intensity extrema across chromosomes the novelty of our approach is that we base our inference procedures on equilibrium points namely those locations at which the first derivative of the intensity curve is zero the proposed smoothing technique provides both point and interval estimation for the location of local extrema also this technique can be used to test for the hypothesis of either one or multiple suspected locations being the true equilibrium points we illustrate the proposed method on a microarray data set from an experiment designed to study the replication origins in the yeast genome in that the locations of autonomous replication sequence ars elements are identified through the equilibrium points of the smoothed intensity profile curve our method found a few ars elements that were not detected by the current smoothing methods such as the fourier convolution smoothing

modified riemann liouville derivative and fractional taylor series of nondifferentiable functions further results the paper gives some results and improves the derivation of the fractional taylor s series of nondifferentiable functions obtained recently in the form f g h e a h ad g a f g 0 a 1 where e a is the mittag leffier function here one defines fractional derivative as the limit of fractional difference and by this way one can circumvent the problem which arises with the definition of the fractional derivative of constant using riemann liouville definition as a result a modified riemann liouville definition is proposed which is fully consistent with the fractional difference definition and avoids any reference to the derivative of order greater than the considered one s in order to support this f taylor series one shows how its first term can be obtained directly in the form of a mean value formula the fractional derivative of the dirac delta function is obtained together with the fractional taylor s series of multivariate functions the relation with irreversibility of time and symmetry breaking is exhibited and to some extent this f taylor s series generalizes the fractional mean value formula obtained a few years ago by kolwantar

properties of principal component methods for functional and longitudinal data analysis the use of principal component methods to analyze functional data is appropriate in a wide range of different settings in studies of functional data analysis it has often been assumed that a sample of random functions is observed precisely in the continuum and without noise while this has been the traditional setting for functional data analysis in the context of longitudinal data analysis a random function typically represents a patient or subject who is observed at only a small number of randomly distributed points with nonnegligible measurement error nevertheless essentially the same methods can be used in both these cases as well as in the vast number of settings that lie between them how is performance affected by the sampling plan in this paper we answer that question we show that if there is a sample of n functions or subjects then estimation of eigenvalues is a semiparametric problem with root n consistent estimators even if only a few observations are made of each function and if each observation is encumbered by noise however estimation of eigenfunctions becomes a nonparametric problem when observations are sparse the optimal convergence rates in this case are those which pertain to more familiar function estimation settings we also describe the effects of sampling at regularly spaced points as opposed to random points in particular it is shown that there are often advantages in sampling randomly however even in the case of noisy data there is a threshold sampling rate depending on the number of functions treated above which the rate of sampling either randomly or regularly has negligible impact on estimator performance no matter whether eigenfunctions or eigenvectors are being estimated

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

improved bounds and containing ellipsoids in karmarkar s linear programming algorithm karmarkar s projective algorithm for linear programming provides not only primal solutions but dual solutions giving bounds on the optimal value here we show how improved bounds can be obtained at the expense of solving a two dimensional linear programming problem at every iteration and also how an ellipsoid containing all dual optimal solutions can be generated from available information we also give the results of limited computational experiments related to these topics

low order approximations in deconvolution and regression with errors in variables summary we suggest two new methods which are applicable to both deconvolution and regression with errors in explanatory variables for nonparametric inference the two approaches involve kernel or orthogonal series methods they are based on defining a low order approximation to the problem at hand and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently of course both techniques could be employed to construct consistent estimators but in many contexts of importance e g those where the errors are gaussian consistency is from a practical viewpoint an unattainable goal we rephrase the problem in a form where an explicit interpretable low order approximation is available the information that we require about the error distribution the error in variables distribution in the case of regression is only in the form of low order moments and so is readily obtainable by a rudimentary analysis of indirect measurements of errors e g through repeated measurements in particular we do not need to estimate a function such as a characteristic function which expresses detailed properties of the error distribution this feature of our methods coupled with the fact that all our estimators are explicitly defined in terms of readily computable averages means that the methods are particularly economical in computing time

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

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

a build down scheme for linear programming we propose a build down scheme for karmarkar s algorithm and the simplex method for linear programming the scheme starts with an optimal basis candidate set including all columns of the constraint matrix then constructs a dual ellipsoid containing all optimal dual solutions a pricing rule is developed for checking whether or not a dual hyperplane corresponding to a column intersects the containing ellipsoid if the dual hyperplane has no intersection with the ellipsoid its corresponding column will not appear in any of the optimal bases and can be eliminated from as these methods iterate is eventually built down to a set that contains only the optimal basic columns

analytical solutions of multi term time fractional differential equations and application to unsteady flows of generalized viscoelastic fluid this paper derives analytical solutions for a class of new multi term fractional order partial differential equations which include the terms for spatial diffusion time fractional diffusion multi term and reaction these models can be used to describe the nonlinear relationship between the shear stress and shear rate of generalized viscoelastic oldroyd b fluid and burgers fluid by using a modified separation of variables method the governing fractional order partial differential equations are transformed into a set of fractional order ordinary differential equations mikusiski type operational calculus is then employed to obtain the exact solutions of the linear fractional ordinary differential equations with constant coefficients the solutions are expressed in terms of multivariate mittag leffler functions different situations for the unsteady flows of generalized oldroyd b fluid and burgers fluid due to a moving plate are considered via examples integral representations of the solutions are presented it is shown that the presented results reduce to the corresponding results for classical navierstokes oldroyd b maxwell and second grade fluids as special cases

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

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

a stochastic model for thermal transport of nanofluid in porous media derivation and applications abstract in this paper a stochastic thermal transport model is developed for nanofluid flowing through porous media this model incorporates the influences of nanoparticle migration on convective heat transfer of the colloidal solution we show that levy flight movement patterns of nanoparticles result in the derived model using fractional derivative for the diffusion term the new thermal transport model is then applied to the mixed convective problem which is solved using finite difference method numerical results show that the smaller values of levy index lead to larger nusselt numbers thus the occurrence of long jumps for nanoparticles increases the heat transport of nanofluids the effects of other involved physical parameters are also presented and discussed

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

numerical algorithms to estimate relaxation parameters and caputo fractional derivative for a fractional thermal wave model in spherical composite medium in this paper we formulate a fractional thermal wave model for a bi layered spherical tissue implicit finite difference method is employed to obtain the solution of the direct problem the inverse analysis for simultaneously estimating the caputo fractional derivative and the relaxation time parameters is implemented by means of the levenberg marquardt method compared with the experimental data we can obviously find out that the estimated temperature increase values are excellently consistent with the measured temperature increase values in the experiment we have also discussed the effect of the fractional derivative the relaxation time parameters the initial guess as well as the sensitivity problem all the results show that the proposed fractional thermal wave model is efficient and accurate in modeling the heat transfer in the hyperthermia experiment and the proposed numerical method for simultaneously estimating multiple parameters for the fractional thermal wave model in a spherical composite medium is effective

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

existence result for fractional neutral stochastic integro differential equations with infinite delay this paper is concerned with the existence of mild solutions for a class of fractional neutral stochastic integro differential equations with infinite delay in hilbert spaces a sufficient condition for the existence is obtained under non lipschitz conditions by means of sadovskii s fixed point theorem an example is given to illustrate the theory

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

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

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

recovering optimal dual solutions on karmarkar s polynomial algorithm for linear programming this paper presents a standard form variant of karmarkar s algorithm for linear programming the tecniques of using duality and cutting objective are combined in this variant to maintain polynomial time complexity and to bypass the difficulties found in karmarkar s original algorithm the variant works with problems in standard form and simultaneously generates sequences of primal and dual feasible solutions whose objective function values converge to the unknown optimal value some computational results are also reported

the ellipsoid method generates dual variables we show that the ellipsoid algorithm applied to a system of linear inequalities can be implemented in such a way that at each iteration there is a short proof of the containment of the feasible region in the current ellipsoid moreover the data describing each ellipsoid also generate dual variables that provide bounds on the linear functions appearing in the inequalities

smoothing spline models for the analysis of nested and crossed samples of curves abstract we introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors generalizing smoothing splines to such samples by associating them with a corresponding mixed effects model the models are also useful for imputation of missing data and exploratory analysis of variance we prove that the best linear unbiased predictors blups from the extended mixed effects model correspond to solutions of a generalized penalized regression where smoothing parameters are directly related to variance components and we show that these solutions are natural cubic splines the model parameters are estimated using a highly efficient implementation of the em algorithm for restricted maximum likelihood reml estimation based on a preliminary eigenvector decomposition variability of computed estimates can be assessed with asymptotic techniques or with a novel hierarchical bootstrap resampling scheme for nested mixed effects models our methods are applied to me

fractional diffusion equation with a generalized riemann liouville time fractional derivative in this paper the solution of a fractional diffusion equation with a hilfer generalized riemann liouville time fractional derivative is obtained in terms of mittag leffler type functions and fox s h function the considered equation represents a quite general extension of the classical diffusion heat conduction equation the methods of separation of variables laplace transform and analysis of the sturm liouville problem are used to solve the fractional diffusion equation defined in a bounded domain by using the fourier laplace transform method it is shown that the fundamental solution of the fractional diffusion equation with a generalized riemann liouville time fractional derivative defined in the infinite domain can be expressed via fox s h function it is shown that the corresponding solutions of the diffusion equations with time fractional derivative in the caputo and riemann liouville sense are special cases of those diffusion equations with the hilfer generalized riemann liouville time fractional derivative the asymptotic behaviour of the solutions are found for large values of the spatial variable the fractional moments of the fundamental solution of the fractional diffusion equation are obtained the obtained results are relevant in the context of glass relaxation and aquifer problems

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

effective dimension reduction for sparse functional data we propose a method of effective dimension reduction for functional data emphasizing the sparse design where one observes only a few noisy and irregular measurements for some or all of the subjects the proposed method borrows strength across the entire sample and provides a way to characterize the effective dimension reduction space via functional cumulative slicing our theoretical study reveals a bias variance trade off associated with the regularizing truncation and decaying structures of the predictor process and the effective dimension reduction space a simulation study and an application illustrate the superior finite sample performance of the method

a semiparametric transformation approach to estimating usual daily intake distributions abstract the distribution of usual intakes of dietary components is important to individuals formulating food policy and to persons designing nutrition education programs the usual intake of a dietary component for a person is the long run average of daily intakes of that component for that person because it is impossible to directly observe usual intake for an individual it is necessary to develop an estimator of the distribution of usual intakes based on a sample of individuals with a small number of daily observations on a subsample of the individuals daily intake data for individuals are nonnegative and often very skewed also there is large day to day variation relative to the individual to individual variation and the within individual variance is correlated with the individual means we suggest a methodology for estimating usual intake distributions that allows for varying degrees of departure from normality and recognizes the measurement error associated with one day dietary intakes the est

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

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

local estimating equations abstract estimating equations have found wide popularity recently in parametric problems yielding consistent estimators with asymptotically valid inferences obtained via the sandwich formula motivated by a problem in nutritional epidemiology we use estimating equations to derive nonparametric estimators of a parameter depending on a predictor the nonparametric component is estimated via local polynomials with loess or kernel weighting asymptotic theory is derived for the latter in keeping with the estimating equation paradigm variances of the nonparametric function estimate are estimated using the sandwich method in an automatic fashion without the need typical in the literature to derive asymptotic formulas and plug in an estimate of a density function the same philosophy is used in estimating the bias of the nonparametric function that is an empirical method is used without deriving asymptotic theory on a case by case basis the methods are applied to a series of examples the applicatio

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

smooth coefficient estimation of a seemingly unrelated regression abstract this paper proposes estimation and inference for the semiparametric smooth coefficient seemingly unrelated regression model we discuss the imposition of cross equation restrictions which are required by economic theory as well as methods for data driven bandwidth selection a test of correct functional form for the entire system of equations is also constructed asymptotic and finite sample results are given we illustrate our estimator by applying it to a cost system for us commercial banks our results show that most of the banks are operating under increasing returns to scale but that returns to scale decrease with bank size