nonparametric quantile estimations for dynamic smooth coefficient models in this article quantile regression methods are suggested for a class of smooth coefficient time series models we use both local polynomial and local constant fitting schemes to estimate the smooth coefficients in a quantile framework we establish the asymptotic properties of both the local polynomial and local constant estimators for mixing time series also a bandwidth selector based on the nonparametric version of the akaike information criterion is suggested together with a consistent estimate of the asymptotic covariance matrix furthermore the asymptotic behaviors of the estimators at boundaries are examined a comparison of the local polynomial quantile estimator with the local constant estimator is presented a simulation study is carried out to illustrate the performance of estimates an empirical application of the model to real data further demonstrates the potential of the proposed modeling procedures

multitask quantile regression under the transnormal model abstractwe consider estimating multitask quantile regression under the transnormal model with focus on high dimensional setting we derive a surprisingly simple closed form solution through rank based covariance regularization in particular we propose the rank based l1 penalization with positive definite constraints for estimating sparse covariance matrices and the rank based banded cholesky decomposition regularization for estimating banded precision matrices by taking advantage of the alternating direction method of multipliers nearest correlation matrix projection is introduced that inherits sampling properties of the unprojected one our work combines strengths of quantile regression and rank based covariance regularization to simultaneously deal with nonlinearity and nonnormality for high dimensional regression furthermore the proposed method strikes a good balance between robustness and efficiency achieves the oracle like convergence rate and provides the provable prediction interval und

new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis semiparametric regression models are very useful for longitudinal data analysis the complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis in this article two new approaches are proposed for estimating the regression coefficients in a semiparametric model the asymptotic normality of the resulting estimators is established an innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models the proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters rates of convergence of the resulting estimators are established with a proper choice of regularization parameters and penalty functions the proposed variable selection procedures are shown to perform as well as an oracle estimator a robust standard error formula is derived usi

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

estimating regional centile curves from mixed data sources and countries regional or national growth distributions can provide vital information on the health status of populations in most resource poor countries however the required anthropometric data from purpose designed growth surveys are not readily available we propose a practical method for estimating regional multi country age conditional weight distributions based on existing survey data from different countries we developed a two step method by which one is able to model data with widely different age ranges and sample sizes the method produces references both at the country level and at the regional multi country level the first step models country specific centile curves by box cox t and box cox power exponential distributions implemented in generalized additive model for location scale and shape through a common model individual countries may vary in location and spread the second step defines the regional reference from a finite mixture of the country distributions weighted by population size to demonstrate the method we fitted the weight for age distribution of 12 countries in south east asia and the western pacific based on 273 270 observations we modeled both the raw body weight and the corresponding z score and obtained a good fit between the final models and the original data for both solutions we briefly discuss an application of the generated regional references to obtain appropriate region specific age based dosing regimens of drugs used in the tropics the method is an affordable and efficient strategy to estimate regional growth distributions where the standard costly alternatives are not an option copyright 2009 john wiley sons ltd

simplified estimation of age specific reference intervals for skewed data age specific reference intervals are commonly used in medical screening and clinical practice where interest lies in the detection of extreme values many different statistical approaches have been published on this topic the advantages of a parametric method are that they necessarily produce smooth centile curves the entire density is estimated and an explicit formula is available for the centiles the method proposed here is a simplified version of a recent approach proposed by royston and wright basic transformations of the data and multiple regression techniques are combined to model the mean standard deviation and skewness using these simple tools which are implemented in almost all statistical computer packages age specific reference intervals may be obtained the scope of the method is illustrated by fitting models to several real data sets and assessing each model using goodness of fit techniques

inference on the quantile regression process tests based on the quantile regression process can be formulated like the classical kolmogorov smirnov and cramer von mises tests of goodness of fit employing the theory of bessel processes as in kiefer 1959 however it is frequently desirable to formulate hypotheses involving unknown nuisance parameters thereby jeopardizing the distribution free character of these tests we characterize this situation as the durbin problem since it was posed in durbin 1973 for parametric empirical processes in this paper we consider an approach to the durbin problem involving a martingale transformation of the parametric empirical process suggested by khmaladze 1981 and show that it can be adapted to a wide variety of inference problems involving the quantile regression process in particular we suggest new tests of the location shift and location scale shift models that underlie much of classical econometric inference the methods are illustrated with a reanalysis of data on unemployment durations from the pennsylvania reemployment bonus experiments the pennsylvania experiments conducted in 1988 89 were designed to test the efficacy of cash bonuses paid for early reemployment in shortening the duration of insured unemployment spells

parabolic control problems in measure spaces with sparse solutions optimal control problems in measure spaces lead to controls that have small support which is desirable e g in the context of optimal actuator placement for problems governed by parabolic partial differential equations well posedness is guaranteed in the space of square integrable measure valued functions which leads to controls with a spatial sparsity structure a conforming approximation framework allows one to derive numerically accessible optimality conditions as well as convergence rates in particular although the state is discretized the control problem can still be formulated and solved in the measure space numerical examples illustrate the structural features of the optimal controls

identifying risk factors for severe childhood malnutrition by boosting additive quantile regression we investigated the risk factors for childhood malnutrition in india based on the 2005 2006 demographic and health survey by applying a novel estimation technique for additive quantile regression ordinary linear and generalized linear regression models relate the mean of a response variable to a linear combination of covariate effects and as a consequence focus on average properties of the response the use of such a regression model for analyzing childhood malnutrition in developing or transition countries implies that the estimated effects describe the average nutritional status however it is of even greater interest to analyze quantiles of the response distribution such as the 5 or 10 quantile which relate to the risk of extreme malnutrition our investigation is based on a semiparametric extension of quantile regression models where different types of nonlinear effects are included in the model equation leading to additive quantile regression we addressed the variable selection and model c

choice of scale for cubic smoothing spline models in medical applications the determination of the functional form of the relationship between an outcome variable and one or more continuous covariates is an important aspect of the modelling of medical data for correct interpretation of the data it is essential that the functional form be specified at least approximately correctly i show that for given model complexity logarithmic transformation of a covariate can greatly improve the fit of one of the most useful and convenient non parametric regression models the cubic smoothing spline a mathematical rationale for the idea is given i propose a diagnostic for deciding initially whether a log transformation is needed the method is illustrated using several medical data sets no special software other than that used for fitting the spline models is needed

infant growth modelling using a shape invariant model with random effects models for infant growth have usually been based on parametric forms commonly an exponential or similar model which have been shown to fit poorly especially during the first year of life an alternative approach is to use a non parametric model based on a shape invariant model sim where a single function is transformed by shifting and scaling to fit each subject in the model a regression spline is used as the function with log transformation of the data and a simplification of the sim obtained from the relationship with the exponential model all subjects are fitted as a nonlinear mixed effects model allowing the variation in the parameters between subjects to be determined methods for the inclusion of covariates in growth models based on sim are developed with parameters for time independent covariates included in the model by varying either the shape the size parameter or the growth parameter and time dependent co variates included by transforming the time axis to either increase or decrease the growth rate dependent on the co variate similar to methods used for accelerated failure time models the model is used to fit weight data for 602 infants measured from 0 to 2 years as part of the childhood asthma prevention study caps trial and to determine the effect of breastfeeding on infant weight

cumulative regression function tests for regression models for longitudinal data the longitudinal regression model y i j m v i ti j e i j where y i j is the jth measurement of the ith subject at random time i j m is the regression function v i j i is a predictable covariate process observed at time i j and e i j is noise often provides an adequate framework for modeling and comparing groups of data the proposed longitudinal regression model is based on marked point process theory and allows a quite general dependency structure among the observations in this paper we find the asymptotic distribution of the cumulative regression function crf and present a nonparametric test to compare the regression functions for two groups of longitudinal data the proposed test denoted the crf test is based on the cumulative regression function crf and is the regression equivalent of the log rank test in survival analysis we show as a special case that the crf test is valid for groups of independent identically distributed regression data apart from the crf test we also consider a maximal deviation statistic that may be used when the crf test is inefficient

smoothing methods and semismooth methods for nondifferentiable operator equations we consider superlinearly convergent analogues of newton methods for nondifferentiable operator equations in function spaces the superlinear convergence analysis of semismooth methods for nondifferentiable equations described by a locally lipschitzian operator in rn is based on rademacher s theorem which does not hold in function spaces we introduce a concept of slant differentiability and use it to study superlinear convergence of smoothing methods and semismooth methods in a unified framework we show that a function is slantly differentiable at a point if and only if it is lipschitz continuous at that point an application to the dirichlet problems for a simple class of nonsmooth elliptic partial differential equations is discussed

an approach to the analysis of repeated measurements summary a linear model for repeated measurements is proposed in which the correlation structure within each time sequence of measurements includes parameters for measurement error variation between experimental units and serial correlation within units an approach to data analysis is presented which involves preliminary analysis by ordinary least squares use of the empirical semi variogram of residuals to suggest a suitable correlation structure and formal inference using likelihood based methods applications to two biological data sets are described

prediction and creation of smooth curves for temporally correlated longitudinal data abstract this article presents a method of obtaining smoothed curves for a sample of individuals that permits an arbitrary number and spacing of observations for each individual we consider the case where each individual s curve cannot be separately estimated because either the n i s are too small or no suitable parametric forms for the random effects are available the model assumes a parametric form for the population mean curve and the correlation of the repeated measures the assumed correlation structure is evaluated using the empirical semivariogram a function of the sum of the squared differences of within individual residuals a method is proposed to validate the form and stationarity of the correlation structure maximum likelihood estimates for the population mean parameters and variance components are obtained simultaneously these estimates may be used to create a semiparametric differentiable curve and to predict future values for each individual using a method called kriging this method

multi level repeated measures growth modelling using extended spline functions this paper explores the fitting of multi level models to growth data over a wide age range using a new class of extended spline models these extend conventional splines based on a function representation by allowing variable order functions and by including fractional polynomial terms the work focuses on modelling human growth in height and head circumference with example data sets the procedures can be used with covariates and for comparing population parameters

directional sparsity in optimal control of partial differential equations we study optimal control problems in which controls with certain sparsity patterns are preferred for time dependent problems the approach can be used to find locations for control devices that allow controlling the system in an optimal way over the entire time interval the approach uses a nondifferentiable cost functional to implement the sparsity requirements additionally bound constraints for the optimal controls can be included we study the resulting problem in appropriate function spaces and present two solution methods of newton type based on different formulations of the optimality system using elliptic and parabolic test problems we research the sparsity properties of the optimal controls and analyze the behavior of the proposed solution algorithms

optimal smoothing in nonparametric conditional quantile derivative function estimation abstract marginal effect in nonparametric quantile regression is of special interest as it quantitatively measures how one unit change in explanatory variable heterogeneously affects dependent variable ceteris paribus at distinct quantiles in this paper we propose a data driven bandwidth selection procedure based on the gradient of an unknown quantile regression function our method delivers the bandwidth with the oracle property in the sense that it is asymptotically equivalent to the optimal bandwidth if the true gradient were known the results of monte carlo simulations are reported and the finite sample performance of our proposed method confirms our theoretical analysis an empirical application is also provided showing that our proposed method delivers more reasonable and reliable quantile derivative estimates than traditional cross validation method

valid post selection inference in high dimensional approximately sparse quantile regression models this work proposes new inference methods for a regression coefficient of interest in a heterogenous quantile regression model we consider a high dimensional model where the number of regressors

transformed dynamic quantile regression on censored data we propose a class of power transformed linear quantile regression models for time to event observations subject to censoring by introducing a process of power transformation with different transf

penalized quasi likelihood estimation in partial linear models consider a partial linear model where the expectation of a random variable y depends on covariates x z through f theta 0 x m 0 z with theta 0 an unknown parameter and m 0 an unknown function we apply the theory of empirical processes to derive the asymptotic properties of the penalized quasi likelihood estimator

improving point and interval estimators of monotone functions by rearrangement suppose that a target function is monotonic and an available original estimate of this target function is not monotonic rearrangements univariate and multivariate transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function furthermore suppose an original confidence interval which covers the target function with probability at least 1 is defined by an upper and lower endpoint functions that are not monotonic then the rearranged confidence interval defined by the rearranged upper and lower endpoint functions is monotonic shorter in length in common norms than the original interval and covers the target function with probability at least 1 we illustrate the results with a growth chart example

regression rank scores and regression quantiles we show that regression quantiles which could be computed as solutions of a linear programming problem and the solutions of the corresponding dual problem which we call the regression rank scores generalize the duality of order statistics and of ranks from the location to the linear model noting this fact we study the regression quantile and regression rank score processes in the heteroscedastic linear regression model obtaining some new estimators and interesting comparisons with existing estimators

a lack of fit test for quantile regression we propose an omnibus lack of fit test for linear or nonlinear quantile regression based on a cusum process of the gradient vector the test does not involve nonparametric smoothing but is consistent for all nonparametric alternatives without any moment conditions on the regression error in addition the test is suitable for detecting the local alternatives of any order arbitrarily close to n 1 2 from the null hypothesis the limiting distribution of the proposed test statistic is non gaussian but can be characterized by a gaussian process we propose a simple sequential resampling scheme to carry out the test whose nominal levels are well approximated in our empirical study for

multivariate quantiles and multiple output regression quantiles from l1 optimization to halfspace depth a new multivariate concept of quantile based on a directional version of koenker and bassett s traditional regression quantiles is introduced for multivariate location and multiple output regression problems in their empirical version those quantiles can be computed efficiently via linear programming techniques consistency bahadur representation and asymptotic normality results are established most importantly the contours generated by those quantiles are shown to coincide with the classical halfspace depth contours associated with the name of tukey this relation does not only allow for efficient depth contour computations by means of parametric linear programming but also for transferring from the quantile to the depth universe such asymptotic results as bahadur representations finally linear programming duality opens the way to promising developments in depth related multivariate rank based inference

evaluation of diagnostic scores with adjustment for covariates diagnostic tests yield measurements on very different types of scales quantitative scales may consist of non negative integers either unbounded or bounded with a fixed number of different values or they may consist of continuous or percentage values remembering a different threshold value for each diagnostic variable would be cumbersome in particular if covariates have to be taken into account as a convenient way to overcome such problems we propose to compute z scores for all measurements they will be adjusted for covariates so that any individual can be judged on any test result on one single scale with an appropriate standard normal quantile as threshold two issues need to be addressed selection of covariates in the regression model which delivers the adjustment and normality of the residuals the first will be treated by cross validation and the latter by applying an appropriate transformation we apply this methodology to neuropsychological tests and adjust for age length of education and sex normality of residuals is needed on the diagnostically relevant side only this allows to use parametric transformations which can be easily implemented e g in database systems since we have measurements at baseline and at follow up we also analyze change values in a similar manner for ease of interpretation we transform the resulting z scores back to the original scale

goodness of fit statistics for age specific reference intervals the age specific reference interval is a commonly used screening tool in medicine it involves estimation of extreme quantile curves such as the 5th and 95th centiles of a reference distribution of clinically normal individuals it is crucial that models used to estimate such intervals fit the data extremely well however few procedures to assess goodness of fit have been proposed in the literature and even fewer have been evaluated systematically here we consider procedures based on the distribution of the z scores standardized residuals from a model and on pearson chi 2 statistics for observed and expected counts in groups defined by age and the estimated reference centile curves two of the procedures q and grid tests are mainly inferential whereas the third permutation bands and b tests is essentially graphical we obtain approximations to the null distributions of several relevant test statistics and examine their size and power for a range of models based on real data sets we recommend q tests in all situations where z scores are available since they are general simple to calculate and usually have the highest power among the three classes of test considered for the cases considered the grid tests are always inferior to the q and b tests

a new polynomial approximation for jν bessel functions abstract new approximate solutions to the order bessel function of the first kind are derived the solution is expressed as a polynomial for bessel function of all fractional order polynomial comparisons are made between the exact solution and the new approximation one utility of this derivation is to allow researchers to analytically evaluate integrals containing bessel functions

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

nonparametric estimation of conditional distributions and rank tracking probabilities with time varying transformation models in longitudinal studies an objective of longitudinal analysis is to estimate the conditional distributions of an outcome variable through a regression model the approaches based on modeling the conditional means are not appropriate for this task when the conditional distributions are skewed or cannot be approximated by a normal distribution through a known transformation we study a class of time varying transformation models and a two step smoothing method for the estimation of the conditional distribution functions based on our models we propose a rank tracking probability and a rank tracking probability ratio to measure the strength of tracking ability of an outcome variable at two different time points our models and estimation method can be applied to a wide range of scientific objectives that cannot be evaluated by the conditional mean based models we derive the asymptotic properties for the two step local polynomial estimators of the conditional distribution functions finite sample properties of our procedures are i

new expansions of bessel functions of first kind and complex argument we present accurate trigonometric expansions of bessel functions of first kind and integer order for complex arguments of the form j v z sum k alpha k s beta k z where alpha k and beta k are constants and s is a sinusoidal function using the new expansions varying levels of accuracy and range of applicability can be achieved by varying the number of terms in the expansions for example a four term expansion of j 0 z yields an average relative error of for vert z vert leq 2 pi and same accuracy is achieved for an eight term expansion for an extended range vert z vert leq 5 pi further a phase and amplitude corrected large argument asymptotic formula is studied such that the lower limit of its usage is reduced to medium magnitude ranges of arguments the new set of formulas can not only be incorporated into math libraries very easily but also be useful for treatment of radiation and scattering problems involving bessel functions

british 1990 growth reference centiles for weight height body mass index and head circumference fitted by maximum penalized likelihood to update the british growth reference anthropometric data for weight height body mass index weight height2 and head circumference from 17 distinct surveys representative of england scotland and wales 37 700 children age range 23 weeks gestation to 23 years were analysed by maximum penalized likelihood using the lms method this estimates the measurement centiles in terms of three age sex specific cubic spline curves the l curve box cox power to remove skewness m curve median and s curve coefficient of variation a two stage fitting procedure was developed to model the age trends in median weight and height and simulation was used to estimate confidence intervals for the fitted centiles the reference converts measurements to standard deviation scores sds that are very close to normally distributed the means medians and skewness for the four measurements are effectively zero overall with standard deviations very close to one and only slight evidence of positive kurtosis beyond 2 sds the ability to express anthropometry as sds greatly simplifies growth assessment

optimal designs for quantile regression models despite their importance optimal designs for quantile regression models have not been developed so far in this article we investigate the d optimal design problem for nonlinear quantile regression analysis we provide a necessary condition to check the optimality of a given design and use it to determine bounds for the number of support points of locally d optimal designs the results are illustrated determining locally bayesian and standardized maximin d optimal designs for quantile regression analysis in the michaelis menten and emax model which are widely used in such important fields as toxicology pharmacokinetics and dose response modeling

quantile regression methods for reference growth charts estimation of reference growth curves for children s height and weight has traditionally relied on normal theory to construct families of quantile curves based on samples from the reference population age specific parametric transformation has been used to significantly broaden the applicability of these normal theory methods non parametric quantile regression methods offer a complementary strategy for estimating conditional quantile functions we compare estimated reference curves for height using the penalized likelihood approach of cole and green statistics in medicine 1992 11 1305 1319 with quantile regression curves based on data used for modern finnish reference charts an advantage of the quantile regression approach is that it is relatively easy to incorporate prior growth and other covariates into the analysis of longitudinal growth data quantile specific autoregressive models for unequally spaced measurements are introduced and their application to diagnostic screening is illustrated copyright 2005 john wiley sons ltd

reference curves based on non parametric quantile regression reference curves which take time into account such as those for age are often required in medicine but simple systematic and efficient statistical methods for constructing them are lacking classical methods are based on parametric fitting polynomial curves semi parametric methods are also widely used especially in europe here we propose a new methodology for the estimation of reference intervals for data sets based on non parametric estimation of conditional quantiles the derived methods should be applicable to all clinical or more generally biological variables that are measured on a continuous quantitative scale as an example we analyse a data set collected to establish reference curves for biophysical properties of the skin of healthy french women the results are compared to those obtained with royston s polynomial parametric method and the semi parametric lms approach

application of nonparametric quantile regression to body mass index percentile curves from survey data increasing rates of overweight among children in the u s stimulated interest in obtaining national percentile curves of body size to serve as a benchmark in assessing growth development in clinical and population settings in 2000 the u s centers for disease control and prevention cdc developed conditional percentile curves for body mass index bmi for ages 2 20 years the 2000 cdc bmi for age curves are partially parametric and only partially incorporated the survey sample weights in the curve estimation as a result they may not fully reflect the underlying pattern of bmi for age in the population this motivated us to develop a nonparametric double kernel based method and automatic bandwidth selection procedure we include sample weights in the bandwidth selection conduct median correction to reduce small sample smoothing bias and rescale the bandwidth to make it scale invariant using this procedure we re estimate the national percentile bmi for age curves and the prevalence of high bmi children in the u s

improving estimates of monotone functions by rearrangement suppose that a target function f0 r r is monotonic namely weakly increasing and an original estimate f of the target function is available which is not weakly increasing many common estimation methods used in statistics produce such estimates f we show that these estimates can always be improved with no harm using rearrangement techniques the rearrangement methods univariate and multivariate transform the original estimate to a monotonic estimate f and the resulting estimate is closer to the true curve f0 in common metrics than the original estimate f we illustrate the results with a computational example and an empirical example dealing with age height growth charts

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

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

worm plot a simple diagnostic device for modelling growth reference curves the worm plot visualizes differences between two distributions conditional on the values of a covariate though the worm plot is a general diagnostic tool for the analysis of residuals this paper focuses on an application in constructing growth reference curves where the covariate of interest is age the lms model of cole and green is used to construct reference curves in the fourth dutch growth study 1997 if the model fits the measurements in the reference sample follow a standard normal distribution on all ages after a suitably chosen box cox transformation the coefficients of this transformation are modelled as smooth age dependent parameter curves for the median variation and skewness respectively the major modelling task is to choose the appropriate amount of smoothness of each parameter curve the worm plot assesses the age conditional normality of the transformed data under a variety of lms models the fit of each parameter curve is closely related to particular features in the worm plot namely its offset slope and curvature application of the worm plot to the dutch growth data resulted in satisfactory reference curves for a variety of anthropometric measures it was found that the lms method generally models the age conditional mean and skewness better than the age related deviation and kurtosis copyright 2001 john wiley sons ltd

quantile correlations and quantile autoregressive modeling in this article we propose two important measures quantile correlation qcor and quantile partial correlation qpcor we then apply them to quantile autoregressive qar models and introduce two valuable quantities the quantile autocorrelation function qacf and the quantile partial autocorrelation function qpacf this allows us to extend the box jenkins three stage procedure model identification model parameter estimation and model diagnostic checking from classical autoregressive models to quantile autoregressive models specifically the qpacf of an observed time series can be employed to identify the autoregressive order while the qacf of residuals obtained from the fitted model can be used to assess the model adequacy we not only demonstrate the asymptotic properties of qcor and qpcor but also show the large sample results of qacf qpacf and the quantile version of the box pierce test moreover we obtain the bootstrap approximations to the distributions of parameter estimators and p

multi level models for longitudinal growth norms multi level models for estimating conditional and unconditional longitudinal growth norms are presented the procedure involves transforming the original growth measurements to normality and modelling these with a two level random coefficient model growth norms for any desired time interval and function can be derived height and weight data are used for illustration

optimality conditions and error analysis of semilinear elliptic control problems with l 1 cost functional semilinear elliptic optimal control problems involving the l 1 norm of the control in the objective are considered necessary and sufficient second order optimality conditions are derived a priori finite element error estimates for piecewise constant discretizations for the control and piecewise linear discretizations of the state are shown error estimates for the variational discretization of the problem in the sense of m hinze comput optim appl 30 2005 pp 45 61 are also obtained numerical experiments confirm the convergence rates

the numerical computation of bessel functions of the first and second kind for integer orders and complex arguments a rigorous algorithm for computing integer order bessel functions of the first and second kind with complex arguments is discussed the algorithm makes use of backward recurrence for computing bessel functions of the first kind where applicable and of hankel s asymptotic expansion for large arguments the argument is limited only by the ability of the computer to handle large numbers orders up to a few thousand have been computed to 13 digit accuracy

solution stability of iterative schemes utilizing the discrete fourier transform em scattering the fredholm integral equation of the first kind can be solved numerically using iterative schemes which minimize the integral square error when the kernal is of the convolution type the discrete fourier transform dft can be used when evaluating the operator equation in the iterative schemes however the dft imposes an artificial periodicity thus changing the nature of the problem the effect of this on the solution has been studied and convergence investigated by comparison with a method of moments solution a proposed method of avoiding the periodicity problem has been studied the effect of introducing losses in the medium surrounding the scatterer has been investigated provided losses are low there is little effect on the solution

correlation models for monitoring child growth growth measurements of children such as weight and height are monitored regularly particularly in infancy to assess whether or not a child s growth is normal when compared with a reference population of the same age and sex here after a suitable power transformation to normality of the reference population we model temporal evolution of the standardized deviation z score of the transformed measurement of a normal child from the reference population as a gaussian process with zero mean and unit variance this paper concentrates on modelling and fitting the serial correlation structure of the process with the benefit that monitoring growth at specific ages is not crucial statistically exploratory analysis of various observed correlation matrices has suggested that a particular two parameter markovian form is a good representation of the correlation function in infancy the main implication for growth monitoring is that we only need to condition on the most recent z score to inform a clinician s judgement about a child s growth based on its current z score inferences about the correlation parameters derive from likelihood methods based either on observed z scores or if raw data are unavailable on an observed correlation matrix the markov model is compared with a previously studied six parameter correlation model data from major child growth studies in newcastle and cambridge are used to illustrate the methods and compare predictions from the two models we argue that the markov model serves as a pragmatic choice for growth monitoring in infancy

proximal point method and elliptic regularization abstract a generalized proximal point method for solving variational inequalities with maximal monotone operators is developed it admits a successive approximation of the feasible set and of a symmetric component of the operator as well as an inexact solving of the regularized problems the conditions on the approximation are coordinated with the properties of finite element methods for solving problems in mathematical physics the choice of the regularizing functional exploits a possible reserve of monotonicity of the operator in the variational inequality for the minimal surface problem and related variational inequalities as well as for the convection diffusion problem the studied method extends the principle of elliptic regularization a special convergence analysis shows a more qualitative convergence of the method applied to these problems than it follows from the general theory of proximal point methods also applications to some variational inequalities from the elasticity theory are investigated

an approach to multivariate covariate dependent quantile contours with application to bivariate conditional growth charts multivariate quantile contours are useful in numerous applications and have been studied in different contexts however no easy solutions exist when dynamic and conditional quantile contours are needed without strong distributional assumptions in this article we propose a new form of bivariate quantile contours and a two stage estimation procedure to take time effect into account the proposed procedure relies on quantile regression for longitudinal data and is flexible to include potentially important covariates as necessary in addition we propose a visual model assessment tool and discuss a practical guideline for model selection the performance of the proposed methodology is demonstrated by a simulation study as well as an application to joint height weight screening of young children in the united states we construct bivariate growth charts by a nested sequence of age dependent and covariate varying quantile contours of height and weight and use it to locate an individual subject s percentile

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

the encompassing principle and its application to testing nonnested hypotheses the encompassing principle is used to develop a testing framework which unifies the literature on non nested testing allowing analysis of the relationship between alternative tests and in particular enabling asymptotic and finite sample equivalences and identities to be established easily when they exist as well as embracing nested hypothesis testing the concept of the implicit null hypothesis of a test is introduced to show that the effective acceptance region for some tests extends beyond the acceptance region corresponding to the null of interest and so such tests can be inconsistent against fixed alternatives closely related to the nominal null and alternative the analysis is illustrated by an application to two non nested linear regression models and it is shown that the conventional f test as well as all the one degree of freedom non nested tests has an encompassing interpretation and that the f test is a complete parametric encompassing test

sample size determination for studies designed to estimate covariate dependent reference quantile curves accuracy and sample size issues concerning the estimation of covariate dependent quantile curves are considered it is proposed to measure the precision of an estimate of the pth quantile at a given covariate value by the probability with which this estimate lies between the p1 th and p2 th quantile where p1 p p2 requiring that this probability exceeds a given confidence bound for all covariate values in a specified range leads to a sample size criterion approximate formulae for the precision and sample size are derived for the normal parametric regression approach and for the semiparametric quantile regression method a simulation study is performed to evaluate the accuracy of the approximations numerical evaluations show that rather large numbers of subjects are needed to construct quantile curves with a reasonable amount of accuracy especially if the quantile regression method is applied

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

a fast finite difference method for propagation predictions over irregular inhomogeneous terrain propagation of electromagnetic waves over irregular inhomogeneous terrain is solved by a finite difference scheme the method is fast and requires considerably less memory than the integral equation methods the method requires a storage space of order o n and an execution time of order o n sup 2 fields generated by a te sub 2 line source are represented in an integral form in terms of the field over a flat constant impedance plane the incident field and the field scattered by the terrain irregularities and inhomogeneities accurate expressions are provided for the incident field and the green s function whose evaluation is otherwise accomplished by the rather time consuming sommerfeld s integrals measured equation of invariance is used to terminate the computational domain the sparse matrix generated by the method is inverted by the ricatti transform numerical results are presented for the ground wave as well as for the sky wave comparison is made for known geometries to establish the validity and limitations of the method

model robust designs for quantile regression we give methods for the construction of designs for regression models when the purpose of the investigation is the estimation of the conditional quantile function and the estimation method is quantile regression the designs are robust against misspecified response functions and against unanticipated heteroscedasticity the methods are illustrated by example and in a case study in which they are applied to growth charts

equivalent kernels of smoothing splines in nonparametric regression for clustered longitudinal data correlation we show that a smoothing spline estimator is asymptotically equivalent to a recently proposed seemingly unrelated kernel estimator of wang 2003 for any working covariance matrix we show that both estimators can be obtained iteratively by applying conventional kernel or spline smoothing to pseudo observations this result allows us to study the asymptotic properties of the smoothing spline estimator by deriving its asymptotic bias and variance we show that smoothing splines are consistent for an arbitrary working covariance and have the smallest variance when assuming the true covariance we further show that both the seemingly unrelated kernel estimator and the smoothing spline estimator are nonlocal unless working independence is assumed but have asymptotically negligible bias their finite sample performance is compared through simulations our results justify the use of efficient non local estimators such as smoothing splines for clustered longitudinal data

quantile regression with nominated samples an application to a bone mineral density study this paper studies quantile regression analysis with maxima or minima nomination sampling designs these designs are often used to obtain more representative samples from the tails of the underlying distribution using the easy to access rank information during the sampling process we propose new loss functions to incorporate the rank information of nominated samples in the estimation process also we provide an alternative approach that translates estimation problems with nominated samples to corresponding problems under simple random sampling srs strategies are given to choose proper nomination sampling designs for a given population quantile numerical studies show that quantile regression models with maxima or minima nominated samples have higher relative efficiencies compared with their counterparts under srs for analyzing the upper or lower tail quantiles of the distribution of the response variable results are then implemented on a large cohort study in the canadian province of manitoba to analyze quantiles of bone mineral density using available covariates we show that in some cases methods based on nomination sampling designs require about one tenth of the sample used in srs to estimate the lower or upper tail conditional quantiles with comparable mean squared errors this is a dramatic reduction in time and cost compared with the usual srs approach

centile estimation for a proportion response variable this paper introduces two general models for computing centiles when the response variable y can take values between 0 and 1 inclusive of 0 or 1 the models developed are more flexible alternatives to the beta inflated distribution the first proposed model employs a flexible four parameter logit skew student t logitsst distribution to model the response variable y on the unit interval 0 1 excluding 0 and 1 this model is then extended to the inflated logitsst distribution for y on the unit interval including 1 the second model developed in this paper is a generalised tobit model for y on the unit interval including 1 applying these two models to 1 y rather than y enables modelling of y on the unit interval including 0 rather than 1 an application of the new models to real data shows that they can provide superior fits

new approximations to j sub 0 and j sub 1 bessel functions new approximate solutions to the 0th and 1st order bessel functions of the first kind are derived the formulations are based upon using a new integral with no previously known solution the new integral in the limiting case is identical to the 0th order bessel function integral it is solved in closed form and the solution is expressed as a simple even order polynomial with integer coefficients the polynomial coefficients are all of integer value the 1st order bessel function approximation can then be found through a simple derivative comparisons are made between the exact solution classic solutions and the new approximation the new approximation proves to be much more accurate than the classic small argument approximation it is also sufficiently accurate to bridge the gap between the classic large and small argument approximations and has potential applications in allowing one to analytically evaluate integrals containing bessel functions

smooth centile curves for skew and kurtotic data modelled using the box cox power exponential distribution the box cox power exponential bcpe distribution developed in this paper provides a model for a dependent variable y exhibiting both skewness and kurtosis leptokurtosis or platykurtosis the distribution is defined by a power transformation y having a shifted and scaled truncated standard power exponential distribution with parameter the distribution has four parameters and is denoted bcpe the parameters and may be interpreted as relating to location median scale approximate coefficient of variation skewness transformation to symmetry and kurtosis power exponential parameter respectively smooth centile curves are obtained by modelling each of the four parameters of the distribution as a smooth non parametric function of an explanatory variable a fisher scoring algorithm is used to fit the non parametric model by maximizing a penalized likelihood the first and expected second and cross derivatives of the likelihood with respect to and required for the algorithm are provided the centiles of the bcpe distribution are easy to calculate so it is highly suited to centile estimation this application of the bcpe distribution to smooth centile estimation provides a generalization of the lms method of the centile estimation to data exhibiting kurtosis as well as skewness different from that of a normal distribution and is named here the lmsp method of centile estimation the lmsp method of centile estimation is applied to modelling the body mass index of dutch males against age copyright 2004 john wiley sons ltd

estimating age related trends in cross sectional studies using s distributions growth trends in children are often based on cross sectional studies in which a sample of the population is investigated at one given point in time estimating age related percentiles in such studies involves fitting data distributions each of which is specific for one age group and a subsequent smoothing of the percentile curves the first requirement for this process is the selection of a distributional form that is expected to be consistent with the observed data if a goodness of fit test reveals significant discrepancies between the data and the best fitting member of this distributional form an alternative distribution must be found in practice there is seldom an objective argument for selecting any particular distribution also different distributions can yield very similar fits so that any selection is somewhat arbitrary finally the shapes of the observed distributions may change throughout the age range so drastically that no single traditional distribution can fit them all in a satisfactory manner to overcome these difficulties in population studies non parametric smoothing techniques and normalizing transformations have been used to derive percentile curves in this paper we present an alternative strategy in the form of a flexible parametric family of statistical distributions the s distribution we suggest a method that guides the search for well fitting s distributions for groups of observed distributions the method is first tested with simulated data sets and subsequently applied to actual weight distributions of girls of different ages as far as the results can be tested they are consistent with observations and with results from other methods

time trends and forecasts of body mass index from repeated cross sectional data a different approach in this paper we report a case study on a technical generalization of the lee carter model originally developed to project mortality to forecast body mass index bmi kg m2 we present the method on an annually repeated cross sectional data set the dutch health survey covering years between 1981 and 2008 we applied generalized additive models for location scale and shape semi parametric regression models to estimate the probability distribution of bmi for each combination of age gender and year assuming that bmi follows a box cox power exponential distribution we modelled and extrapolated the distribution parameters as a function of age and calendar time using the lee carter model the projected parameters defined future bmi distributions from which we derived the prevalence of normal weight overweight and obesity our analysis showed that important changes occurred not only in the location and scale of the bmi distribution but also in the shape of it the bmi distribution became flatter and more shifted to the right assuming that past trends in the distribution of bmi will continue in the future we predicted a stable or slow increase in the prevalence of overweight until 2020 among men and women we conclude that our adaptation of the lee carter model provides an insightful and flexible way of forecasting bmi and that ignoring changes in the shape of the bmi distribution would likely result in biased forecasts

sympercents symmetric percentage differences on the 100 loge scale simplify the presentation of log transformed data the results of analyses on log transformed data are usually back transformed and interpreted on the original scale yet if natural logs are used this is not necessary the log scale can be interpreted as it stands a difference of natural logs corresponds to a fractional difference on the original scale the agreement is exact if the fractional difference is based on the logarithmic mean the transform y 100 log e x leads to differences standard deviations and regression coefficients of y that are equivalent to symmetric percentage differences standard deviations and regression coefficients of x several simple clinical examples show that the 100 log e scale is the natural scale on which to express percentage differences the term sympercent or s is proposed for them sympercents should improve the presentation of log transformed data and lead to a wider understanding of the natural log transformation

conditional growth charts growth charts are often more informative when they are customized per subject taking into account prior measurements and possibly other covariates of the subject we study a global semiparametric quantile regression model that has the ability to estimate conditional quantiles without the usual distributional assumptions the model can be estimated from longitudinal reference data with irregular measurement times and with some level of robustness against outliers and it is also flexible for including covariate information we propose a rank score test for large sample inference on covariates and develop a new model assessment tool for longitudinal growth data our research indicates that the global model has the potential to be a very useful tool in conditional growth chart analysis

the concept of residual confounding in regression models and some applications in this paper the concept of residual confounding is generalized to various types of regression models such as logistic regression or cox regression residual confounding and a newly suggested parameter the relative residual confounding are defined on the regression parameters of the models the estimator gives the proportion of confounding which has been removed by incomplete adjustment the concept quantifies the effects of categorizing continuous covariables and of model misspecification these are investigated by a simulation study and with data from an epidemiological investigation a case control study of laryngeal cancer is used to illustrate the residual confounding effect of arbitrary transformation of a continuous confounder smoking on the effect of alcohol consumption on laryngeal cancer risk the data also showed that categorization into two levels can yield high residual confounding the parameters described in this paper are of some use in quantifying the effect of inadequate adjustment for confounding variables

proximal schemes for parabolic optimal control problems with sparsity promoting cost functionals abstractfast first order proximal methods that solve linear and bilinear parabolic optimal control problems with a sparsity cost functional are discussed weak convergence of these methods is proved and for benchmarking purposes the proposed inexact proximal schemes are compared to an inexact semi smooth newton method results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes and to validate the theoretical estimates