discontinuous spectral element methods for time and space fractional advection equations we develop spectral element methods for a time and space fractional advection equation of the form prescript 0 mathcal d tau t u x t theta prescript 0 mathcal d nu x u x t f x t of order tau in 0 1 nu in 0 1 subject to dirichlet initial boundary conditions we present two spectrally accurate and efficient methods for global discretization of both temporal and spatial terms instead of employing traditional low order time integration methods to this end we first develop a petrov galerkin in time and discontinuous galerkin in space pg dg method where we carry out the time integration using a single time domain spectral method sm and we perform the spatial discretization using the discontinuous spectral hp element method dsem this scheme also leads to a more efficient time integration when the time derivative is integer order i e tau 1 we develop the sm dsem scheme based on a new spectral theory for fractional sturm liouville problems

rank preserving regression a more robust rank regression model against outliers mean based semi parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models unfortunately such models are quite sensitive to outlying observations the wilcoxon score based rank regression rr provides more robust estimates over generalized estimating equations against outliers however the rr and its extensions do not sufficiently address missing data arising in longitudinal studies in this paper we propose a new approach to address outliers under a different framework based on the functional response models this functional response model based alternative not only addresses limitations of the rr and its extensions for longitudinal data but with its rank preserving property even provides more robust estimates than these alternatives the proposed approach is illustrated with both real and simulated data copyright 2016 john wiley sons ltd

an advanced boundary element fast fourier transform axisymmetric formulation for acoustic radiation and wave scattering problems an advanced boundary element fast fourier transform be fft methodology for solving axisymmetric acoustic wave scattering and radiation problems with non axisymmetric boundary conditions is reported the boundary quantities of the problem are expanded in complex fourier series with respect to the circumferencial direction each of the expanding coefficients satisfies a surface integral equation which due to axisymmetry is reduced to a line integral along the surface generator of the body and an integral over the angle of revolution the first integral is evaluated through gauss quadrature by employing a two dimensional boundary element methodology the integration over the circumferencial direction is performed simultaneously for all the fourier coefficients through the fft the singular and hyper singular integrals are computed directly by employing highly accurate three dimensional integration techniques the accuracy of the proposed boundary element methodology is demonstrated by means of representative numerical examples

fractional sturm liouville eigen problems we first consider a regular fractional sturm liouville problem of two kinds rfslp i and rfslp ii of order 0 2 the corresponding fractional differential operators in these problems are both of riemann liouville and caputo type of the same fractional order 2 0 1 we obtain the analytical eigensolutions to rfslp i ii as non polynomial functions which we define as jacobi poly fractonomials these eigenfunctions are orthogonal with respect to the weight function associated with rfslp i ii subsequently we extend the fractional operators to a new family of singular fractional sturm liouville problems of two kinds sfslp i and sfslp ii we show that the primary regular boundary value problems rfslp i ii are indeed asymptotic cases for the singular counterparts sfslp i ii furthermore we prove that the eigenvalues of the singular problems are real valued and the corresponding eigenfunctions are orthogonal in addition we obtain the eigen solutions to sfslp i ii analytically also as non polynomial functions hence completing the whole family of the jacobi poly fractonomials in numerical examples we employ the new poly fractonomial bases to demonstrate the exponential convergence of the approximation in agreement with the theoretical results

smooth bootstrap methods for analysis of longitudinal data in analysis of longitudinal data the variance matrix of the parameter estimates is usually estimated by the sandwich method in which the variance for each subject is estimated by its residual products we propose smooth bootstrap methods by perturbing the estimating functions to obtain bootstrapped realizations of the parameter estimates for statistical inference our extensive simulation studies indicate that the variance estimators by our proposed methods can not only correct the bias of the sandwich estimator but also improve the confidence interval coverage we applied the proposed method to a data set from a clinical trial of antibiotics for leprosy

tests of linear hypotheses and l 1 estimation statistics of a linear hypothesis in the standard linear model these test statistics which correspond to wald likelihood ratio and lagrange multiplier tests are shown to have the same limiting chi square behavior under mild regularity conditions on design and the distribution of errors the asymptotic theory of the tests is derived for a large class of error distributions thus in huber s 10 terminology we investigate the behavior of the likelihood ratio test under non standard conditions the asymptotic efficiency of the 11 tests involves a modest sacrifice of power compared to classical tests in cases of strictly gaussian errors but may yield large efficiency gains in non gaussian situations the lagrange multiplier test seems particularly attractive from a computational standpoint we derive the asymptotic distribution of the three alternative 11 test statistics for a simple linear exclusion hypothesis extension of these results to hypotheses of the form r 8 r is a straightforward exercise when the density of the error distribution is strictly positive at the median all three test statistics have the same limiting central x2 behavior at the null and noncentral x2 behavior for local alternatives to the null when the variance of the error distribution is bounded analogous results are well known for classical forms of the wald likelihood ratio and lagrange multipler tests based on least squares methods see for example silvey 18 and the discussion in section 4 below

median regression models for longitudinal data with dropouts summary recently median regression models have received increasing attention when continuous responses follow a distribution that is quite different from a normal distribution usual mean regression models may fail to produce efficient estimators whereas median regression models may perform satisfactorily in this article we discuss using median regression models to deal with longitudinal data with dropouts weighted estimating equations are proposed to estimate the median regression parameters for incomplete longitudinal data where the weights are determined by modeling the dropout process consistency and the asymptotic distribution of the resultant estimators are established the proposed method is used to analyze a longitudinal data set arising from a controlled trial of hiv disease volberding et al 1990 the new england journal of medicine 322 941 949 simulation studies are conducted to assess the performance of the proposed method under various situations an extension to estimation of the association parameters is outlined

spectral and discontinuous spectral element methods for fractional delay equations we first develop a spectrally accurate petrov galerkin spectral method for fractional delay differential equations fddes this scheme is developed based on a new spectral theory for fractional sturm liouville problems fslps which has been recently presented in m zayernouri and g e karniadakis j comput phys 252 2013 pp 495 517 specifically we obtain solutions to fddes in terms of new nonpolynomial basis functions called jacobi polyfractonomials which are the eigenfunctions of the fslp of the first kind fslp i correspondingly we employ another space of test functions as the span of polyfractonomial eigenfunctions of the fslp of the second kind fslp ii we prove the wellposedness of the problem and carry out the corresponding stability and error analysis of the pg spectral method in contrast to standard nondelay fractional differential equations the delay character of fddes might induce solutions which are either nonsmooth or piecewise smooth in order to effectively trea

stable multi domain spectral penalty methods for fractional partial differential equations we propose stable multi domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order first a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials the approximation order is analyzed and verified through numerical examples based on the discrete fractional derivative we introduce stable multi domain spectral penalty methods for solving fractional advection and diffusion equations the equations are discretized in each sub domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes

a boundary integral approach for acoustic radiation of axisymmetric bodies with arbitrary boundary conditions valid for all wave numbers a boundary integral method for solving the exterior acoustic radiation problem of axisymmetric bodies with arbitrary boundary conditions is developed the new formulation derives from the method proposed by burton and miller proc r soc london ser a 323 201 210 1971 which uses a linear combination of the helmholtz integral equation and its normal derivative to ensure the uniqueness of the numerical solution at all frequencies it is shown that the use of tangential operators enables one to easily compute the hypersingular integral without much extra effort by taking advantage of the properties of axisymmetric geometry and using the expansion of the boundary conditions and the surface distribution functions in fourier series with respect to the angle of revolution the surface integral is reduced to a line integral along the generator of the body and fourier integrals of the green s function and its derivatives over the circumferential angle the fourier integrals with singular kernels are eval

the accuracy and stability of an implicit solution method for the fractional diffusion equation we have investigated the accuracy and stability of an implicit numerical scheme for solving the fractional diffusion equation this model equation governs the evolution for the probability density function that describes anomalously diffusing particles anomalous diffusion is ubiquitous in physical and biological systems where trapping and binding of particles can occur the implicit numerical scheme that we have investigated is based on finite difference approximations and is straightforward to implement the accuracy of the scheme is o dx 2 in the spatial grid size and o dt 1 c in the fractional time step where 0 email protected 1 is the order of the fractional derivative and c 1 is standard diffusion we have provided algebraic and numerical evidence that the scheme is unconditionally stable for 0 c 1

elastic scatterer interaction via generalized born series and far field approximations methods for solving elastic wave scattering problems in three dimensions 3d with multiple inhomogeneities are discussed a problem of homogeneous isotropic elastic defects in an otherwise homogeneous isotropic elastic full space is formulated as a boundary integral equation this equation is solved by discretizing the surface of each scatterer in a fashion known as the boundary element method the resulting matrix equation may be solved in a fully implicit manner but an implicit iterative method is more efficient with this hybrid method a portion of the nonsingular integral operator is expanded in a neumann series terms in this series correspond physically to nth order born approximations of the scatterers interaction the relative advantage of this hybrid scheme depends on the number of iterations required except for closely situated strong scatterers terms beyond the first few orders are not significant and thus the method can be quite advantageous when the separation is large another appro

tempered fractional sturm liouville eigenproblems continuum time random walk is a general model for particle kinetics which allows for incorporating waiting times and or non gaussian jump distributions with divergent second moments to account for levy flights exponentially tempering the probability distribution of the waiting times and the anomalously large displacements results in tempered stable levy processes with finite moments where the fluid continuous limit leads to the tempered fractional diffusion equation the development of fast and accurate numerical schemes for such nonlocal problems requires a new spectral theory and suitable choice of basis functions in this study we introduce two classes of regular and singular tempered fractional sturm liouville problems of two kinds tfslp i and tfslp ii of order nu in 0 2 in the regular case the corresponding tempered differential operators are associated with tempering functions p i x exp 2 tau and p ii x exp 2 tau tau geq 0 respectively in the regular tfslp i

a radial basis functions method for fractional diffusion equations one of the ongoing issues with fractional diffusion models is the design of an efficient high order numerical discretization this is one of the reasons why fractional diffusion models are not yet more widely used to describe complex systems in this paper we derive a radial basis functions rbf discretization of the one dimensional space fractional diffusion equation in order to remove the ill conditioning that often impairs the convergence rate of standard rbf methods we use the rbf qr method 1 33 by using this algorithm we can analytically remove the ill conditioning that appears when the number of nodes increases or when basis functions are made increasingly flat the resulting rbf qr based method exhibits an exponential rate of convergence for infinitely smooth solutions that is comparable to the one achieved with pseudo spectral methods we illustrate the flexibility of the algorithm by comparing the standard rbf and rbf qr methods for two numerical examples our results suggest that the global character of the rbfs makes them well suited to fractional diffusion equations they naturally take the global behavior of the solution into account and thus do not result in an extra computational cost when moving from a second order to a fractional order diffusion model as such they should be considered as one of the methods of choice to discretize fractional diffusion models of complex systems

rank based regression with repeated measurements data summary a rank based regression method is proposed for repeated measurements data it is a generalisation of the classical wilcoxon mann whitney rank statistic for independent observations the method is valid under a weak condition on the error terms that can accommodate certain heteroscedasticity and within subject dependency the asymptotic normality of the proposed estimator is proved using empirical process theory a variance estimator shown to be consistent is also constructed the proposed method is illustrated using data from a clinical trial on treating labour pain robustness and efficiency of the estimator is demonstrated in simulation studies

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

a boundary integral formulation for the prediction of acoustic scattering from periodic structures the scattering of sound by reflecting surfaces is an important feature in room acoustics the boundary element method has been shown in the past to be an accurate method to calculate the scattering pattern of complex surfaces however this numerical method is expensive to use on large surfaces where a large number of elements is required this paper proposes a method of reducing the number of boundary elements required to model large but periodic structures the method is based on a consideration of the relationship between the field variables at two points exactly one period apart the problem is reduced to the modeling of just one period of the structure in cases of plane wave incidence the prediction using this method agrees very well with the prediction obtained by modeling the complete structure with the point source in the near field of the surface the incidence field is no longer periodic and the assumption of a constant periodic factor does not hold in this case it is shown that the metho

inference for censored quantile regression models in longitudinal studies we develop inference procedures for longitudinal data where some of the measurements are censored by fixed constants we consider a semi parametric quantile regression model that makes no distributional assumptions our research is motivated by the lack of proper inference procedures for data from biomedical studies where measurements are censored due to a fixed quantification limit in such studies the focus is often on testing hypotheses about treatment equality to this end we propose a rank score test for large sample inference on a subset of the covariates we demonstrate the importance of accounting for both censoring and intra subject dependency and evaluate the performance of our proposed methodology in a simulation study we then apply the proposed inference procedures to data from an aids related clinical trial we conclude that our framework and proposed methodology is very valuable for differentiating the influences of predictors at different locations in the conditional distribution of a response variable

least squares finite element solution of a fractional order two point boundary value problem in this paper a theoretical framework for the least squares finite element approximation of a fractional order differential equation is presented mapping properties for fractional dimensional operators on suitable fractional dimensional spaces are established using these properties existence and uniqueness of the least squares approximation is proven optimal error estimates are proven for piecewise linear trial elements numerical results are included which confirm the theoretical results

quantile regression analysis of censored longitudinal data with irregular outcome dependent follow up in many observational longitudinal studies the outcome of interest presents a skewed distribution is subject to censoring due to detection limit or other reasons and is observed at irregular times that may follow a outcome dependent pattern in this work we consider quantile regression modeling of such longitudinal data because quantile regression is generally robust in handling skewed and censored outcomes and is flexible to accommodate dynamic covariate outcome relationships specifically we study a longitudinal quantile regression model that specifies covariate effects on the marginal quantiles of the longitudinal outcome such a model is easy to interpret and can accommodate dynamic outcome profile changes over time we propose estimation and inference procedures that can appropriately account for censoring and irregular outcome dependent follow up our proposals can be readily implemented based on existing software for quantile regression we establish the asymptotic properties of the proposed estimator including uniform consistency and weak convergence extensive simulations suggest good finite sample performance of the new method we also present an analysis of data from a long term study of a population exposed to polybrominated biphenyls pbb which uncovers an inhomogeneous pbb elimination pattern that would not be detected by traditional longitudinal data analysis

a numerical method for a partial integro differential equation a method is considered for the integration in time of a partial integro differential equation the discretization technique employed is patterned after an idea of ch lubich error bounds are derived for both smooth and nonsmooth initial data

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

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

estimation of nonlinear trends in water quality an improved approach using generalized additive models 1 this paper advocates the use of generalized additive models gams for the estimation of nonlinear trends in water quality in the presence of serially correlated errors the gam methodology is applicable to a range of physical chemical and biological water quality variates comparison with the estimate based on seasonal kendall s slope and robust regression is discussed an example is given concerning log transformed stream electrical conductivity which is adjusted for flow the monthly data have first order autocorrelation exceeding 0 5 and the trend is markedly nonlinear seasonal effects are shown to have been changing over time

fractional adams bashforth moulton methods we first formulate a fractional class of explicit adams bashforth a b and implicit adams moulton a m methods of first and second order accuracy for the time integration of d t 0 c u x t g t u 0 1 where d t 0 c denotes the fractional derivative in the caputo sense in this fractional setting and in contrast to the standard adams methods an extra history load term emerges and the associated weight coefficients are dependent however when 1 the developed schemes reduce to the well known a b and a m methods with standard coefficients hence in terms of scientific computing our approach constitutes a minimal modification of the existing adams libraries next we develop an implicit explicit imex splitting scheme for linear and nonlinear fractional pdes of a general advection reaction diffusion type and we apply our scheme to the time space fractional keller segel chemotaxis system in this context we evaluate the nonlinear advection term explicitly employing the fractional a b method in the prediction step and we treat the corresponding diffusion term implicitly in the correction step using the fractional a m scheme moreover we perform the corresponding spatial discretization by employing an efficient and spectrally accurate fractional spectral collocation method our numerical experiments exhibit the efficiency of the proposed imex scheme in solving nonlinear fractional pdes

serial and nonserial sign and rank statistics asymptotic representation and asymptotic normality the classical theory of rank based inference is entirely based either on ordinary ranks which do not allow for considering location nor intercept parameters or on signed ranks which require an assumption of symmetry if the median in the absence of a symmetry assumption is considered as a location parameter the maximal invariance property of ordinary ranks is lost to the ranks and the signs as shown in hallin and werker 2003 conditioning on a maximal invariant in such situations is essential if semiparametric efficiency is to be reached this new maximal invariant thus suggests a new class of statistics based on ordinary ranks and signs an asymptotic representation theory a la h ajek is developed here for such statistics both in the nonserial and in the serial case the corresponding asymptotic normality results clearly show how the signs are adding a separate contribution to the asymptotic variance hence potentially to asymptotic e ciency applications to semiparametric inference in regression and time series models with median restrictions are treated in detail in a companion paper hallin werker and vermandele 2003

composite marginal quantile regression analysis for longitudinal adolescent body mass index data childhood and adolescenthood overweight or obesity which may be quantified through the body mass index bmi is strongly associated with adult obesity and other health problems motivated by the child and adolescent behaviors in long term evolution cable study we are interested in individual family and school factors associated with marginal quantiles of longitudinal adolescent bmi values we propose a new method for composite marginal quantile regression analysis for longitudinal outcome data which performs marginal quantile regressions at multiple quantile levels simultaneously the proposed method extends the quantile regression coefficient modeling method introduced by frumento and bottai biometrics 2016 72 74 84 to longitudinal data accounting suitably for the correlation structure in longitudinal observations a goodness of fit test for the proposed modeling is also developed simulation results show that the proposed method can be much more efficient than the analysis without taking correlation into account and the analysis performing separate quantile regressions at different quantile levels the application to the longitudinal adolescent bmi data from the cable study demonstrates the practical utility of our proposal copyright 2017 john wiley sons ltd

a space time spectral method for the time fractional diffusion equation in this paper we consider the numerical solution of the time fractional diffusion equation essentially the time fractional diffusion equation differs from the standard diffusion equation in the time derivative term in the former case the first order time derivative is replaced by a fractional derivative making the problem global in time we propose a spectral method in both temporal and spatial discretizations for this equation the convergence of the method is proven by providing a priori error estimate numerical tests are carried out to confirm the theoretical results thanks to the spectral accuracy in both space and time of the proposed method the storage requirement due to the global time dependence can be considerably relaxed and therefore calculation of the long time solution becomes possible

conditional quantile regression models of melanoma tumor growth curves for assessing treatment effect in small sample studies tumor growth curves provide a simple way to understand how tumors change over time the traditional approach to fitting such curves to empirical data has been to estimate conditional mean regression functions which describe the average effect of covariates on growth however this method ignores the possibility that tumor growth dynamics are different for different quantiles of the possible distribution of growth patterns furthermore typical individual preclinical cancer drug study designs have very small sample sizes and can have lower power to detect a statistically significant difference in tumor volume between treatment groups in our work we begin to address these issues by combining several independent small sample studies of an experimental cancer treatment with differing study designs to construct quantile tumor growth curves for modeling we use a penalized fixed effects quantile regression with added study effects to control for study differences we demonstrate this approach using data from a series of small sample studies that investigated the effect of a naturally derived biological peptide p28 on tumor volumes in mice grafted with human melanoma cells we find a statistically significant quantile treatment effect on tumor volume trajectories and baseline values in particular the experimental treatment and a corresponding conventional chemotherapy had different effects on tumor growth by quantile the conventional treatment dacarbazine dtic tended to inhibit growth for smaller quantiles while the experimental treatment p28 produced slower rates of growth in the upper quantiles especially in the 95th quantile copyright 2014 john wiley sons ltd

finite difference spectral approximations for the time fractional diffusion equation in this paper we consider the numerical resolution of a time fractional diffusion equation which is obtained from the standard diffusion equation by replacing the first order time derivative with a fractional derivative of order a with 0 a 1 the main purpose of this work is to construct and analyze stable and high order scheme to efficiently solve the time fractional diffusion equation the proposed method is based on a finite difference scheme in time and legendre spectral methods in space stability and convergence of the method are rigourously established we prove that the full discretization is unconditionally stable and the numerical solution converges to the exact one with order o dt 2 a n m where dt n and m are the time step size polynomial degree and regularity of the exact solution respectively numerical experiments are carried out to support the theoretical claims

a petrov galerkin spectral element method for fractional elliptic problems abstract we develop a new c 0 continuous petrov galerkin spectral element method for one dimensional fractional elliptic problems of the form 0 d x u x u x f x 1 2 subject to homogeneous boundary conditions we employ the standard modal spectral element basis and the jacobi poly fractonomials as the test functions zayernouri and karniadakis 2013 we formulate a new procedure for assembling the global linear system from elemental local mass and stiffness matrices the petrov galerkin formulation requires performing elemental local construction of mass and stiffness matrices in the standard domain only once moreover we efficiently obtain the non local history stiffness matrices in which the non locality is presented analytically for uniform grids we also investigate two distinct choices of basis test functions i local basis test functions and ii local basis with global test functions we show that the former choice leads to a better conditioned system and accuracy while the latter results in ill conditioned linear systems and therefore that is not an efficient and a proper choice of test function we consider smooth and singular solutions where the singularity can occur at boundary points as well as in the interior domain we also construct two non uniform grids over the whole computational domain in order to capture singular solutions finally we perform a systematic numerical study of non local effects via full and partial history fading in order to further enhance the efficiency of the scheme

a novel technique in boundary integral equations for analyzing acoustic radiation from axisymmetric bodies a novel technique is suggested to avoid singular integrals of boundary integral equations bie for exterior sound radiation problems the technique reproduction of diagonal terms rdt utilizes special solutions of some monopole sources which give the distribution of theoretical surface pressure and velocity to reproduce diagonal terms in the bie matrices it is proposed to employ three monopole sources in reproduction of diagonal terms in both pressure and velocity matrices although the interior points are applied to generate monopole solutions the concept is basically different from that of general interior helmholtz equations so the present technique is different from those traditional methods to improve bie method through added interior helmholtz equations several examples are presented to demonstrate the effectiveness of the proposed technique for closed axisymmetric surfaces numerical results show that the technique of rdt can improve the accuracy of the solution up to 10 times compared to the conventional techniques such as shf chief shf

statistical inference in a growth curve quantile regression model for longitudinal data this article describes a polynomial growth curve quantile regression model that provides a comprehensive assessment about the treatment effects on the changes of the distribution of outcomes over time the proposed model has the flexibility as it allows the degree of a polynomial to vary across quantiles a high degree polynomial model fits the data adequately yet it is not desirable due to the complexity of the model we propose the model selection criterion based on an empirical loglikelihood that consistently identifies the optimal degree of a polynomial at each quantile after the parsimonious model is fitted to the data the hypothesis test is further developed to evaluate the treatment effects by comparing the growth curves it is shown that the proposed empirical loglikelihood ratio test statistic follows a chi square distribution asymptotically under the null hypothesis various simulation studies confirm that the proposed test successfully detects the difference between the curves across quantiles when the empirical loglikelihood is employed we incorporate the within subject correlation commonly existing in longitudinal data and gain estimation efficiency of the quantile regression parameters in the growth curve model the proposed process is illustrated through the analysis of randomized controlled longitudinal depression data

least absolute deviations estimation for the censored regression model this paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression or censored tobit model the proposed estimator is a generalization of least absolute deviations estimation for the standard linear model and unlike estimation methods based on the assumption of normally distributed error terms the estimator is consistent and asymptotically normal for a wide class of error distributions and is also robust to heteroscedasticity the paper gives the regularity conditions and proofs of these large sample results and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances

quasi likelihood for median regression models abstract this article proposes quasi likelihood equations for median regression models the quasi likelihood can be used for dependent observations such as repeated measurements or time series data to construct a quasi likelihood equation we need to specify the relation between the median and the dispersion and also specify the dependency of the observations if a monotone transformation of the original observation has a laplace distribution then the quasi likelihood is the exact likelihood under moderate assumptions the quasi likelihood estimates are consistent and have asymptotically normal distributions the estimates are also shown to have minimal asymptotic variance within a certain class of consistent estimates the proposed method is illustrated using data from a clinical trial

a multi domain spectral method for time fractional differential equations this paper proposes an approach for high order time integration within a multi domain setting for time fractional differential equations since the kernel is singular or nearly singular two main difficulties arise after the domain decomposition how to properly account for the history memory part and how to perform the integration accurately to address these issues we propose a novel hybrid approach for the numerical integration based on the combination of three term recurrence relations of jacobi polynomials and high order gauss quadrature the different approximations used in the hybrid approach are justified theoretically and through numerical examples based on this we propose a new multi domain spectral method for high order accurate time integrations and study its stability properties by identifying the method as a generalized linear method numerical experiments confirm hp convergence for both time fractional differential equations and time fractional partial differential equations

regression on quantile residual life a time specific log linear regression method on quantile residual lifetime is proposed under the proposed regression model any quantile of a time to event distribution among survivors beyond a certain time point is associated with selected covariates under right censoring consistency and asymptotic normality of the regression estimator are established an asymptotic test statistic is proposed to evaluate the covariate effects on the quantile residual lifetimes at a specific time point evaluation of the test statistic does not require estimation of the variance covariance matrix of the regression estimators which involves the probability density function of the survival distribution with censoring simulation studies are performed to assess finite sample properties of the regression parameter estimator and test statistic the new regression method is applied to a breast cancer data set with long term follow up to estimate the patients median residual lifetimes adjusting for important prognostic factors

robust estimating functions and bias correction for longitudinal data analysis robust methods are useful in making reliable statistical inferences when there are small deviations from the model assumptions the widely used method of the generalized estimating equations can be robustified by replacing the standardized residuals with the m residuals if the pearson residuals are assumed to be unbiased from zero parameter estimators from the robust approach are asymptotically biased when error distributions are not symmetric we propose a distribution free method for correcting this bias our extensive numerical studies show that the proposed method can reduce the bias substantially examples are given for illustration

boundedness vs blow up in a chemotaxis system abstract we determine the critical blow up exponent for a keller segel type chemotaxis model where the chemotactic sensitivity equals some nonlinear function of the particle density assuming some growth conditions for the chemotactic sensitivity function we establish an a priori estimate for the solution of the problem considered and conclude the global existence and boundedness of the solution furthermore we prove the existence of solutions that become unbounded in finite or infinite time in that situation where this a priori estimate fails

quantile regression models with multivariate failure time data en tant qu alternative a la classique modelisation de la moyenne par regression la modelisation des quantiles a ete largement etudiee surtout celle de la mediane dans le cas de donnees de survie independantes cependant les correlations naturelles ou artificielles entre donnees font qu il est courant de rencontrer en recherche biomedicale des donnees de survie multivariees pour lesquelles une correlation intra groupe doit etre ajustee pour des donnees de survie correlees et censurees a droite nous explorons ici la modelisation des quantiles et adaptons une approche par equations d estimation destinee a estimer les parametres sous hypothese d independance nous adaptons egalement une version ponderee de cette meme approche qui en ameliore l efficacite nous montrons que les estimateurs des parametres sont robustes et suivent asymptotiquement une distribution normale l estimation de la variance obtenue par approximation asymptotique utilise une estimation non parametrique de la densite cependant que la matrice de variance covariance est estimee par bootstrap et methodes de re echantillonnage perturbe des simulations montrent que l approche proposee convient aux echantillons de taille finie cette nouvelle demarche est appliquee pour illustration a des donnees issues d un essai clinique dans l otite

fractional chemotaxis diffusion equations we introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding the mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations different models are proposed depending on the timing of the chemotactic forcing generalizations of the models to include linear reaction dynamics are also derived finally a monte carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations the model equations developed here could be used to replace keller segel type equations in biological systems with transport hindered by traps macromolecular crowding or other obstacles

a boundary integral method for acoustic radiation and scattering in this article a computational method is proposed for computing the helmholtz integral equation for acoustic radiation and scattering problems with a three dimensional body shape unlike the previous boundary element method the integration of acoustic properties is based on the global body surface instead of local elements the approximation function of body geometry and the weighting function of numerical integration are independently chosen when the singular kernels of helmholtz equation are regularized as bounded discontinuous functions the order of integration polynomials for acoustic properties can be arbitrarily chosen therefore the accuracy and efficiency of computation can be increased

a fast wave superposition spectral method with complex radius vector combined with two dimensional fast fourier transform algorithm for acoustic radiation of axisymmetric bodies abstract based on the two dimensional fast fourier transform 2d fft algorithm a wave superposition spectral method with complex radius vector has been proposed to efficiently analyze the acoustic radiation from an axisymmetric body first the complex fourier series are used along both circumferential and meridian directions to expand the integral kernel function and unknown source strength density distributed function then by means of the rectangular integral formula the radiation sound pressure is described in the form of two dimensional discrete fourier transform and generalized through 2d fft algorithm finally several numerical examples are performed to verify the accuracy and efficiency of the present method comparing with the other existing analysis ways the present method has three different characteristics 1 there is no singular integral in the numerical computation 2 the unique solution can be given for all eigen wavenumbers owing to the application of the virtual boundary technology with complex radius vector and 3 the computational efficiency is improved remarkably because all fourier terms are calculated simultaneously through 2d fft algorithm

semiparametric approach to a random effects quantile regression model we consider a random effects quantile regression analysis of clustered data and propose a semiparametric approach using empirical likelihood the random regression coefficients are assumed independent with a common mean following parametrically specified distributions the common mean corresponds to the population average effects of explanatory variables on the conditional quantile of interest whereas the random coefficients represent cluster specific deviations in the covariate effects we formulate the estimation of the random coefficients as an estimating equations problem and use empirical likelihood to incorporate the parametric likelihood of the random coefficients a likelihood like statistical criterion function is proposed that which we show is asymptotically concave in a neighborhood of the true parameter value and motivates its maximizer as a natural estimator we use markov chain monte carlo samplers in the bayesian framework and propose the resulting quasi posterior mean as an estimator

exponentially accurate spectral and spectral element methods for fractional odes current discretizations of fractional differential equations lead to numerical solutions of low order of accuracy here we present different methods for fractional odes that lead to exponentially fast decay of the error first we develop a petrov galerkin pg spectral method for fractional initial value problems fivps of the form d t 0 u t f t and fractional final value problems ffvps d t t u t g t where 0 1 subject to dirichlet initial final conditions these schemes are developed based on a new spectral theory for fractional sturm liouville problems fslps which has been recently developed in 1 specifically we obtain solutions to fivps and ffvps in terms of the new fractional non polynomial basis functions called jacobi polyfractonomials which are the eigenfunctions of the fslp of first kind fslp i correspondingly we employ another space of test functions as the span of polyfractonomial eigenfunctions of the fslp of second kind fslp ii subsequently we develop a discontinuous spectral method dsm of petrov galerkin sense for the aforementioned fivps and ffvps where the basis functions do not satisfy the initial final conditions finally we extend the dsm scheme to a discontinuous spectral element method dsem for efficient longer time integration and adaptive refinement in these discontinuous schemes we employ the asymptotic eigensolutions to fslp i ii which are of jacobi polynomial forms as basis and test functions our numerical tests confirm the exponential algebraic convergence respectively in p and h refinements for various test cases with integer and fractional order solutions

sample size estimation for gee method for comparing slopes in repeated measurements data sample size calculation is an important component at the design stage of clinical trials controlled clinical trials often use a repeated measurement design in which individuals are randomly assigned to treatment groups and followed up for measurements at intervals across a treatment period of fixed duration in studies with repeated measurements one of the popular primary interests is the comparison of the rates of change in a response variable between groups statistical models for calculating sample sizes for repeated measurement designs often fail to take into account the impact of missing data correctly in this paper we propose to use the generalized estimating equation gee method in comparing the rates of change in repeated measurements and introduce closed form formulae for sample size and power that can be calculated using a scientific calculator since the sample size formula is based on asymptotic theory we investigate the performance of the estimated sample size in practical settings through simulations

logistic quantile regression for bounded outcomes when research interest lies in continuous outcome variables that take on values within a known range e g a visual analog scale for pain within 0 and 100 mm the traditional statistical methods such as least squares regression mixed effects models and even classic nonparametric methods such as the wilcoxon s test may prove inadequate frequency distributions of bounded outcomes are often unimodal u shaped and j shaped to the best of our knowledge in the biomedical and epidemiological literature bounded outcomes have seldom been analyzed by appropriate methods that for one correctly constrain inference to lie within the feasible range of values in many respects continuous bounded outcomes can be likened to probabilities or propensities yet what has long been heeded when modeling the probability of binary outcomes with the widespread use of logistic and probit regression so far appears to have been overlooked with continuous bounded outcomes with consequences at times disastrous logistic quantile regression constitutes an effective method to fill this gap

least absolute deviations fits for generalized linear models reference stap article 1992 004view record in web of science record created on 2006 04 04 modified on 2016 08 08

rank based regression for analysis of repeated measures we consider rank based regression models for repeated measures to account for possible within subject correlations we decompose the total ranks into between and within subject ranks and obtain two different estimators based on between and within subject ranks a simple perturbation method is then introduced to generate bootstrap replicates of the estimating functions and the parameter estimates this provides a convenient way for combining the corresponding two types of estimating function for more efficient estimation

an analysis of the modified l1 scheme for time fractional partial differential equations with nonsmooth data we introduce a modified l1 scheme for solving time fractional partial differential equations and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and inhomogeneous c

fractional spectral collocation methods for linear and nonlinear variable order fpdes while several high order methods have been developed for fractional pdes fpdes with fixed order there are no such methods for fpdes with field variable order these equations allow multiphysics simulations seamlessly e g from diffusion to sub diffusion or from wave dynamics transitioning to diffusion by simply varying the fractional order as a function of space or time we develop an exponentially accurate fractional spectral collocation method for solving linear nonlinear fpdes with field variable order following the spectral theory developed in 1 for fractional sturm liouville eigenproblems we introduce a new family of interpolants called left right sided and central fractional lagrange interpolants we employ the fractional derivatives of left right sided riemann liouville and riesz type and obtain the corresponding fractional differentiation matrices by collocating the field variable fractional orders we solve several fpdes including time and space fractional advection equation time and space fractional advection diffusion equation and finally the space fractional burgers equation to demonstrate the performance of the method in addition we develop a spectral penalty method for enforcing inhomogeneous initial conditions our numerical results confirm the exponential like convergence of the proposed fractional collocation methods

a special integral equation formulation for acoustic radiation and scattering for axisymmetric bodies and boundary conditions this paper presents a simplified model of the helmholtz integral equation for bodies with axisymmetric shape and boundary conditions by taking advantage of a body s axisymmetric properties the surface integral is reduced to a line integral along the generator of the body and an integral over the angle of revolution the integration over the angle is performed partly analytically in terms of elliptic integrals and partly numerically using a gaussian quadrature formula the analytical formulation leading to elliptic integrals deals directly with the singularities in the green s function and its normal derivative examples are shown for scattering from a single sphere and two spheres and radiation from a finite cylinder the results are compared with analytical approximate and other accepted solutions

cholesky residuals for assessing normal errors in a linear model with correlated outcomes despite the widespread popularity of linear models for correlated outcomes e g linear mixed models and time series models distribution diagnostic methodology remains relatively underdeveloped in this context in this article we present an easy to implement approach that lends itself to graphical displays of model fit our approach involves multiplying the estimated marginal residual vector by the cholesky decomposition of the inverse of the estimated marginal variance matrix the resulting rotated residuals are used to construct an empirical cumulative distribution function and pointwise standard errors the theoretical framework including conditions and asymptotic properties involves technical details that are motivated by lange and ryan pierce and randles our method appears to work well in a variety of circumstances including models having independent units of sampling clustered data and models for which all observations are correlated e g a single time series our methods can produce

a unified spectral method for fpdes with two sided derivatives part ii stability and error analysis abstract we present the stability and error analysis of the unified petrov galerkin spectral method developed in 1 for linear fractional partial differential equations with two sided derivatives and constant coefficients in any 1 d dimensional space time hypercube d 1 2 3 subject to homogeneous dirichlet initial boundary conditions specifically we prove the existence and uniqueness of the weak form and perform the corresponding stability and error analysis of the proposed method finally we perform several numerical simulations to compare the theoretical and computational rates of convergence

survival analysis with median regression models abstract the median is a simple and meaningful measure for the center of a long tailed survival distribution to examine the covariate effects on survival a natural alternative to the usual mean regression model is to regress the median of the failure time variable or a transformation thereof on the covariates in this article we propose semiparametric procedures to make inferences for such median regression models with possibly censored observations our proposals can be implemented efficiently using a simulated annealing algorithm numerical studies are conducted to show the advantage of the new procedures over some recently developed methods for the accelerated failure time model a special type of mean regression models in the survival analysis the proposals discussed in the article are illustrated with a lung cancer data set

fractional spectral collocation method we develop an exponentially accurate fractional spectral collocation method for solving steady state and time dependent fractional pdes fpdes we first introduce a new family of interpolants called fractional lagrange interpolants which satisfy the kronecker delta property at collocation points we perform such a construction following a spectral theory recently developed in m zayernouri and g e karniadakis j comput phys 47 2013 pp 2108 2131 for fractional sturm liouville eigenproblems subsequently we obtain the corresponding fractional differentiation matrices and we solve a number of linear fodes in addition to linear and nonlinear fpdes to investigate the numerical performance of the fractional collocation method we first examine space fractional advection diffusion problem and generalized space fractional multiterm fodes next we solve fpdes including the time and space fractional advection diffusion equation time and space fractional multiterm fpdes and finally the space

a high order schema for the numerical solution of the fractional ordinary differential equations in this paper we present a general technique to construct high order schemes for the numerical solution of the fractional ordinary differential equations fodes this technique is based on the so called block by block approach which is a common method for the integral equations in our approach the classical block by block approach is improved in order to avoiding the coupling of the unknown solutions at each block step with an exception in the first two steps while preserving the good stability property of the block by block schemes by using this new approach we are able to construct a high order schema for fodes of the order a a 0 the stability and convergence of the schema is rigorously established we prove that the numerical solution converges to the exact solution with order 3 a for 0 1 a series of numerical examples are provided to support the theoretical claims

on the fractional adams method the generalized adams bashforth moulton method often simply called the fractional adams method is a useful numerical algorithm for solving a fractional ordinary differential equation d ay t f t y t y k 0 y 0 k k 0 1 n 1 where a 0 email protected email protected is the first integer not less than a and d ay t is the ath order fractional derivative of y t in the caputo sense although error analyses for this fractional adams method have been given for a 0 1 email protected c 1 a 0 t c 0 1 email protected c 3 g there are still some unsolved problems i the error estimates for email protected 0 1 email protected c 3 g ii the error estimates for email protected 0 1 email protected c 2 g iii the solution y t having some special forms in this paper we mainly study the error analyses of the fractional adams method for the fractional ordinary differential equations for the three cases i iii numerical simulations are also included which are in line with the theoretical analysis

an advanced boundary element method for axisymmetric elastodynamic analysis an advanced boundary element method is appropriately combined with the fast fourier transform fft to analyze general axisymmetric problems in frequency domain elastodynamics the problems are characterized by axisymmetric geometry and non axisymmetric boundary conditions boundary quantities are expanded in complex fourier series in the circumferential direction and the problem is efficiently decomposed into a series of problems which are solved by the bem for the fourier coefficients of the boundary quantities discretizing only the surface generator of the axisymmetric body quadratic boundary elements are used and bem integrations are done by fft algorithm in the circumferential direction and by gauss quadrature in the generator direction singular integrals are evaluated directly in a highly accurate way the fourier transformed solution is then numerically inverted by the fft to provide the final solution the method combines high accuracy and efficiency and this is demonstrated by illustrative numerical examples

evaluation of the helmholtz boundary integral equation and its normal and tangential derivatives in two dimensions abstract this paper presents a means of evaluating singular integrals in the helmholtz boundary integral equation and its normal and tangential derivatives in two dimensions the subtraction addition technique is applied to the singular integral equations to convert the singular integrals to either ordinary integrals with bounded integrands or modified singular integrals including hypersingular integrals with exact integration values this regularization is performed before any discretization the modified integral equations can be calculated by directly applying standard quadrature rules over the entire integration domain numerical computations involve evaluating the acoustic field associated with a radiating inverse elliptic cylinder the velocity potential is obtained by applying the burton miller method which linearly combines the helmholtz boundary integral equation with its normal derivative to treat the fictitious characteristic frequencies further substituting the velocity potential into the regularized tangential derivative yields the surface tangential velocity comparing the numerical results with the analytical solutions verifies the effectiveness of the presented approach

semi parametric and non parametric methods for the analysis of repeated measurements with applications to clinical trials techniques applicable for the analysis of longitudinal data when the response variable is non normal are not nearly as comprehensive as for normally distributed outcomes however there have been several recent developments semi parametric and non parametric methodology for the analysis of repeated measurements is reviewed the commonly encountered design in which for each subject one assesses a univariate response variable at multiple fixed time points is considered the types of outcomes considered include binary ordered categorical and continuous but extremely non normal response variables all of the methods considered allow for incomplete data due to the occurrence of missing observations in addition discrete and or continuous covariates which may be time dependent are accommodated by some of the approaches the methods are demonstrated using data from three clinical trials

bayesian quantile regression for longitudinal studies with nonignorable missing data summary we study quantile regression qr for longitudinal measurements with nonignorable intermittent missing data and dropout compared to conventional mean regression quantile regression can characterize the entire conditional distribution of the outcome variable and is more robust to outliers and misspecification of the error distribution we account for the within subject correlation by introducing a l2 penalty in the usual qr check function to shrink the subject specific intercepts and slopes toward the common population values the informative missing data are assumed to be related to the longitudinal outcome process through the shared latent random effects we assess the performance of the proposed method using simulation studies and illustrate it with data from a pediatric aids clinical trial

linear regression analysis for multivariate failure time observations abstract in this article we consider the case that each patient in a longitudinal study may experience two or more distinct failures the corresponding failure times which are possible censored are recorded for each patient the logarithm of each marginal failure time is assumed to be linearly related to its covariates however the distributional form of the error term in the model does not have to be specified in the analysis furthermore no specific structure of dependence among the distinct failure times on each subject has to be imposed various linear regression methods for analyzing multivariate failure time observations are proposed our procedures do not involve the unstable nonparametric hazard function estimation extensive numerical studies are conducted to evaluate the new proposals recommendations are also made for their practical usage