limiting distributions for l sb 1 regression estimators under general conditions it is well known that l 1 estimators of regression parameters are asymptotically normal if the distribution function has a positive derivative at 0 in this paper we derive the asymptotic distributions under more general conditions on the behavior of the distribution function near 0

numerical analysis of a new space time variable fractional order advection dispersion equation many physical processes appear to exhibit fractional order behavior that may vary with time and or space the continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable in this paper we consider a new space time variable fractional order advection dispersion equation on a finite domain the equation is obtained from the standard advection dispersion equation by replacing the first order time derivative by coimbra s variable fractional derivative of order x 0 1 x 0 1 and the first order and second order space derivatives by the riemann liouville derivatives of order x t 0 1 x t 0 1 and x t 1 2 x t 1 2 respectively we propose an implicit euler approximation for the equation and investigate the stability and convergence of the approximation finally numerical examples are provided to show that the implicit euler approximation is computationally efficient

variable order fractional differential operators in anomalous diffusion modeling abstract the purpose of this paper is to offer a unified discussion of variable order differential operators in anomalous diffusion modeling the characteristics of the new models in contrast to constant order fractional diffusion models change with time space concentration or other independent quantities we introduced a classification of variable order fractional diffusion models based on the possible physical origins which prompt the variable order some potential applications of the variable order fractional diffusion models are also discussed

temporal second order difference schemes for the multi dimensional variable order time fractional sub diffusion equations abstract a special point on each time interval is found for the approximation of the variable order time caputo derivative which makes at least second order approximation accuracy be obtained on this basis two difference schemes are proposed for the multi dimensional variable order time fractional sub diffusion equations which have second order accuracy in time second order and fourth order accuracy in space respectively the obtained difference schemes are proved to be uniquely solvable the convergence and stability of the schemes in the discrete h 1 norm are analyzed by utilizing the energy method some numerical examples are presented to verify the theoretical results

estimation of extreme conditional quantiles through power transformation the estimation of extreme conditional quantiles is an important issue in numerous disciplines quantile regression qr provides a natural way to capture the covariate effects at different tails of the response distribution however without any distributional assumptions estimation from conventional qr is often unstable at the tails especially for heavy tailed distributions due to data sparsity in this article we develop a new three stage estimation procedure that integrates qr and extreme value theory by estimating intermediate conditional quantiles using qr and extrapolating these estimates to tails based on extreme value theory using the power transformed qr the proposed method allows more flexibility than existing methods that rely on the linearity of quantiles on the original scale while extending the applicability of parametric models to borrow information across covariates without resorting to nonparametric smoothing in addition we propose a test procedure to assess the commonality of ext

iteration method for equation of viscoelastic motion with fractional differential operator of damping abstract mechanical properties of viscoelastic materials depend on the loading conditions and their history the work is devoted to the analysis of oscillation processes in viscoelastic media with loading prehistory taken into account by means of fractional derivative terms in the governing equations the paper suggests convergent procedure for numerical solution of this type of differential equations and their system for any combination of damping operator orders the order of the fractional derivative may be as constant so variable analysis of the amplitude frequency behavior of the oscillator versus the damping operator order is provided

a novel numerical method for the time variable fractional order mobile immobile advection dispersion model evolution equations containing fractional derivatives can provide suitable mathematical models for describing anomalous diffusion and transport dynamics in complex systems that cannot be modeled accurately by normal integer order equations recently researchers have found that many physical processes exhibit fractional order behavior that varies with time or space the continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable in this paper we consider the mobile immobile advection dispersion model with the coimbra variable time fractional derivative which is preferable for modeling dynamical systems and is more efficient from the numerical standpoint a novel implicit numerical method for the equation is proposed and the stability of the approximation is investigated as for the convergence of the numerical method we only consider a special case i e the time fractional derivative is independent of the time variable t the case where the time fractional derivative depends on both the time variable t and the space variable x will be considered in a future work finally numerical examples are provided to show that the implicit difference approximation is computationally efficient

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

improving generalised estimating equations using quadratic inference functions summary generalised estimating equations enable one to estimate regression parameters consistently in longitudinal data analysis even when the correlation structure is misspecified however under such misspecification the estimator of the regression parameter can be inefficient in this paper we introduce a method of quadratic inference functions that does not involve direct estimation of the correlation parameter and that remains optimal even if the working correlation structure is misspecified the idea is to represent the inverse of the working correlation matrix by the linear combination of basis matrices a representation that is valid for the working correlations most commonly used both asymptotic theory and simulation show that under misspecified working assumptions these estimators are more efficient than estimators from generalised estimating equations this approach also provides a chi squared inference function for testing nested models and a chi squared regression misspecification test furthermore the test statistic follows a chi squared distribution asymptotically whether or not the working correlation structure is correctly specified

a general bahadur representation of m estimators and its application to linear regression with nonstochastic designs we obtain strong bahadur representations for a general class of m estimators that satisfies sigma i psi x i theta o delta n where the x i s are independent but not necessarily identically distributed random variables the results apply readily to m estimators of regression with nonstochastic designs more specifically we consider the minimum l p distance estimators bounded influence gm estimators and regression quantiles under appropriate design conditions the error ratesobtained for the first order approximations are sharp in these cases we also provide weaker and more easily verifiable conditions that suffice for an error rate that is suboptimal but strong enough for deriving the asymptotic distribution of m estimators in a wide variety of problems

fractional calculus a different approach to the analysis of viscoelastically damped structures fractional calculus is used to construct stress strain relationships for viscoelastic materials these relationships are used in the finite element analysis of viscoelastically damped structures and closed form solutions to the equations of motion are found the attractive feature of this approach is that very few empirical parameters are required to model the viscoelastic material and calculate the response of the structure for general loading conditions

power transformation toward a linear regression quantile in this article we consider the linear quantile regression model with a power transformation on the dependent variable like the classical box cox transformation approach it extends the applicability of linear models without resorting to nonparametric smoothing but transformations on the quantile models are more natural due to the equivariance property of the quantiles under monotone transformations we propose an estimation procedure and establish its consistency and asymptotic normality under some regularity conditions the objective function employed in the estimation can also be used to check inadequacy of a power transformed linear quantile regression model and to obtain inference on the transformation parameter the proposed approach is shown to be valuable through illustrative examples

numerical techniques for the variable order time fractional diffusion equation abstract in this paper we consider the variable order time fractional diffusion equation we adopt the coimbra variable order vo time fractional operator which defines a consistent method for vo differentiation of physical variables the coimbra variable order fractional operator also can be viewed as a caputo type definition although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature here an approximate scheme is first proposed the stability convergence and solvability of this numerical scheme are discussed via the technique of fourier analysis numerical examples are provided to show that the numerical method is computationally efficient

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

median regression for longitudinal data we review and compare three estimators of median regression in linear models with longitudinal data the estimators are constructed based on well known ideas of weighting decorrelating and the working assumption of independence both asymptotic efficiency calculations and finite sample monte carlo studies are used to assess the performance of these estimators we find that their relative performances depend on the nature of covariates the estimator under the working assumption of independence is computationally simple and yet has good relative performance when the covariates are invariant over time or when the within subject correlations are small its relative performance in finite samples is also found to be more favourable than suggested by the asymptotic comparisons

control of damping oscillations by fractional differential operator with time dependent order abstract the aim of the present paper is application of a differential operator of variable order in constitutive relations for viscoelastic materials this operator is used for studying the vibrations of a one degree of freedom oscillator in which the viscoelastic deformation is governed by a servo order function a method for numerical determination of the eigenfrequency of the fractional differential equation is proposed

time domain finite element analysis of viscoelastic structures with fractional derivatives constitutive relations numerical procedures for the time integration of the spatially discretized finite element equations for viscoelastic structures governed by a constitutive equation involving fractional calculus operators are presented to avoid difficulties concerning fractional order initial conditions a form of the fractlonal calculus model of viscoelasticity involving a convolution integral with a singular memory kernel of mittag lefler type is used the constitutive equation is generalized to three dimensional states for isotropic materials a simplification of the fractional derivative of the memory kernel is used in connection with grunwald s definition of fractional differentiation and a backward euler rule for the time evolution of the convolution term a desirable feature of this process is that no actual evaluation of the memory kernel is needed this together with the newmark method for time integration enables the direct calculation of the time evolution of the nodal degrees of freedom to illustrate the ability of the numerical procedure a few numerical examples are presented in one example the numerically obtained solution is compared with a time series expansion of the analytical solution

goal oriented error estimation and adaptivity for fluid structure interaction using exact linearized adjoints we develop duality based a posteriori error estimates for functional outputs of solutions of steady fluid structure interaction problems the crucial complication in obtaining these estimates pertains to the derivation of the coupled dual exact linearized adjoint problem owing to the free boundary character of fluid structure interaction we present two approaches to derive the dual problem in the domain map linearization approach the fluid subproblem is first transformed to a fixed reference domain after which one essentially linearizes with respect to the domain transformation map in the shape linearization approach fluid unknowns are fixed in the current configuration and a very weak formulation of the fluid subproblem is then linearized using shape derivative techniques we show that the dual problems correspond to coupled fluid structure problems with nonstandard coupling conditions furthermore we present numerical experiments that demonstrate the consistency of the dual based error estimates and their usefulness in goal oriented adaptive mesh refinement

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

unified empirical likelihood ratio tests for functional concurrent linear models and the phase transition from sparse to dense functional data summary we consider the problem of testing functional constraints in a class of functional concurrent linear models where both the predictors and the response are functional data measured at discrete time points we propose test procedures based on the empirical likelihood with bias corrected estimating equations to conduct both pointwise and simultaneous inferences the asymptotic distributions of the test statistics are derived under the null and local alternative hypotheses where sparse and dense functional data are considered in a unified framework we find a phase transition in the asymptotic null distributions and the orders of detectable alternatives from sparse to dense functional data specifically the tests proposed can detect alternatives of n order when the number of repeated measurements per curve is of an order larger than n 0 with n being the number of curves the transition points 0 for pointwise and simultaneous tests are different and both are smaller than the transition point in the estimation problem simulation studies and real data analyses are conducted to demonstrate the methods proposed

modal synthesis when modeling damping by use of fractional derivatives the fractional derivative damping model and some of its properties are discussed small problems involving fractional derivatives may be solved in the fourier domain here modal synthesis is used to solve the equatlons of motion in the time domain a state space vector containing fractional derivatives of the displacements is then introduced and the system of equations is expanded the resulting system of equations is decoupled by use of the complex eigenvectors of the system the solutions of the decoupled equations are superposed weighted by the eigenmodes to give the response of the structure the computational effort can be reduced by taking into account some of the properties of the system

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

bayesian latent variable models for median regression on multiple outcomes souvent il est impossible de mesurer une reponse d interet et on doit necessairement faire appel a des grandeurs accessoires multiples qu on suppose independantes conditionnellement aux valeurs de la variable latente et des covariables observees de facon typique les modeles en variable latente supposent que les residuees sont gaussions cet article propose une regression bayesienne modelisant la mediane et qui dispense d hypothese sur les distributions des residus en s appuyant sur une approximation basee sur les quartiles pour traiter de la dependance intra sujet les quartiles de la reponse des variables de remplacement sont liees a des distributions normales sous jacentes dependant d une variable latente normale la structure de covariance gaussienne qui en resulte simplifie l interpretatin et l ajustement sans limiter les distributions marginales des variables de remplacement pour les calculs des distributions a posteriori nous proposons un algorithme de chaine de markov monte carlo les methodes sont appliquees sont appliquees pour d une etude de toxicologie genetique aux dosages par electrophorese sur cellule unique essai cornet

empirical likelihood and quantile regression in longitudinal data analysis we propose a novel quantile regression approach for longitudinal data analysis which naturally incorporates auxiliary information from the conditional mean model to account for within subject correlations the efficiency gain is quantified theoretically and demonstrated empirically via simulation studies and the analysis of a real dataset