a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

empirical estimation of a distribution function with truncated and doubly interval censored data and its application to aids studies in this paper we discuss the non parametric estimation of a distribution function based on incomplete data for which the measurement origin of a survival time or the date of enrollment in a study is known only to belong to an interval also the survival time of interest itself is observed from a truncated distribution and is known only to lie in an interval to estimate the distribution function a simple self consistency algorithm a generalization of turnbull s 1976 journal of the royal statistical association series b 38 290 295 self consistency algorithm is proposed this method is then used to analyze two aids cohort studies for which direct use of the em algorithm dempster laird and rubin 1976 journal of the royal statistical association series b 39 1 38 which is computationally complicated has previously been the usual method of the analysis

the strong law under random truncation the random truncation model is defined by the conditional probability distribution h x y p x x y y x y where x and y are independent random variables a problem of interest is the estimation of the distribution function f of x with data from the distribution h under random truncation f need not be fully identifiable from h and only a part of it say f 0 is we show that the nonparametric mle f n of f 0 obeys the strong law of large numbers in the sense that for any nonnegative measurable function o x the integrals o x df n x o x df 0 x almost surely as n tends to infinity similar results were first obtained by stute and wang for the right censoring model the results are useful in establishing the strong consistency of various estimates some of our results are derived from the weak consistency of f n obtained by woodroofe

smooth inference for survival functions with arbitrarily censored data we propose a procedure for estimating the survival function of a time to event random variable under arbitrary patterns of censoring the method is predicated on the mild assumption that the distribution of the random variable and hence the survival function has a density that lies in a class of smooth densities whose elements can be represented by an infinite hermite series truncation of the series yields a parametric expression that can well approximate any plausible survival density and hence survival function provided the degree of truncation is suitably chosen the representation admits a convenient expression for the likelihood for the parameters in the approximation under arbitrary censoring truncation that is straightforward to compute and maximize a test statistic for comparing two survival functions which is based on an integrated weighted difference of estimates of each under this representation is proposed via simulation studies and application to a number of data sets we demonstrate that the approach yields reliable inferences and can result in gains in efficiency over traditional nonparametric methods

a proportional hazards model for arbitrarily censored and truncated data turnbull 1976 journal of royal statistical society series b 38 290 295 proposed a method for nonparametric estimation of the distribution function when the data are incomplete because of censoring and truncation however as noted by frydman 1994 journal of royal statistical society series b 56 71 74 turnbull s method has to be modified to accommodate both truncation and censoring this paper presents a detailed correction of turnbull s method and an extension to the regression analysis a method of fitting the proportional hazards model for arbitrarily censored and truncated data is developed the method allows partial testing for zero regression coefficients the test can be performed using the likelihood ratio test or the wald test the methodology is applied to estimate the distribution of the induction time of patients diagnosed with transfusion associated aids and to estimate the distribution of time from diabetes onset to development of diabetic nephropathy for insulin dependent diabetics

the theory of linear models preface simple lenear regression the general linear model one sample and one factor analysis of variance multiple regression models analysis of residuals analysis of variance with two or three factors references and bibliography index

asymptotic properties of the product limit estimate under random truncation on donne une description precise du comportement asymptotique de l estimateur limite produit incluant une forme explicite simple de la structure de covariance asymptotique

nonparametric estimation of a delay distribution based on left censored and right truncated data this paper proposes a nonparametric method for estimating a delay distribution based on left censored and right truncated data a variance covariance estimator is provided the method is applied to the australian aids data in which some data are left censored and some data are not left censored this situation arises with aids case reporting data in australia because reporting delays were recorded only from november 1990 rather than from the beginning of the epidemic there it is shown that inclusion of the left censored data as opposed to analyzing only the uncensored data improves the precision of the estimate

a unified approach to semiparametric transformation models under general biased sampling schemes we propose a unified estimation method for semiparametric linear transformation models under general biased sampling schemes the new estimator is obtained from a set of counting process based unbiased estimating equations developed through introducing a general weighting scheme that offsets the sampling bias the usual asymptotic properties including consistency and asymptotic normality are established under suitable regularity conditions a closed form formula is derived for the limiting variance and the plug in estimator is shown to be consistent we demonstrate the unified approach through the special cases of left truncation length bias the case cohort design and variants thereof simulation studies and applications to real datasets are presented

semiparametric regression analysis of length biased interval censored data in prevalent cohort design subjects who have experienced an initial event but not the failure event are preferentially enrolled and the observed failure times are often length biased moreover the prospective follow up may not be continuously monitored and failure times are subject to interval censoring we study the nonparametric maximum likelihood estimation for the proportional hazards model with length biased interval censored data direct maximization of likelihood function is intractable thus we develop a computationally simple and stable expectation maximization algorithm through introducing two layers of data augmentation we establish the strong consistency asymptotic normality and efficiency of the proposed estimator and provide an inferential procedure through profile likelihood we assess the performance of the proposed methods through extensive simulations and apply the proposed methods to the massachusetts health care panel study

regression models for the restricted residual mean life for right censored and left truncated data the hazard ratios resulting from a cox s regression hazards model are hard to interpret and to be converted into prolonged survival time as the main goal is often to study survival functions there is increasing interest in summary measures based on the survival function that are easier to interpret than the hazard ratio the residual mean time is an important example of those measures however because of the presence of right censoring the tail of the survival distribution is often difficult to estimate correctly therefore we consider the restricted residual mean time which represents a partial area under the survival function given any time horizon and is interpreted as the residual life expectancy up to of a subject surviving up to time t we present a class of regression models for this measure based on weighted estimating equations and inverse probability of censoring weighted estimators to model potential right censoring furthermore we show how to extend the models and the estimators to deal with delayed entries we demonstrate that the restricted residual mean life estimator is equivalent to integrals of kaplan meier estimates in the case of simple factor variables estimation performance is investigated by simulation studies using real data from danish monitoring cardiovascular risk factor surveys we illustrate an application to additive regression models and discuss the general assumption of right censoring and left truncation being dependent on covariates copyright 2017 john wiley sons ltd

general entropy criteria for inverse problems with applications to data compression pattern classification and cluster analysis minimum distance approaches are considered for the reconstruction of a real function from finitely many linear functional values an optimal class of distances satisfying an orthogonality condition analogous to that enjoyed by linear projections in hilbert space is derived these optimal distances are related to measures of distances between probability distributions recently introduced by c r rao and t k nayak 1985 and possess the geometric properties of cross entropy useful in speech and image compression pattern classification and cluster analysis several examples from spectrum estimation and image processing are discussed

nonparametric estimation of transition probabilities for a general progressive multi state model under cross sectional sampling nonparametric estimation of the transition probability matrix of a progressive multi state model is considered under cross sectional sampling two different estimators adapted to possibly right censored and left truncated data are proposed the estimators require full retrospective information before the truncation time which when exploited increases efficiency they are obtained as differences between two survival functions constructed for sub samples of subjects occupying specific states at a certain time point both estimators correct the oversampling of relatively large survival times by using the left truncation times associated with the cross sectional observation asymptotic results are established and finite sample performance is investigated through simulations one of the proposed estimators performs better when there is no censoring while the second one is strongly recommended with censored data the new estimators are applied to data on patients in intensive care units icus

good weights and hyperbolic kernels for neural networks projection pursuit and pattern classification fourier strategies for extracting information from high dimensional data fourier approximation and estimation of discriminant regression and density functions are considered a preference order is established for the frequency weights in multiple fourier expansions and the connection weights in single hidden layer neural networks these preferred weight vectors called good weights good lattice weights for estimation of periodic functions are generalizations for arbitrary periods of the hyperbolic lattice points of korobov 1959 and hlawka 1962 associated with classes of smooth functions of period one in each variable although previous results on approximation and quadrature are affinely invariant to the scale of the underlying periods some of our results deal with optimization over finite sets and strongly depend on the choice of scale it is shown how to count and generate good lattice weights finite sample bounds on mean integrated squared error are calculated for ridge estimates of periodic pattern class densities the bounds are combined with a table of cardinalities of good lattice weight sets to furnish classifier design with prescribed class density estimation errors applications are presented for neural networks and projection pursuit a hyperbolic kernel gradient transform is developed which automatically determines the training weights projection directions its sampling properties are discussed algorithms are presented for generating good weights for projection pursuit

efficient agnostic learning of neural networks with bounded fan in we show that the class of two layer neural networks with bounded fan in is efficiently learnable in a realistic extension to the probably approximately correct pac learning model in this model a joint probability distribution is assumed to exist on the observations and the learner is required to approximate the neural network which minimizes the expected quadratic error as special cases the model allows learning real valued functions with bounded noise learning probabilistic concepts and learning the best approximation to a target function that cannot be well approximated by the neural network the networks we consider have real valued inputs and outputs an unlimited number of threshold hidden units with bounded fan in and a bound on the sum of the absolute values of the output weights the number of computation steps of the learning algorithm is bounded by a polynomial in 1 spl epsiv 1 spl delta n and b where spl epsiv is the desired accuracy spl delta is the probability that the algorithm fails n is the input dimension and b is the bound on both the absolute value of the target which may be a random variable and the sum of the absolute values of the output weights in obtaining the result we also extended some results on iterative approximation of functions in the closure of the convex hull of a function class and on the sample complexity of agnostic learning with the quadratic loss function

variance estimation of a survival function for interval censored survival data interval censored survival data often occur in medical studies especially in clinical trials in this case many authors have considered estimation of a survival function there is however relatively little discussion on estimating the variance of estimated survival functions for right censored data a special case of interval censored data the most commonly used method for variance estimation is to use the greenwood formula in this paper we propose a generalization of the greenwood formula for variance estimation of a survival function based on interval censored data also a simple bootstrap approach is presented the two methods are evaluated and compared using simulation studies and a real data set the simulation results suggest that the methods work well

weakly p compact p banach saks and super reflexive banach spaces abstract new techniques are introduced to extract subsequences satisfying certain upper estimates in suitable banach spaces using these methods alternative proofs of results of rakov math notes 26 1979 909 916 and godun and rakov math notes 31 1982 32 39 are obtained moreover these methods provide a useful tool to obtain new examples of spaces in the sense of carne et al trans amer math soc 314 1989 639 659

a simple lemma on greedy approximation in hilbert space and convergence rates for projection pursuit regression and neural network training a general convergence criterion for certain iterative sequences in hilbert space is presented for an important subclass of these sequences estimates of the rate of convergence are given under very mild assumptions these results establish an 0 1 f4n nonsampling convergence rate for projection pursuit regression and neural network training where n represents the number of ridge functions neurons or coefficients in a greedy basis expansion

a semiparametric model for randomly truncated data abstract for randomly censored data it is known that the maximum likelihood estimate mle of the survival curve is not affected by parametric assumption on the censoring variable the kaplan meier 1958 estimate is the mle for both nonparametric and semiparametric models for randomly truncated data the truncation product limit estimate is the mle for nonparametric models this is not the case if the truncation mechanism is parameterized however specifically let x be a generic random variable and t be the truncation variable if the distribution of t is parameterized and the distribution of x is left unspecified it can be shown that the truncation product limit estimate is not the mle for this semiparametric model even though it is for the fully nonparametric model in this article the mle is characterized for the semiparametric model and the large sample properties of the estimate are established the results show that unlike censoring the parametric information from the truncation mechanism

successive overrelaxation for support vector machines successive overrelaxation sor for symmetric linear complementarity problems and quadratic programs is used to train a support vector machine svm for discriminating between the elements of two massive datasets each with millions of points because sor handles one point at a time similar to platt s sequential minimal optimization smo algorithm 1999 which handles two constraints at a time and joachims svm sup light 1998 which handles a small number of points at a time sor can process very large datasets that need not reside in memory the algorithm converges linearly to a solution encouraging numerical results are presented on datasets with up to 10 000 000 points such massive discrimination problems cannot be processed by conventional linear or quadratic programming methods and to our knowledge have not been solved by other methods on smaller problems sor was faster than svm sup light and comparable or faster than smo

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

nonparametric estimation for right censored length biased data a pseudo partial likelihood approach to estimate the lifetime distribution of right censored length biased data we propose a pseudo partial likelihood approach that allows us to derive two nonparametric estimators with its closed form estimators and explicit limiting variances this approach retains the simplicity of conditional analysis and has only a small efficiency loss compared with the unconditional analysis under some regularity conditions we show that the two estimators are uniformly consistent and converge weakly to gaussian processes a simulation study demonstrates that the proposed estimators have satisfactory finite sample performance application to an alzheimer s disease study is reported

nonparametric estimation from cross sectional survival data abstract in many follow up studies survival data are often observed according to a cross sectional sampling scheme data of this type are subject to left truncation in addition to the usual right censoring a number of characteristics and properties of the product limit estimate for left truncated and right censored data have been explored and found to be similar to those of the kaplan meier estimate under the stationarity assumption however it is believed that an alternative estimate has much better efficiency in this article the conditional maximum likelihood estimate mle property of the product limit estimate is visited the non parametric mle of the truncation distribution is derived use of this estimate includes testing the stationarity assumption estimating the proportion of truncated data and other applications in prevalent cohort studies the analysis of the estimation is based on a working data approach the asymptotic properties of the proposed estimates are developed through nonpar

estimation of the survival function with increasing failure rate based on left truncated and right censored data summary the maximum conditional likelihood estimator of the survival function with increasing hazard rate is derived based on left truncated and right censored data this estimator always exists whereas the fully nonparametric conditional maximum likelihood estimator may not exist a strong consistency theorem is established based on the total time on test transformation right censored survival observations arise naturally in biomedical studies of survival when some of the patients are not followed until death parametric and nonparametric methods for analysing such data have been considered by many authors in the single sample problem kaplan meier 1958 derived the nonparametric maximum likelihood estimator of the survival function based on right censored data in addition to right censoring data may be subject to left truncation this arises when the individuals enter the study at some known time after the time origin for example in studying the effects on mortality of occupational exposure to agents in a certain industry age would normally be taken as the primary time variable but observation on an individual would not commence until work in this industry started specifically we consider the following let x be a random variable representing lifetimes and let t c be the random variables describing the left truncation times and right censoring times respectively suppose that x follows the distribution f with associated survival function s 1 f we also assume that t c is independent of x and follows the joint distribution g with pr t c 1 the quantities observed are y min x c t and 8 where 8 1 if t x c and 8 0 if c x nothing is observed if x t in effect observations are made from the distribution of y t 8

a polynomial hutton theorem with applications abstract extending a classical linear result due to hutton to a nonlinear setting we prove that a continuous homogeneous polynomial between banach spaces can be approximated by finite rank polynomials if and only if its adjoint can be approximated by finite rank linear operators among other consequences we apply this result to generalize a classical result due to aron and schottenloher about the approximation property on spaces of polynomials and a recent result due to caliskan and rueda about the quasi approximation property on projective symmetric tensor products

a note on the product limit estimator under right censoring and left truncation summary in many applications involving follow up studies individuals lifetimes may be subject to left truncation in addition to the usual right censoring here we consider the product limit estimator of the survival curve s or an appropriate conditional version of s the asymptotic behaviour of the estimator is briefly described together with an example

semiparametric analysis of survival data with left truncation and dependent right censoring summary studies of chronic life threatening diseases often involve both mortality and morbidity in observational studies the data may also be subject to administrative left truncation and right censoring because mortality and morbidity may be correlated and mortality may censor morbidity the lynden bell estimator for left truncated and right censored data may be biased for estimating the marginal survival function of the nonterminal event we propose a semiparametric estimator for this survival function based on a joint model for the two time to event variables which utilizes the gamma frailty specification in the region of the observable data first we develop a novel estimator for the gamma frailty parameter under left truncation using this estimator we then derive a closed form estimator for the marginal distribution of the nonterminal event the large sample properties of the estimators are established via asymptotic theory the methodology performs well with moderate sample sizes both in simulations and in an analysis of data from a diabetes registry

weak strong continuity of multilinear mappings and the pelczynski pitt theorem abstract in generalizing a result of pelczynski the sequential weak to norm continuity ofn linear mappings between certain banach spaces including spaces of type and cotype will be studied in particular it is shown that everyn linear continuous mapping from lp1 lpninto lqis compact if and only if i 1n 1 pi

weakly continuous mappings on banach spaces abstract it is shown that every n homogeneous continuous polynomial on a banach space e which is weakly continuous on the unit ball of e is weakly uniformly continuous on the unit ball of e applications of the result to spaces of polynomials and holomorphic mappings on e are given

smooth estimation of the survival function for interval censored data interval censored data arise naturally in large scale panel studies where subjects can only be followed periodically and the event of interest can only be observed in some time intervals to estimate the survival function the non parametric maximum likelihood estimator npmle is commonly used which is a step function having some large jumps however in many applications the underlying survival function can be reasonably assumed to be smooth and then the npmle does not efficiently use this information two smooth estimators have been proposed in the literature one is based on the kernel smoothing of the npmle another is the logspline density model however to our knowledge there is no finite sample study yet to assess their performance in the literature in this paper we first show by simulation that both smooth estimators improve over the npmle for smooth survival functions we then apply these estimators to compare two survival curves the test statistics based on the maximum difference between two survival functions kolmogorov smirnov test and on the integrated weighted difference of two survival functions iwdb test are investigated via the bootstrap from our simulation studies the iwdb test seems particularly promising for some stochastically ordered survival functions that do not satisfy the proportional hazards model the methods are illustrated by reanalysing the breast cosmesis study data set copyright 2000 john wiley sons ltd

quantile regression for doubly censored data double censoring often occurs in registry studies when left censoring is present in addition to right censoring in this work we propose a new analysis strategy for such doubly censored data by adopting a quantile regression model we develop computationally simple estimation and inference procedures by appropriately using the embedded martingale structure asymptotic properties including the uniform consistency and weak convergence are established for the resulting estimators moreover we propose conditional inference to address the special identifiability issues attached to the double censoring setting we further show that the proposed method can be readily adapted to handle left truncation simulation studies demonstrate good finite sample performance of the new inferential procedures the practical utility of our method is illustrated by an analysis of the onset of the most commonly investigated respiratory infection pseudomonas aeruginosa in children with cystic fibrosis through the use of the u s cystic fibrosis registry

length biased sampling with right censoring when survival data arise from prevalent cases ascertained through a cross sectional study it is well known that the survivor function corresponding to these data is length biased and different from the survivor function derived from incident cases length biased data have been treated both unconditionally and conditionally in the literature in the latter case where length bias is viewed as being induced by random left truncation of the survival times the truncating distribution is assumed to be unknown conditioning on the observed truncation times hence causes very little loss of information in many instances however it can be supposed that the truncating distribution is uniform and it has been pointed out that under these circumstances an unconditional analysis will be more informative there are no results in the current literature that give the asymptotic properties of the unconditional nonparametric maximum likelihood estimator npmle of the unbiased survivor function in the presence of cen

estimating survival curves with left truncated and interval censored data under monotone hazards we show that the nonparametric maximum likelihood estimator npmle of a survival function may severely underestimate the survival probabilities at very early times for left truncated and interval censored data as an alternative we propose to compute the nonparametric mle under a nondecreasing hazard assumption the monotone mle by a gradient projection algorithm when the assumption holds the projection step is accomplished via an isotonic regression algorithm the pool adjacent violators algorithm this gradient projection algorithm is computationally efficient and converges globally monte carlo simulations show superior performance of the monotone mle over that of the npmle in terms of either bias or variance even for large samples the methodology is illustrated with the application to the wisconsin epidemiological study of diabetic retinopathy data to estimate the probability of incidence of retinopathy

bases in the space of regular multilinear operators on banach lattices abstract for banach lattices e 1 e m and f with 1 unconditional bases we show that the monomial sequence forms a 1 unconditional basis of l r e 1 e m f the banach lattice of all regular m linear operators from e 1 e m to f if and only if each basis of e 1 e m is shrinking and every positive m linear operator from e 1 e m to f is weakly sequentially continuous as a consequence we obtain necessary and sufficient conditions for which the m fold fremlin projective tensor product e 1 e m resp the m fold positive injective tensor product e 1 e m has a shrinking basis or a boundedly complete basis

an interpolation approach to hardy littlewood inequalities for norms of operators on sequence spaces we revisit estimates of hardy and littlewood for norms of operators on sequence spaces and exploit recent advances in interpolation theory to provide relatively simple proofs

interval censored parametric regression survival models and the analysis of longitudinal trials this paper develops interval censoring likelihood methods in the context of parametric proportional hazard ph and non ph regression models in the longitudinal study setting to reanalyze the medical research council s randomized controlled trial of teletherapy in age related macular degeneration we compare the performance of the interval censoring likelihood with proxy likelihoods that were used to analyze the original data it is shown analytically that the use of such proxy likelihoods in selected ph models leads to biased estimators such estimators are artificially precise further the magnitude of their percentage bias is quantified in a data directed simulation study for non ph models we demonstrate that these results obtained from ph models do not hold uniformly and explain the implications of this finding for the reanalysis of proxy likelihood trial data our final analysis of the age related macular degeneration trial data based on fitting ph and non ph models reassuringly confirms the published findings from the original trial copyright 2013 john wiley sons ltd

maximization of the marginal likelihood of grouped survival data summary grouped failure time data occur in studies where subjects are monitored periodically to determine whether failure has occurred in the intervening interval here the model under consideration is cox s 1972 1975 proportional hazards model but the commonly used method of partial likelihood needs modification with grouped data due to a potentially large number of ties this paper demonstrates how the monte carlo em algorithm wei tanner 1990 can be used on grouped data to find the maximum likelihood estimate from the marginal likelihood based on the incomplete ranks of the event times the methodology is exemplified with a data set with precise failure times after artificially introducing grouping

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

smooth semiparametric regression analysis for arbitrarily censored time to event data a general framework for regression analysis of time to event data subject to arbitrary patterns of censoring is proposed the approach is relevant when the analyst is willing to assume that distributions governing model components that are ordinarily left unspecified in popular semiparametric regression models such as the baseline hazard function in the proportional hazards model have densities satisfying mild smoothness conditions densities are approximated by a truncated series expansion that for fixed degree of truncation results in a parametric representation which makes likelihood based inference coupled with adaptive choice of the degree of truncation and hence flexibility of the model computationally and conceptually straightforward with data subject to any pattern of censoring the formulation allows popular models such as the proportional hazards proportional odds and accelerated failure time models to be placed in a common framework provides a principled basis for choosing among them and renders useful extensions of the models straightforward the utility and performance of the methods are demonstrated via simulations and by application to data from time to event studies

estimating a distribution function with truncated data let mathscr p be a finite population with n geq 1 elements for each e in mathscr p let x e and y e be independent positive random variables with unknown distribution functions f and g and suppose that the pairs x e y e are i i d we consider the problem of estimating f g and n when the data consist of those pairs x e y e for which e in mathscr p and y e leq x e the nonparametric maximum likelihood estimators mles of f and g are described and their asymptotic properties as n rightarrow infty are derived it is shown that the mles are consistent against pairs f g for which f and g are continuous g 1 0 leq f 1 0 and g 1 1 leq f 1 1 sqrt n times estimation error for f converges in distribution to a gaussian process if int infty 0 1 g df infty but may fail to converge if this integral is infinite

continuum regression cross validated sequentially constructed prediction embracing ordinary least squares partial least squares and principal components regression read before the royal statistical society at a meeting organized by the research section on wednesday october 25th 1989 professor d v hinkley in the chair summary the paper addresses the evergreen problem of construction of regressors for use in least squares multiple regression in the context of a general sequential procedure for doing this it is shown that with a particular objective criterion for the construction the procedures of ordinary least squares and principal components regression occupy the opposite ends of a continuous spectrum with partial least squares lying in between there are two adjustable parameters controlling the procedure alpha in the continuum 0 11 and omega the number of regressors finally accepted these control parameters are chosen by crossvalidation the method is illustrated by a range of examples of its application

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

confidence bands for survival functions with censored data a comparative study consider the problem of obtaining simultaneous confidence bands for the survival function s x when the data are arbitrarily right censored the usual pointwise confidence intervals based on greenwood s variance formula can be adapted to yield a large sample confidence band this band has in a certain sense equal precision at each point of s x it is compared with the censored versions of the kolmogorov band and the renyi band the comparisons are made in terms of the widths and the adequacy of large sample approximations and are carried out under various censoring models and degrees of censoring the bands are illustrated by applying them to data from a mechanical switch life test

local algorithms for pattern recognition and dependencies estimation in previous publications bottou and vapnik 1992 vapnik 1992 we described local learning algorithms which result in performance improvements for real problems we present here the theoretical framework on which these algorithms are based first we present a new statement of certain learning problems namely the local risk minimization we review the basic results of the uniform convergence theory of learning and extend these results to local risk minimization we also extend the structural risk minimization principle for both pattern recognition problems and regression problems this extended induction principle is the basis for a new class of algorithms

local greedy approximation for nonlinear regression and neural network training a criterion for local estimation and approximation in nonlinear regres sion and neural network training is introduced and motivated n th order greedy approximation for the regression or target function based on the criterion is shown to converge at rate o 1 n 1 2 in the nonsampling case

asymptotic structure lp estimates of sequences and compactness of multilinear mappings abstract we relate the moduli of asymptotic uniform smoothness and convexity of a banach space with the existence of upper and lower l p estimates of sequences in the space to this end we introduce two properties which are related to the m p property defined by kalton and werner in this way we obtain a connection between the moduli of asymptotic uniform smoothness and convexity and compactness or weak sequential continuity of multilinear mappings finally we give some applications to the existence of analytic and asymptotically flat norms on a banach space

local minimax learning of functions with best finite sample estimation error bounds applications to ridge and lasso regression boosting tree learning kernel machines and inverse problems optimal local estimation is formulated in the minimax sense for inverse problems and nonlinear regression this theory provides best mean squared finite sample error bounds for some popular statistical learning algorithms and also for several optimal improvements of other existing learning algorithms such as smoothing splines and kernel regularization the bounds and improved algorithms are not based on asymptotics or bayesian assumptions and are truly local for each query not depending on cross validating estimates at other queries to optimize modeling parameters results are given for optimal local learning of approximately linear functions with side information context using real algebraic geometry in particular finite sample error bounds are given for ridge regression and for a local version of lasso regression the new regression methods require only quadratic programming with linear or quadratic inequality constraints for implementation greedy additive expansions are then combined with local minimax learning via a change in metric an optimal strategy is presented for fusing the local minimax estimators of a class of experts providing optimal finite sample prediction error bounds from random forests local minimax learning is extended to kernel machines best local prediction error bounds for finite samples are given for tikhonov regularization the geometry of reproducing kernel hilbert space is used to derive improved estimators with finite sample mean squared error mse bounds for class membership probability in two class pattern classification problems a purely local cross validation free algorithm is proposed which uses fisher information with these bounds to determine best local kernel shape in vector machine learning finally a locally quadratic solution to the finite fourier moments problem is presented after reading the first three sections the reader may proceed directly to any of the subsequent applications sections

polynomial sequential continuity on c k e spaces we show that for bounded sequences in c k e the polynomial sequential convergence is not equivalent to the pointwise polynomial sequential convergence we introduce several conditions on e under which different versions of the result are true when k is a scattered compact space these conditions are related with some others appeared in the literature and they seem to be of independent interest

pseudo partial likelihood for proportional hazards models with biased sampling data we obtain a pseudo partial likelihood for proportional hazards models with biased sampling data by embedding the biased sampling data into left truncated data the log pseudo partial likelihood of the biased sampling data is the expectation of the log partial likelihood of the left truncated data conditioned on the observed data in addition asymptotic properties of the estimator that maximize the pseudo partial likelihood are derived applications to length biased data biased samples with right censoring and proportional hazards models with missing covariates are discussed

estimation in the cox proportional hazards model with left truncated and interval censored data nous montrons que l estimateur non parametrique du maximum de vraisemblance npmle du coefficient de regression obtenu a partir de la vraisemblance jointe du coefficient de regression et de la survie de base est correct pour le modele de cox a hasards proportionnels avec des donnees tronquees a gauche et censurees par intervalle mais le npmle pent sous estimer la survie de base deux alternatives sont egalement etudiees premierement la vraisemblance marginale en etendant satten 1996 aux donnees tronquees la survie de base etant eliminee comme un parametre nuisible deuxiemement l estimateur monotone du maximum de vraisemblance qui maximise la vraisemblance jointe en supposant que la fonction de hasard est non decroissante pour la distribution de base ceci a ete initialement propose pour resoudre la sous estimation de la survie par le npmle dans le cas de donnees tronquees a gauche sans covariate tsai 1988 le boostrap est utilise a des fins d inference et des simulations sont realisees pour evaluer leur performance les methodes sont appliquees pour evaluer leur performance les methodes sont appliquees aux donnees de l etude du massachusetts health care panel afin de comparer chez les seniors en fonction du sexe les probabilites de perte d independance fonctionnelle

a multiple imputation approach to regression analysis for doubly censored data with application to aids studies sun liao and pagano 1999 proposed an interesting estimating equation approach to cox regression with doubly censored data here we point out that a modification of their proposal leads to a multiple imputation approach where the double censoring is reduced to single censoring by imputing for the censored initiating times for each imputed data set one can take advantage of many existing techniques and software for singly censored data under the general framework of multiple imputation the proposed method is simple to implement and can accommodate modeling issues such as model checking which has not been adequately discussed previously in the literature for doubly censored data here we illustrate our method with an application to a formal goodness of fit test and a graphical check for the proportional hazards model for doubly censored data we reanalyze a well known aids data set

designing follow up intervals when an examination is needed to determine if an event has occurred there will be a loss of efficiency in using the resulting interval censored data instead of the exact event times in designing follow up intervals this loss for longer intervals needs to be weighed against extra visits required by shorter intervals we obtain results to quantify this for the estimation of the median and mean survival and for covariates in parametric regression models with equally spaced examination times asymptotic information loss for the log normal and weibull distributions are similar when comparisons are made between corresponding members of the two families for distributions with coefficients of variation of 50 per cent or more a choice of interval from 0 25 to 0 7 times the median is recommended copyright 2004 john wiley sons ltd

on a conjecture of huber concerning the convergence of projection pursuit regression we generalize the projection pursuit procedure of friedman and stuetzle abstract version and prove strong convergence this answers a question of huber

nonparametric estimation and regression analysis with left truncated and right censored data abstract in many prospective and retrospective studies survival data are subject to left truncation in addition to the usual right censoring for left truncated data without covariates only the conditional distribution of the survival time y given y can be estimated nonparametrically where is the lower boundary of the support of the left truncation variable t if the data are also right censored then the conditional distribution can be consistently estimated only at points not larger than where is the upper boundary of the support of the right censoring variable c in this article we first consider nonparametric estimation of trimmed functionals of the conditional distribution of y with the trimming inside the observable range between and we then extend the approach to regression analysis and curve fitting in the presence of left truncation and right censoring on the response variable y asymptotic normality of m estimators of the regression parameters derived from this approach is

bases in spaces of multilinear forms over banach spaces fil dimant veronica universidad de san andres departamento de matematica y ciencias argentina

mixture cure model with random effects for clustered interval censored survival data the mixture cure model is an effective tool for analysis of survival data with a cure fraction this approach integrates the logistic regression model for the proportion of cured subjects and the survival model either the cox proportional hazards or accelerated failure time model for uncured subjects methods based on the mixture cure model have been extensively investigated in the literature for data with exact failure censoring times in this paper we propose a mixture cure modeling procedure for analyzing clustered and interval censored survival time data by incorporating random effects in both the logistic regression and ph regression components under the generalized linear mixed model framework we develop the reml estimation for the parameters as well as an iterative algorithm for estimation of the survival function for interval censored data the estimation procedure is implemented via an em algorithm a simulation study is conducted to evaluate the performance of the proposed method in various practical situations to demonstrate its usefulness we apply the proposed method to analyze the interval censored relapse time data from a smoking cessation study whose subjects were recruited from 51 zip code regions in the southeastern corner of minnesota