order preserving nonparametric regression with applications to conditional distribution and quantile function estimation in some regression problems we observe a response yti to level t of a treatment applied to an individual with level xi of a given characteristic where it has been established that response is monotone increasing in the level of the treatment a related problem arises when estimating conditional distributions where the raw data are typically independent and identically distributed pairs xi zi and yti denotes the proportion of zi s that do not exceed t we expect the regression means gt x e yti xi x to enjoy the same order relation as the responses that is gt gs whenever s t this requirement is necessary to obtain bona fide conditional distribution functions for example if we estimate gt by passing a linear smoother through each dataset t xi yti 1 i n then the order preserving property is guaranteed if and only if the smoother has nonnegative weights however in such cases the estimators generally have high levels of boundary bias on the other hand the order preser

new analysis and results for the frank wolfe method we present new results for the frank wolfe method also known as the conditional gradient method we derive computational guarantees for arbitrary step size sequences which are then applied to various step size rules including simple averaging and constant step sizes we also develop step size rules and computational guarantees that depend naturally on the warm start quality of the initial and subsequent iterates our results include computational guarantees for both duality bound gaps and the so called fw gaps lastly we present complexity bounds in the presence of approximate computation of gradients and or linear optimization subproblem solutions

conditional quantile analysis when covariates are functions with application to growth data summary motivated by the conditional growth charts problem we develop a method for conditional quantile analysis when predictors take values in a functional space the method proposed aims at estimating conditional distribution functions under a generalized functional regression framework this approach facilitates balancing of model flexibility and the curse of dimensionality for the infinite dimensional functional predictors its good performance in comparison with other methods both for sparsely and for densely observed functional covariates is demonstrated through theory as well as in simulations and an application to growth curves where the method proposed can for example be used to assess the entire growth pattern of a child by relating it to the predicted quantiles of adult height

functional data analysis for sparse longitudinal data we propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data the method aims at irregularly spaced longitudinal data where the number of repeated measurements available per subject is small in contrast classical functional data analysis requires a large number of regularly spaced measurements per subject we assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random subject specific trajectory plus measurement errors basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories and the estimation of the variance of the measurement errors the eigenfunction basis is estimated from the data and functional principal components score estimates are obtained by a conditioning step this conditional estimation method is conceptually simple and straightforward to implement

nonparametric regression analysis of growth curves in recent years nonparametric curve estimates have been extensively explored in theoretical work there has however been a certain lack of convincing applications in particular involving comparisons with parametric techniques the present investigation deals with the analysis of human height growth where longitudinal measurements were collected for a sample of boys and a sample of girls evidence is presented that kernel estimates of acceleration and velocity of height and of height itself might offer advantages over a parametric fitting via functional models recently introduced for the specific problem considered both approaches are biased but the parametric one shows qualitative and quantitative distortion which both are not easily predictable data analytic problems involved with kernel estimation concern the choice of kernels the choice of the smoothing parameter and also whether the smoothing parameter should be chosen uniformly for all subjects or individually

generalized linear models with functional predictors summary we present a technique for extending generalized linear models to the situation where some of the predictor variables are observations from a curve or function the technique is particularly useful when only fragments of each curve have been observed we demonstrate on both simulated and real data sets how this approach can be used to perform linear logistic and censored regression with functional predictors in addition we show how functional principal components can be used to gain insight into the relationship between the response and functional predictors finally we extend the methodology to apply generalized linear models and principal components to standard missing data problems

quantile regression in reproducing kernel hilbert spaces in this article we consider quantile regression in reproducing kernel hilbert spaces which we call kernel quantile regression kqr we make three contributions 1 we propose an efficient algorithm that computes the entire solution path of the kqr with essentially the same computational cost as fitting one kqr model 2 we derive a simple formula for the effective dimension of the kqr model which allows convenient selection of the regularization parameter and 3 we develop an asymptotic theory for the kqr model

time varying functional regression for predicting remaining lifetime distributions from longitudinal trajectories a recurring objective in longitudinal studies on aging and longevity has been the investigation of the relationship between age at death and current values of a longitudinal covariate trajectory that quantifies reproductive or other behavioral activity we propose a novel technique for predicting age at death distributions for situations where an entire covariate history is included in the predictor the predictor trajectories up to current time are represented by time varying functional principal component scores which are continuously updated as time progresses and are considered to be time varying predictor variables that are entered into a class of time varying functional regression models that we propose we demonstrate for biodemographic data how these methods can be applied to obtain predictions for age at death and estimates of remaining lifetime distributions including estimates of quantiles and of prediction intervals for remaining lifetime estimates and predictions are obtained for individual subjects based on their observed behavioral trajectories and include a dimension reduction step that is implemented by projecting on a single index the proposed techniques are illustrated with data on longitudinal daily egg laying for female medflies predicting remaining lifetime and age at death distributions from individual event histories observed up to current time

searching for structure in curve samples abstract the shape of a regression curve can to a large extent be characterized by the succession of structural features like extrema inflection points and so on when analyzing a sample of regression curves it is often important to know at an early stage of data analysis which structural features are occurring consistently in each curve of the sample such a definition is usually not easy due to substantial interindividual variation both in the x and the y axis and due to the influence of noise a method is proposed for identifying typical features without relying on an a priori specified functional model for the curves the approach is based on the frequencies of occurrence of structural features as for example maxima in the curve sample along the x axis important tools are nonparametric regression and differentiation and kernel density estimation apart from a theoretical foundation the usefulness of the method is documented by application to two interesting biomedical areas growth and develop

statistical tools to analyze data representing a sample of curves the paper is concerned with data representing a sample of smooth curves which can be considered as independent realizations of an underlying biological chemical ldots process such samples of curves often possess the following features there is a typical structural pattern common to all curves of the sample on the other hand individual realizations of the typical shape show different dynamics and intensity in particular typical peaks are shifted from individual to individual differences in dynamics complicate the analysis of samples of curves for example the cross sectional average usually does not reflect an average pattern due to shifts structure is smeared or might even disappear our approach consists in synchronizing the individual curves before determining the average or any further statistics pointwise averaging of the synchronized curves then leads to an average curve which represents the common structure with average dynamics and average intensity the method requires the introduction of new statistical objects they are defined mathematically their properties are discussed and possible estimators are proposed the asymptotic bias and variance of the estimators are derived an application to visually evoked brain potentials illustrates the approach

local linear quantile regression abstract in this article we study nonparametric regression quantile estimation by kernel weighted local linear fitting two such estimators are considered one is based on localizing the characterization of a regression quantile as the minimizer of e pp y a x x where p is the appropriate check function the other follows by inverting a local linear conditional distribution estimator and involves two smoothing parameters rather than one our aim is to present fully operational versions of both approaches and to show that each works quite well although either might be used in practice we have a particular preference for the second our automatic smoothing parameter selection method is novel the main regression quantile smoothing parameters are chosen by rule of thumb adaptations of state of the art methods for smoothing parameter selection for regression mean estimation the techniques are illustrated by application to two datasets and compared in simulations

the geometry and cohomology of the mathieu group m12 it is usually very complex to calculate the cohomology of a finite group g to date the most significant results have been on the symmetric and alternating groups n m m ma mu a m m the general linear groups over a finite field q1 and the extra special p groups q2 in the list above only the alternating groups and the gln f2 are simple indeed among the simple groups only a very few aside from those above have been understood it is probable that away from the characteristic p h psln fpn z q is available but even this is not obvious especially for q 2 and certainly we currently have no information on most of the families of groups of lie type for example g2 fq e6 fq e7 fq e8 fq or any of the sporadic groups but m11 and j1 about 15 years ago quillen introduced very powerful techniques that allowed for a much deeper understanding of group cohomology however it is also apparent that successful calculations over z p have only occurred when the group has a well behaved lattice of p elementary abelian subgroups formidable combinatorial problems arise in the general situation as well as necessarily complicated multiplicative relations for example the general calculation of h gln fp z p remains quite inaccessible and there has been only marginal progress since quillen s landmark results

calculation of unconditional and conditional reference intervals for foetal size and growth from longitudinal measurements methods for estimating unconditional and conditional reference intervals for foetal size and growth based on longitudinal observations are presented the methods are based on simple random effects regression models and involve transforming both the response and the covariate timepoint a dataset from a designed longitudinal study of foetal size is analysed in detail as a motivating example

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

methods for estimating a conditional distribution function abstract motivated by the problem of setting prediction intervals in time series analysis we suggest two new methods for conditional distribution estimation the first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation it produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1 the second method involves an adjusted form of the nadaraya watson estimator it preserves the bias and variance properties of a class of second order estimators introduced by yu and jones but has the added advantage of always being a distribution itself our methods also have application outside the time series setting for example to quantile estimation for independent data this problem motivated the work of yu and jones

cohomology of the double cover of the mathieu group m12 abstract in this paper we calculate the mod two cohomology of the double cover of the mathieu group m 12 the starting point is the calculation by adem maginnis and milgram of the mod two cohomology of m 12 we use a hypercohomology spectral sequence to determine a differential in the lyndon hochschild serre spectral sequence of the central extension and this gets us as far as the e page ungrading requires restriction to the sylow 2 subgroup and here some computer calculations come to our rescue

estimation of conditional densities and sensitivity measures in nonlinear dynamical systems using locally polynomial regression we develop nonparametric estimators for the conditional density function and its square root and their partial derivatives two measures of sensitivity to initial conditions in nonlinear stochastic dynamic systems are proposed one of which relates fisher information with initial value sensitivity in dynamical systems we propose estimators for these and show asymptotic normality for one of them we further propose a simple method for choosing the bandwidth the methods are illustrated by simulation of two well known models in dynamical systems

quantile smoothing splines summary although nonparametric regression has traditionally focused on the estimation of conditional mean functions nonparametric estimation of conditional quantile functions is often of substantial practical interest we explore a class of quantile smoothing splines defined as solutions to

nonparametric mixed effects models for unequally sampled noisy curves we propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients the method is applicable when the individual curves are sampled at variable and irregularly spaced points this produces a low rank low frequency approximation to the covariance structure which can be estimated naturally by the em algorithm smooth curves for individual trajectories are constructed as best linear unbiased predictor blup estimates combining data from that individual and the entire collection this framework leads naturally to methods for examining the effects of covariates on the shapes of the curves we use model selection techniques akaike information criterion aic bayesian information criterion bic and cross validation to select the number of breakpoints for the spline approximation we believe that the methodology we propose provides a simple flexible and computationally efficient means of functional data analysis