nonparametric estimation of distributional policy effects this paper proposes a fully nonparametric procedure to evaluate the effect of a counterfactual change in the distribution of some covariates on the unconditional distribution of an outcome variable of interest in contrast to other methods we do not restrict attention to the effect on the mean in particular our method can be used to conduct inference on the change of the distribution function as a whole its moments and quantiles inequality measures such as the lorenz curve or gini coefficient and to test for stochastic dominance the practical applicability of our procedure is illustrated via a simulation study and an empirical example

an approach to inference following model selection with applications to transformation based and adaptive inference abstract a decision theory approach is formulated for inference following model selection inference here refers to either testing point estimation or confidence estimation the loss function includes components for model selection as well as for inference and allows for flexibility in emphasis on one or the other if such emphasis is desired a general prescription for bayes and generalized bayes procedures is given a procedure consists of model selection and inference the general formulation is applied to transformation based inference where model selection is equated to choice of transformation hinkley and runger 1984 did transformation based inference that has aroused controversy the formulation here is directed to some of these issues in this approach we explicitly define the quantity of interest for which an inference is desired furthermore we evaluate procedures properly an example is given where one is interested in estimating the mean of the model selected and the choice of models is

covariate adjusted regression mue11er wa1d ucdavis edu summary we introduce covariate adjusted regression for situations where both predictors and response in a regression model are not directly observable but are contaminated with a multiplicative factor that is determined by the value of an unknown function of an observable covariate we demonstrate how the regression coefficients can be estimated by establishing a connection to varying coefficient regression the proposed covariate adjustment method is illustrated with an analysis of the regression of plasma fibrinogen concentration as response on serum transferrin level as predictor for 69 haemodialysis patients in this example both response and predictor are thought to be influenced in a multiplicative fashion by body mass index a bootstrap hypothesis test enables us to test the significance of the regression parameters we establish consistency and convergence rates of the parameter estimators for this new covariate adjusted regression model simulation studies demonstrate the efficacy of the proposed method

empirical process approach in a two sample location scale model with censored data to compare two samples of possibly right censored failure times a location scale model without assuming the distribution form is considered for the log transformed data this new accelerated failure time model is introduced to accommodate the possible heterogeneity between within treatment variations of the two groups considered one distinct feature of this model is that with the presence of heterogeneity statistical inferences on both location and scale parameters based on log rank tests or linear rank tests will become inappropriate in this paper we propose the empirical process approach to construct a regression setup derived from the theory of strong approximation of the kaplan meier product limit empirical quantile process a generalized least squares gls estimator is obtained and shown to be semiparametric efficient also it is shown that this estimation is adaptive for a special case at the end results on the two sample setting are applied to the k sample problem

tight closure and projective bundles abstract we formulate problems of tight closure theory in terms of projective bundles and subbundles this provides a geometric interpretation of such problems and allows us to apply intersection theory to them this yields new results concerning the tight closure of a primary ideal in a two dimensional graded domain

the empirical process approach for semiparametric two sample models with heterogeneous treatment effect two types of semiparametric model are proposed for comparing two samples with possibly heterogeneous treatment effects one model is a two sample location scale model which assumes that the q q plot of the two distributions involved is linear the other is the class of two sample transformation models which assume parametric forms for a probability plot the receiver operating characteristic curve the empirical process approach is used to construct strong approximations for the empirical curves of both types of plot and a convenient generalized least squares gls estimator is derived the approximate finite sample precision of the estimators can be easily evaluated asymptotically the gls estimator is shown to be efficient for the first model a difficulty involved in developing the theory of asymptotic efficiency is discussed for the transformation models the gls estimator is shown numerically to approach the fisher information bound for the proportional hazards model

extending the scope of empirical likelihood this article extends the scope of empirical likelihood methodology ill three directions to allow for plug in estimates of nuisance parameters in estimating equations slower than root n rates of convergence and settings in which there are a relatively large number of estimating equations compared to the sample size calibrating empirical likelihood confidence regions with plug in is sometimes intractable due to the complexity of the asymptotics so we introduce a bootstrap approximation that call be used in such situations we provide a range of examples from survival analysis and nonparametric statistics to illustrate the main results

strong approximations of some biometric estimates under random censorship the empirical distribution function has been widely used as an estimator for the distribution function of the elements of a random sample it is not however appropriate when the observations are incomplete this is the case for example when the observations have been randomly censored on the right in the latter case the so called product limit estimate of kaplan and meier 16 has been generally accepted as a substitute for the empirical distribution function and it possesses many of the same properties cf meier 19 developing the corresponding statement of efron 8 weak convergence over a finite interval of the kaplan meier product limit estimate to a gaussian process when there is censorship on the right has been obtained by breslow and crowley 3 cf also meier 19 breslow and crowley obtained their result via the limiting distribution of the closely related cumulative hazard process under random censorship a generalisation of the efron breslow crowley theorem was formulated by yang 24 for the case when censorship on the right is performed by more competing risks these results have numerous statistical applications in areas such as medical follow up studies life testing actuarial sciences and demography koziol and green 18 have computed tables for the limiting distribution of the cram6r von mises statistic based on the kaplan meier product limit estimate under a specific random censorship model a point will be stressed in this paper however that by a certain transformation which seems to have escaped many researchers attention and is due to efron 8 it is always possible to obtain the standard wiener process in the limit the distributions of many functionals of which are well known this transformation was only recently used in a stimulating note by gillespie and fisher 14 to construct asymptotic confidence bands for the unknown distribution function in the kaplan meier model a general scheme of random censorship can be defined in the following way let x be a real random variable with distribution function f t

computing the tight closure in dimension two we study computational aspects of the tight closure of a homogeneous primary ideal in a two dimensional normal standard graded domain we show how to use slope criteria for the sheaf of relations for generators of the ideal to compute its tight closure in particular our method gives an algorithm to compute the tight closure of three elements under the condition that we are able to compute the harder narasimhan filtration we apply this to the computation of x a y a z a in k x y z f where f is a homogeneous polynomial

the analysis of transformed data abstract recently it was suggested bickel and doksum 1981 that when data are used to select a transformation the post transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection we argue that common sense and the work of box and cox 1964 point to a contrary conclusion our argument is based on considerations of parameter interpretation and subsequent bayesian analysis within the context of fitting normal error linear models numerical examples are used to illustrate the main points

semiparametric inference in a partial linear model in a partial linear model the dependence of a response variate y on covariates w x is given by y w x e where e is independent of w x with densities g and f respectively in this paper an asymptotically efficient estimator of is constructed solely under mild smoothness assumptions on the unknown f and g thereby removing the assumption of finite residual variance on which all least squares type estimators available in the literature are based

on prediction and the power transformation family summary the power transformation family is often used for transforming to a normal linear model the variance of the regression parameter estimators can be much larger when the transformation parameter is unknown and must be estimated compared to when the transformation parameter is known we consider prediction of future untransformed observations when the data can be transformed to a linear model when the transformation must be estimated the prediction error is not much larger than when the parameter is known

a robbins monro procedure for estimation in semiparametric regression models this paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model we implement a robbins monro procedure very efficient and easy to handle on the one hand we propose a stochastic algorithm similar to that of robbins monro in order to estimate the shift parameter a preliminary evaluation of the regression function is not necessary for estimating the shift parameter on the other hand we make use of a recursive nadaraya watson estimator for the estimation of the regression function this kernel estimator takes in account the previous estimation of the shift parameter we establish the almost sure convergence for both robbins monro and nadaraya watson estimators the asymptotic normality of our estimates is also provided

uniform convergence rates for nonparametric regression and principal component analysis in functional longitudinal data we consider nonparametric estimation of the mean and covariance functions for functional longitudinal data strong uniform convergence rates are developed for estimators that are local linear smoothers our results are obtained in a unified framework in which the number of observations within each curve cluster can be of any rate relative to the sample size we show that the convergence rates for the procedures depend on both the number of sample curves and the number of observations on each curve for sparse functional data these rates are equivalent to the optimal rates in nonparametric regression for dense functional data root n rates of convergence can be achieved with proper choices of bandwidths we further derive almost sure rates of convergence for principal component analysis using the estimated covariance function the results are illustrated with simulation studies

an analysis of transformations revisited rebutted abstract in a paper written in 1964 box and cox described a method for estimating transformations and showed how in suitable cases valuable increases in simplicity and efficiency were possible since that time this technique has enjoyed wide practical use and considerable success however a recent theoretical paper by bickel and doksum 1981 seems to suggest that serious dangers are associated with the employment of this method and speaks of instability and cost of estimation of the transformation these difficulties seem to be associated with 1 examples which common sense would rule out namely situations where the effect of transformation on the data is almost linear so that it is a matter of indifference which transformation is used 2 the idea that it makes sense to state conclusions in terms of a number measured on an arbitrary scale 3 failure to take proper account of the jacobian of the transformation

test ideals in local rings it is shown that certain aspects of the theory of tight closure are well behaved under localization let j be the parameter test ideal for r a complete local cohen macaulay ring of positive prime characteristic for any multiplicative system u c r it is shown that ju 1r is the parameter test ideal for u 1 r this is proved by proving more general localization results for the here introduced classes of f ideals of r and f submodules of the canonical module of r which are annihilators of r modules with an action of frobenius it also follows that the parameter test ideal cannot be contained in any parameter ideal of r tight closure has produced surprising new results for instance that the absolute integral closure of a complete local domain r of prime characteristic is a cohen macaulay algebra for r as well as tremendously simple proofs for otherwise difficult theorems such as the fact that the ring of invariants of a linearly reductive group acting on a regular ring is cohen macaulay the definition of tight closure is recalled in section 1 but we refer the reader to the papers of hochster and huneke listed in the bibliography for more about its applications while primarily a prime characteristic notion tight closure offers insight into arbitrary commutative rings containing q by fairly standard reduction to characteristic p techniques despite its successes the tight closure operation which in its principal setting is a closure operation performed on ideals in a commutative noetherian ring of prime characteristic remains poorly understood for example tight closure is not known to behave well under localization given an ideal i of a ring r letting i denote the tight closure of i it is not known whether or not

time dependent cross ratio estimation for bivariate failure times in the analysis of bivariate correlated failure time data it is important to measure the strength of association among the correlated failure times one commonly used measure is the cross ratio motivated by cox s partial likelihood idea we propose a novel parametric cross ratio estimator that is a flexible continuous function of both components of the bivariate survival times we show that the proposed estimator is consistent and asymptotically normal its finite sample performance is examined using simulation studies and it is applied to the australian twin data

inference for covariate adjusted regression via varying coefficient models we consider covariate adjusted regression car a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor the distorting factors are unknown functions of an observable covariate where one specific distorting function is associated with each predictor or response the dependence of both response and predictors on the same confounding covariate may alter the underlying regression relation between undistorted but unobserved predictors and response we consider a class of highly flexible adjustment methods for parameter estimation in the underlying regression model which is the model of interest asymptotic normality of the estimates is obtained by establishing a connection to varying coefficient models these distribution results combined with proposed consistent estimates of the asymptotic variance are used for the construction of asymptotic confidence intervals for the regression coefficients the proposed approach is illustrated with data on serum creatinine and finite sample properties of the proposed procedures are investigated through a simulation study

on superheight conditions for the affineness of open subsets in this paper we consider the open complement u of a hypersurface y v a in an affine scheme x we study the relations between the affineness of u the intersection of y with closed subschemes the property that every closed surface in u is affine the property that every analytic closed surface is stein and the superheight of a defining ideal a

a tight closure proof of fujita s freeness conjecture for very ample line bundles the proof here actually proves a stronger statement than theorem 1 above the variety x need not be smooth f rationality is sufficient the definition is recalled in the next section in characteristic zero it is equivalent to rational singularities also the line bundle l need not be very ample it is sufficient if l is globally generated and the dimension the complete linear system l is greater than d these generalizations are summarized in theorem 2 furthermore with a little more work the same ideas prove even stronger statements which are interesting algebraically but difficult to interpret geometrically see theorem 3 fujita s freeness conjecture predicts the same conclusion under the much weaker hypothesis that l is only ample while open in general for varieties defined over a field of characteristic zero it is known in dimension four or less r el ka see also as for important progress on the conjecture and ko for a good survey about it in characteristic zero it is not hard to give a geometric argument of the special case above using the kodaira vanishing theorem the goal here is to give a simple quite different proof that is purely algebraic and valid in any characteristic this argument offers a nice illustration of how tight closure can be used to prove geometric theorems in arbitrary characteristic without the use of the usual tools of desingularization or vanishing theorems

estimation and testing in a two sample generalized odds rate model abstract the generalized odds ratio for a survival variable t is defined as t t c c 1 1 sc t sc t for c 0 and log s t for c 0 where s t pr t t this ratio coincides with the integrated hazard for c 0 and the odds ratio for c 1 when the distribution of t depends on a covariate vector we assume that conditionally on the covariates log t t c is linear in the covariates this model is a generalization of the proportional hazard model phm which has an interpretation both as a phm with random nuisance effects clayton and cuzick 1986 and as a proportional odds rate model with the odds rate defined from the response times of series systems harrington and fleming 1982 and bickel 1986a considered rank tests for this semiparametric model clayton and cuzick 1986 considered estimation we use the odds rate representation to define a class of estimates of the proportionality parameter in the two sample case we show that the estimates are consistent and asymptotica

reductions and special parts of closures abstract we provide an axiomatic framework for working with a wide variety of closure operations on ideals and submodules in commutative algebra including notions of reduction independence spread and special parts of closures this framework is applied to tight frobenius and integral closures applications are given to evolutions and special briancon skoda theorems

a flexible latent trait model for response times in tests latent trait models for response times in tests have become popular recently one challenge for response time modeling is the fact that the distribution of response times can differ considerably even in similar tests in order to reduce the need for tailor made models a model is proposed that unifies two popular approaches to response time modeling proportional hazard models and the accelerated failure time model with log normally distributed response times this is accomplished by resorting to discrete time the categorization of response time allows the formulation of a response time model within the framework of generalized linear models by using a flexible link function item parameters of the proposed model can be estimated with marginal maximum likelihood estimation applicability of the proposed approach is demonstrated with a simulation study and an empirical application additionally means for the evaluation of model fit are suggested

double reduction of pdes from the association of symmetries with conservation laws with applications abstract we use the definition of the association of symmetries of partial differential equations with conservation laws a kara f mahomed the relationship between symmetries and conservation laws int j theor phys 39 1 2000 23 40 to find a double reduction of partial differential equations with two independent variables applications to the linear heat equation the bbm equation the sine gordon equation and a system of differential equations from one dimensional gas dynamics illustrate the new theory

a correction to and improvement of strong approximations of some biometric estimates under random censorship in the proof of the main result of the original paper there is an error instead of repairing that proof to get just the original result at the critical spot we improve the proof and obtain a much better result in particular we approximate the product limit and empirical cumulative hazard processes by suitable copies of the corresponding limiting gaussian processes with rates of approximation that on appropriate fixed half lines reduce to the rates of komlos major and tusnady for the uncensored empirical process

smoothing in adaptive estimation an adaptive maximum likelihood estimator based on the estimation of the log density by b splines is introduced a data driven method of selecting the smoothing paramieter involved in the consequent density estimation is demonstrated a monte carlo study is conducted to evaluate the small sample performance of the estimator in a location and a regression problem the adaptive estimator is seen to compare favorably to some standard estimates we show that the estimator is asymptotically efficient 1 introduction the problem of adaptive estimation was introduced by stein 1956 one wishes to estimate a euclidean parameter 0 in the presence of an infinite dimensional shape parameter g usually the density an adaptive estimate performs asymptotically as well in the sense that the limiting distributions are the same with g unknown as any estimate which utilizes knowledge of g note that the term adaptive estimation has been used elsewhere in the literature in the lesser sense of adapting to the data in some way the estimates considered here are adaptive in a much stronger sense an adaptive estimator of the center of symmetry of an unknown distribution was constructed by stone 1975 bickel 1982 dealt with the multiple regression problem and simplified stein s conditions for the circumstances under which adaptive estimation is possible however all the aforementioned work pertains to large sample behavior problems arise when one tries to apply these procedures in a practical small sample situation the adaptive estimates proposed all depend on nonparametric density estimation and specifically the use of kernel density estimation essentially one replaces the true density used in a one step maximum likelihood estimate by an estimate of that density a problem which pervades nonparametric density estimation is the choice of the smoothing parameters much work has been done on this subject and various schemes for the optimal choice of smoothing parameters have been proposed mostly for the mean integrated square error criteria unfortunately this is of little help in selecting the optimal smoothing parameters for the estimation of the parameters in the location or regression problem since these methods may give a good estimate of the density but that is secondary to the problem at hand we need to estimate the score not the density and our criterion is to minimize the mse say of the estimate of 0 in fact experimentation reveals that the optimal choice of smoothing parameters as regards the estimation of the location parameter tends to produce an under

generic bounds for frobenius closure and tight closure we use geometric and cohomological methods to show that given a degree bound for membership in ideals of a fixed degree type in the polynomial ring p k x 0 ldots x d one obtains a good generic degree bound for membership in the tight closure of an ideal of that degree type in any standard graded k algebra r of dimension d 1 this indicates that the tight closure of an ideal behaves more uniformly than the ideal itself moreover if r is normal one obtains a generic bound for membership in the frobenius closure if d leq 2 then the bound for ideal membership in p can be computed from the known cases of the fr oberg conjecture and yields explicit generic tight closure bounds

a uniform functional law of the logarithm for the local empirical process we prove a uniform functional law of the logarithm for the local empirical process to accomplish this we combine techniques from classical and abstract empirical process theory gaussian distributional approximation and probability on banach spaces the body of techniques we develop should prove useful to the study of the strong consistency of d variate kernel type nonparametric function estimators

asymptotically optimal tests for conditional distributions let xl y1 xn yn be independent replicates of the random vector x y e rd m where x is rd valued and y is rm valued we assume that the conditional distribution p y e ix x qii of y given x x is a member of a parametrie family where the parameter space 0 is an open subset of rh with 0 e 0 under suitable regularity conditions we establish upper bounds for the power functions of asymptotic level a tests for the problem 0 against a sequence of contiguous alternatives as weil as asymptotically optimal tests which attain these bounds since the testing problem involves the joint density of x y as an infinite dimensional nuisance parameter its solution is not standard a monte carlo simulation exemplifies the influence of this nuisance parameter as a main tool we establish local asymptotic normality lan of certain poisson point processes which approximately describe our initial sampie

empirical smoothing parameter selection in adaptive estimation we provide a solution to the smoothing parameter selection problem involved in the construction of adaptive estimates for the symmetric location model and the general linear model linear b splines are used to give a simple form of the estimate of the score function of the underlying density new empirical methods are proposed to locate the knots optimally and to select the number of knots we also give asymptotic bounds for the empirical selection method and show that an estimate with an empirically selected smoothing parameter is adaptive our estimates are easy to compute and possess useful computational features simulation studies reveal that our estimates perform well in comparison with some well known estimates

nonparametric estimation for a scale change with censored observations abstract nonparametric point and interval estimators of the ratio of two scale parameters are given for arbitrarily right censored data based on the idea of hodges and lehmann 1963 these estimators are defined in terms of rank test statistics for testing the equality of two survival distributions the asymptotic properties and efficiencies of estimators corresponding to the tests studied by gill 1980 are investigated

looking out for stable syzygy bundles abstract we study slope stability properties of syzygy bundles on a projective space p n given by ideal generators of a homogeneous primary ideal in particular we give a combinatorial criterion for a monomial ideal to have a semistable syzygy bundle restriction theorems for semistable bundles yield the same stability results on the generic complete intersection curve from this we deduce a numerical formula for the tight closure of an ideal generated by monomials or by generic homogeneous elements in a generic two dimensional complete intersection ring

an extension of partial likelihood methods for proportional hazard models to general transformation models on utilise un schema de reechantillonnage appele echantillonneur de vraisemblance pour calculer la vraisemblance partielle et les estimateurs de vraisemblance partielle maximum

asymptotically optimal bandwidth selection for kernel density estimators from randomly right censored samples abstract this paper makes two important contributions to the theory of bandwidth selection for kernel density estimators under right censorship first an asymptotic representation of the integrated squared error into easily understood variance and squared bias components is given second it is shown that if the bandwidth is chosen by the data based method of least squares cross validation then it is asymptotically optimal in a compelling sense a by product of the first part is an interesting comparison of the two most popular kernel estimators keywords nonparametric density estimation smoothing parameter

statistical tests based on transformed data abstract the problem of testing hypotheses in linear models when the original data have been transformed is considered it is assumed that the transformation involves an unknown parameter that has to be estimated from the data for certain important testing problems it is found that the asymptotic level and power is as if had been assumed known asymptotic efficiency results show that when the box cox transformation is used tests based on transformed data have good power properties simulation results for transformed two sample and linear regression testing problems show this to be true for moderate to small sample sizes as well in particular an trimmed t test based on averages of trimmed transformed variables performs very well in both light tailed and heavy tailed skew models when compared with the usual t test and rank tests

a computation of tight closure in diagonal hypersurfaces the aim of this paper is to settle a question about the tight closure of 2 2 2 w x 3 3 3 the ideal x y z in the ring r s k x y z r x q y q z where k is a field of prime characteristic p 3 lower case letters denote the images of the corresponding variables m mcdermott has studied the tight closure of various irreducible ideals in r and has established that 2 2 2 w x xyz g x y z when p 200 see mc the general case however existed as a classic example of the difficulty involved in tight closure w x 2 2 2 computations see also hu example 1 2 we show that xyz g x y z in arbitrary prime characteristic p and furthermore establish that xyz g 2 2 2 f x y z whenever r is not f pure i e when p 2 mod 3 we move on to generalize these results to the diagonal hypersurfaces r s w x n n k x x r x q qx 1 n 1 n these issues relate to the question whether the tight closure i of an ideal i agrees with its plus closure iqs irql r where r is a domain over a field of characteristic p and rq is the integral closure of r in an algebraic closure of its fraction field in this setting we may think of the frobenius closure of i as i f s ir l r where r is the extension of r obtained by adjoining pth roots of all nonzero elements of r for e g n it is not difficult to see that iq i and equality in general is a formidable open question it should be mentioned that in the case when i is an ideal generated by part of a system of parameters the equality is a result

a transformation model for two survival curves an empirical process approach summary a new transformation model for two survival curves with possibly nonproportional hazards is presented the model assumes the existence of an unknown transformation of the survival curves into weibull distributions with different shape parameters the partial likelihood approach fails in the model a new method of estimation called the empirical process approach is proposed this approach is based on the strong approximation of the kaplan meier product limit estimators and associated quantile functions asymptotic normality of the generalised least squares estimator derived from the approach is discussed a readily defined wald test is an alternative to the log rank test from the empirical process approach a pearson s x2 goodness of fit test of the transformation model assumption can also be derived giving a new test for the proportionality of hazard functions the model can be applied for k sample problems as well

monte carlo evidence on adaptive maximum likelihood estimation of a regression on examine la performance des estimateurs du maximum de vraisemblance adaptatifs lorsque ces parametres sont preselectionnes ou alternativement determines par une methode du bootstrap basee sur les donnees

estimates for a regression parameter using ranks on considere une technique de reechantillonnage de monte carlo due a doksum et plusieurs modifications de celle ci

nonparametric and semiparametric estimation of the receiver operating characteristic curve curve odc given by f g t first we consider nonparametric estimators based on empirical distribution functions and derive asymptotic properties next we consider the so called semiparametric binormal model in which it is assumed that the distributions f and g are normal after some unknown monotonic transformation of the measurement scale for this model we propose a generalized least squares procedure and compare it with the estimation algorithm of dorfman and alf which is based on grouped data asymptotic results are obtained small sample properties are examined via a simulation study finally we describe a minimum distance estimator for the roc curve which does not require grouping the data

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

on average derivative quantile regression for fixed 0 1 the quantile regression function gives the th quantile x in the conditional distribution of a response variable y given the value x x of a vector of covariates it can be used to measure the effect of covariates not only in the center of a population but also in the upper and lower tails a functional that summarizes key features of the quantile specific relationship between x and y is the vector of weighted expected values of the vector of partial derivatives of the quantile function x in a nonparametric setting can be regarded as a vector of quantile specific nonparametric regression coefficients in survival analysis models e g cox s proportional hazard model proportional odds rate model accelerated failure time model and in monotone transformation models used in regression analysis gives the direction of the parameter vector in the parametric part of the model can also be used to estimate the direction of the parameter vector in semiparametric single index models popular in econometrics we show that under suitable regularity conditions the estimate of obtained by using the locally polynomial quantile estimate of chaudhuri 1991a is n 1 2 consistent and asymptotically normal with asymptotic variance equal to the variance of the influence function of the functional we discuss how the estimate of can be used for model diagnostics and in the construction of a link function estimate in general single index models

transfer of tail information in censored regression models consider a heteroscedastic regression model y m x sigma x varepsilon where the functions m and sigma are smooth and varepsilon is independent of x the response variable y is subject to random censoring but it is assumed that there exists a region of the covariate x where the censoring of y is light under this condition it is shown that the assumed nonparametric regression model can be used to transfer tail information from regions of light censoring to regions of heavy censoring crucial for this transfer is the estimator of the distribution of varepsilon based on nonparametric regression residuals whose weak convergence is obtained the idea of transferrring tail information is applied to the estimation of the conditional distribution of y given x x with information on the upper tail borrowed from the region of light censoring and to the estimation of the bivariate distribution p x leq x y leq y with no regions of undefined mass the weak convergence of the two estimators is obtained by products of this investigation include the uniform consistency of the conditional kaplan meier estimator and its derivative the location and scale estimators and the estimators of their derivatives

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

uniform in bandwidth consistency of kernel type function estimators we introduce a general method to prove uniform in bandwidth consistency of kernel type function estimators examples include the kernel density estimator the nadaraya watson regression estimator and the conditional empirical process our results may be useful to establish uniform consistency of data driven bandwidth kernel type function estimators

comparing two samples extensions of the t rank sum and log rank tests abstract i consider the problem of testing that two populations are identical with respect to the distribution of a continuous variable against the alternative that values tend to be larger in one population i observe that the t rank sum and log rank tests are insensitive for a large class of alternatives that may be expected to occur commonly in practice propose a criterion for identifying this problem in a particular data set and propose corresponding extensions of the conventional methods the proposed methods should be useful for both identifying and interpreting group differences

rank regression with log gamma residuals summary a robust analysis for field data is proposed using a stratified rank regression model that analysis follows pettitt 1982 alternatively a new technique is described where residuals are log gamma random variables the log gamma distribution is approximately normal when the shape parameter is large and this parameter is taken as an integer which is either preselected or estimated by a simple grid search algorithms for estimating location parameters by maximizing the likelihood based on within stratum rank information are described and illustrated using a small data set

robust response transformations based on optimal prediction nonlinear regression problems can often be reduced to linearity by transforming the response variable e g using the box cox family of transformations the classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion assuming homoscedastic normal errors for the transformed response these estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic this article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution for this purpose a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an m scale this concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients a finite sample estimate of this criterion based on a robust version of s

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

statistical inference for conditional curves poisson process approach a poisson approximation of a truncated empirical point process enables us to reduce conditional statistical problems to unconditional ones let mathbf x y be a d m dimensional random vector and denote by f cdot mid mathbf x the conditional d f of mathbf y given mathbf x mathbf x applying our approach one may study the fairly general problem of evaluating a functional parameter t f cdot mid mathbf x 1 ldots f cdot mid mathbf x p based on independent replicas mathbf x 1 mathbf y 1 ldots mathbf x n mathbf y n of mathbf x y this will be exemplified in the particular cases of nonparametric estimation of regression means and regression quantiles besides other functionals

slopes of vector bundles on projective curves and applications to tight closure problems we study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems this method gives new degree es timates from above and from below for the tight closure of a homogeneous r primary ideal in a two dimensional normal standard graded algebra r in terms of the minimal and the maximal slope of the sheaf of relations for some ideal generators if moreover this sheaf of relations is semistable then both degree estimates coincide and we get a vanishing type theorem

a convergent and dynamically consistent finite difference method to approximate the positive and bounded solutions of the classical burgers fisher equation in this work we investigate both analytically and numerically a spatially two dimensional advection diffusion reaction equation that generalizes the burgers and the fisher s equations the partial differential equation of interest is a nonlinear model for which the existence and the uniqueness of positive and bounded solutions are analytically established here at the same time we propose an exact finite difference discretization of the burgers fisher model of interest and show that as the continuous counterpart the method proposed is capable of preserving the positivity and the boundedness of the numerical approximations as well as the temporal and spatial monotonicity of the discrete initial boundary conditions it is shown that the method is convergent with first order in time and second order in space we provide some simulations that illustrate the fact that the proposed technique preserves the positivity the boundedness and the monotonicity

estimation in a linear regression model with censored data we consider the semiparametric linear regression model with censored data and with unknown error distribution we describe estimation equations of the buckley james type that admit n consistent and asymptotically normal solutions the derived estimator is efficient at a particular error distribution we show the equivalence between this type of estimator and an estimator based on a linear rank test suggested by tsiatis an extension to an estimator that is efficient everywhere is discussed

the retransformed mean after a fitted power transformation abstract an approximate method is given to estimate the mean of a dependent variable after a linear model is fitted to the box cox power transformation of this variable the estimate is accurate except when the transformation power parameter is near zero the properties of the estimate in the one sample and regression cases are considered by both asymptotic calculations and monte carlo simulations and comparisons are made with the smearing estimate duan 1983 it is shown that there can be some cost due to estimating the power transformation as opposed to assuming it is known however this cost is not severe

covariate adjusted correlation analysis with application to fmr1 premutation female carrier data motivated by molecular data on female premutation carriers of the fragile x mental retardation 1 fmr1 gene we present a new method of covariate adjusted correlation analysis to examine the association of messenger rna mrna and number of cgg repeat expansion in the fmr1 gene the association between the molecular variables in female carriers needs to adjust for activation ratio actratio a measure which accounts for the protective effects of one normal x chromosome in females carriers however there are inherent uncertainties in the exact effects of actratio on the molecular measures of interest to account for these uncertainties we develop a flexible adjustment that accommodates both additive and multiplicative effects of actratio nonparametrically the proposed adjusted correlation uses local conditional correlations which are local method of moments estimators to estimate the pearson correlation between two variables adjusted for a third observable covariate the local method of moments estimators are averaged to arrive at the final covariate adjusted correlation estimator which is shown to be consistent we also develop a test to check the nonparametric joint additive and multiplicative adjustment form simulation studies illustrate the efficacy of the proposed method application to fmr1 premutation data on 165 female carriers indicates that the association between mrna and cgg repeat after adjusting for actratio is stronger finally the results provide independent support for a specific jointly additive and multiplicative adjustment form for actratio previously proposed in the literature

semiparametric linear transformation models effect measures estimators and applications semiparametric linear transformation models form a versatile class of regression models with the cox proportional hazards model being the most well known member these models are well studied for right censored outcomes and are typically used in survival analysis we consider transformation models as a tool for situations with uncensored continuous outcomes where linear regression is not appropriate we introduce the probabilistic index as a uniform effect measure for the class of transformation models we discuss and compare three estimators using a working cox regression model the partial likelihood estimator an estimator based on binary generalized linear models and one based on probabilistic index model estimating equations the latter has a superior performance in terms of bias and variance when the working model is misspecified for the purpose of illustration we analyze data that were collected at an urban alcohol and drug detoxification unit

nonparametric regression with nonparametrically generated covariates we analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable but have be estimated from data in a preliminary step these so called generated covariates appear in numerous applications including two stage nonparametric regression estimation of simultaneous equation models or censored regression models yet so far there seems to be no general theory for their impact on the final estimator s statistical properties our paper provides such results we derive a stochastic expansion that characterizes the influence of the generation step on the final estimator and use it to derive rates of consistency and asymptotic distributions accounting for the presence of generated covariates

dimension reduction for censored regression data without parametric assumptions high dimensional regression analysis is already complex this is made even harder when data are subject to censoring in this article we seek ways of reducing the dimensionality of the regressor before applying nonparametric smoothing techniques if the censoring time is independent of the lifetime then the method of sliced inverse regression can be applied directly otherwise modification is needed to adjust for the censoring bias a key identity leading to the bias correction is derived and the root n consistency of the modified estimate is established patterns of censoring can also be studied under a similar dimension reduction framework some simulation results and an application to a real data set are reported 1 introduction survival data are often subject to censoring when this occurs the incompleteness of the observed data may induce a substantial bias in the sample several approaches have been suggested to overcome the associated difficulties in regression including the accelerated failure time model censored linear regression the cox proportional hazard model and many others survival analysis becomes even more intricate when the dimension of the regressor increases to apply any of the aforementioned methods users are required to specify a functional form which relates the outcome variables to the input ones however in reality knowledge needed for an appropriate model specification is often inadequate as a matter of fact the acquisition of such information may well turn out to be one of the primary goals of the study itself under such circumstances it seems preferable to have exploratory tools that rely less on such model specification this is the issue to be addressed in this article the dimension reduction approach of li 1991 will be extended to settings which allow for censoring in the data we shall offer methods of finding low dimensional projections of the data for visually examining the censoring pattern we shall show how censored regression data can still be analyzed without assuming the functional form a priori

on the arithmetic of tight closure we provide a negative answer to an old question in tight closure theory by showing that the containment x 3y 3 in x 4 y 4 z 4 in k x y z x 7 y 7 z 7 holds for infinitely many but not for almost all prime characteristics of the field k this proves that tight closure exhibits a strong dependence on the arithmetic of the prime characteristic the ideal x y z subset k x y z u v w x 7 y 7 z 7 ux 4 vy 4 wz 4 x 3y 3 has then the property that the cohomological dimension fluctuates arithmetically between 0 and 1

estimations in homoscedastic linear regression models with censored data an empirical process approach pertaining to the estimating equations proposed by tsiatis based on the linear rank test we show the existence of local confounding between the baseline hazard function and the covariates due to the local confounding an estimating equation in tsiatis family with a larger time point of truncation could contain less information about the regression parameter than the estimating equation with a smaller time point of truncation this phenomenon further indicates significant loss of efficiency of tsiatis estimating equations as well as the power loss of log rank type tests when the baseline hazard function goes up and down along the time scale to take care of this local confounding without using nonparametric estimates of the derivative of the baseline hazard function we propose the empirical process approach epa based on an empirical process constructed from tsiatis log rank estimating equation by varying its truncating time point the epa will provide very tractable estimations of the regression parameters as well as pearson s chi squared statistics for testing the model s assumptions specifically the performance of the epa estimator is shown to be very close to the best estimator in tsiatis family

approximate methods using ranks for regression with censored data summary an approximation to marginal rank likelihoods is given and used to make inferences for the linear regression model with censored data the approximations involve linear rank statistics adapted for censored data and estimates of their variance various explicit scores are given for right censored data and logistic scores for doubly censored data inferences using the approximate rank analysis are compared with inferences using fully and partially parametric techniques on two data sets

fitting semiparametric transformation regression models to data from a modified case cohort design summary we consider the problem of fitting semiparametric transformation regression models to data from a modified case cohort study in which the censoring times of all the censored subjects in the cohort are observed we propose to maximise a conditional profile likelihood to obtain the estimator of the regression parameter under the assumption that the censoring is independent of the covariates the estimator is shown to be consistent and asymptotically normally distributed numerical studies suggest that the relative efficiency of the estimator is very high and that the estimator is often less biased than the estimator from the complete case analysis and more accurate than the pseudolikelihood estimator

conservation laws symmetries and exact solutions of the classical burgers fisher equation in two dimensions abstract this work investigates a spatially two dimensional advection diffusion reaction equation that generalizes the burgers and the fisher s equations having the properties of convective phenomenon from burgers equation as well as diffusion transport and reaction phenomena from fisher s equation the two dimensional equation is analysed from the point of view of the theory of symmetry reductions in partial differential equations conservation laws and exact solutions from double reductions are derived finally an explicit shock wave solution is obtained