regression analysis of doubly truncated data abstractdoubly truncated data are found in astronomy econometrics and survival analysis literature they arise when each observation is confined to an interval that is only those which fall wit

maximal inner boxes in parametric ae solution sets with linear shape we consider linear systems of equations a p x b p where the parameters p are linearly dependent and come from prescribed boxes and the sets of solutions defined in various ways which have linear boundary one fundamental problem is to compute a box being inside a parametric solution set we first consider parametric tolerable solution sets being convex polyhedrons for such solution sets we prove that finding a maximal inner box is an np hard problem this justifies our exponential linear programming methods for computing maximal inner boxes we also propose a polynomial heuristic that yields a large but not necessarily the maximal inner box next we discuss how to apply the presented linear programming methods for finding large inner estimations of general parametric ae solution sets with linear shape numerical examples illustrate the properties of the methods and their application

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

conditional gauge with unbounded potential let b be a ball in r d and q be a borel function on it we prove that if mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9gqpe0 rq0dxdd9vqaq jfrvkfhe9pgea0dxdar jb9hs0dxdbpyxe9vr0 vr 0 vqpwqaaeaabigaciaacaqabeaadaqaaqaaaoqaamaaxababagaci 4caiaacwhacaggwbaaleaacawg4bgaeyici4sabmoqayaaraaabeaa ieaakiaa bcadawdrbqaamaalaaabagaaiifaiaadghacaggoagaam yeaiaacmcacagg8baabagaaiifaiaadihacqghsislcawg5bgaaiif amaacaaaleqabagaamizaiabgkhitiaaikdaaaaaaogaa8hiagqaci aa rgacagf5baaleaacawgcbaabeqdcqghrii8aaaa 4fb6 mathop sup limits x in bar b int limits b frac q y x y d 2 dy is sma11 enough then mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9gqpe0 rq0dxdd9vqaq jfrvkfhe9pgea0dxdar jb9hs0dxdbpyxe9vr0 vr 0 vqpwqaaeaabigaciaacaqabeaadaqaaqaaaoqaamaaxababagaci 4caiaacwhacaggwbaaleaadawfqaqaaiaadihacqghiiizcawgcbaa meaacawg6bgaeyici4saeyoaiyraamoqaaqabaaaleqaagqaaogaa8 hiagqaciaa veadaqhaawcbagaa4neaaqaaiaa hhaaagcdawadaqa aigacwgacagg4bgaaiicaiaa bcadawdxbqaaiaa fhacawfoagaa4 heamaabaaaleaacagf0baabeaakiaacmcacawgkbgaamidaawcbaga a8hmaaqaaiaadshadawgaaadbagaamoqaaqabaaaniabguiiydaaki aawufacagldbaacawfgagaa8hpaiaa bcacawfragaa8hiaiabg6hi lcaa 5a6b mathop sup limits mathop x in b limits z in partial b e z x left exp int limits 0 t b q x t dt right infty this paper gives a new proof of one of the two main results by aizenman and simon in 1 by a simple and elementary method a basic theorem in chung and rao 2 is extended to the class of q treated in 1

large sample theory of a modified buckley james estimator for regression analysis with censored data this approach we introduce herein a slight modification of the buckley james estimator to get around the difficulties caused by the instability at the upper tail of the associated kaplan meier estimate of the underlying error distribution and show that the modified buckleyjames estimator is consistent and asymptotically normal under certain regularity conditions a simple formula for the asymptotic variance of the modified buckley james estimator is also derived and is used to study the asymptotic efficiency of the estimator extensions of these results to the multiple regression model are also given

a nonparametric estimation procedure for a periodically observed three state markov process with application to aids estimation in a three state markov process with irreversible transitions in the presence of interval censored data is considered a nonparametric maximum likelihood procedure for the estimation of the cumulative transition intensities is presented a self consistent estimator of the parameters is defined and it is shown that the maximum likelihood estimator is a self consistent estimator this extends the idea of self consistency introduced by efron to the estimation of more than one parameter an algorithm based on selfconsistency equations is provided for the computation of the estimators

tolerance sensitivity and optimality bounds in linear programming traditional sensitivity analysis in linear programming usually focuses on variations of one coefficient or term at a time the tolerance approach was proposed to provide a decision maker with an effective and easy to use method to summarize the effects of simultaneous and independent changes in selected parameters in particular for variations of the objective function coefficients the approach gives a maximum tolerance percentage within which selected coefficients may vary from their estimated values within a priori limits while still retaining the same optimal basic feasible solution although an optimal solution may cease being optimal for variations beyond the maximum tolerance percentage it may still be close to optimal herein we characterize the potential loss of optimality for variations beyond the maximum tolerance percentage as a maximum regret function we consider theoretical properties of this function and propose a method to compute a relevant portion of it

maximum likelihood estimation for the proportional hazards model with partly interval censored data summary the maximum likelihood estimator mle for the proportional hazards model with partly interval censored data is studied under appropriate regularity conditions the mles of the regression parameter and the cumulative hazard function are shown to be consistent and asymptotically normal two methods to estimate the variance covariance matrix of the mle of the regression parameter are considered based on a generalized missing information principle and on a generalized profile information procedure simulation studies show that both methods work well in terms of the bias and variance for samples of moderate size an example illustrates the methods

on profile likelihood abstract we show that semiparametric profile likelihoods where the nuisance parameter has been profiled out behave like ordinary likelihoods in that they have a quadratic expansion in this expansion the score function and the fisher information are replaced by the efficient score function and efficient fisher information the expansion may be used among others to prove the asymptotic normality of the maximum likelihood estimator to derive the asymptotic chi squared distribution of the log likelihood ratio statistic and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance

regression m estimators with doubly censored data the m estimators are proposed for the linear regression model with random design when the response observations are doubly censored the proposed estimators are constructed as some functional of a campbell type estimator f n for a bivariate distribution function based on data which are doubly censored in one coordinate we establish strong uniform consistency and asymptotic normality of f n and derive the asymptotic normality of the proposed regression m estimators through verifying their hadamard differentiability property as corollaries we show that our results on the proposed m estimators also apply to other types of data such as uncensored observations bivariate observations under univariate right censoring bivariate right censored observations and so on computation of the proposed regression m estimators is discussed and the method is applied to a doubly censored data set which was encountered in a recent study on the age dependent growth rate of primary breast cancer

regression m estimators with non i i d doubly censored data considering the linear regression model with fixed design the usual m estimator with a complete sample of the response variables is expressed as a functional of a generalized weighted bivariate empirical process and its asymptotic normality is directly derived through the hadamard differentiability property of this functional and the weak convergence of this generalized weighted empirical process the result reveals the direct relationship between the m estimator and the distribution function of the error variables in the linear model which leads to the construction of the m estimator when the response variables are subject to double censoring for this proposed regression m estimator with non i i d doubly censored data strong consistency and asymptotic normality are established

maximum likelihood for interval censored data consistency and computation summary standard convex optimization techniques are applied to the analysis of interval censored data these methods provide easily verifiable conditions for the self consistent estimator proposed by turnbull 1976 to be a maximum likelihood estimator and for checking whether the maximum likelihood estimate is unique a sufficient condition is given for the almost sure convergence of the maximum likelihood estimator to the true underlying distribution function

semiparametric robust estimation of truncated and censored regression models many estimation methods of truncated and censored regression models such as the maximum likelihood and symmetrically censored least squares scls are sensitive to outliers and data contamination as we document therefore we propose a semiparametric general trimmed estimator gte of truncated and censored regression which is highly robust but relatively imprecise to improve its performance we also propose data adaptive and one step trimmed estimators we derive the robust and asymptotic properties of all proposed estimators and show that the one step estimators e g one step scls are as robust as gte and are asymptotically equivalent to the original estimator e g scls the finite sample properties of existing and proposed estimators are studied by means of monte carlo simulations

multi parametric analysis of the maximum tolerance in a linear programming problem abstract this study intends to propose an alternative approach to the multi parametric sensitivity analysis of a linear programming problem by the concept of a maximum volume in the tolerance region for the purposes of management and control the study first proposes the necessary and sufficient conditions of the focal parameters then those nonfocal parameters that have unlimited variations can be identified and thus because of their low sensitivity in practice and simplicity in analysis they will be deleted for those focal parameters their different levels of sensitivity are investigated and conceived by the proposed maximum volume region so that they can be handled with the greatest flexibility simultaneously and independently this maximum volume region is bounded by a symmetrically rectangular parallelepiped it can be characterized by a maximization problem and solved by the existing technique dynamic programming besides an extension to the extended maximum volume region for the case of semi bounded region is considered theoretical proofs are provided with numerical illustrations the result has been compared to wendell s approach

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

a fresh view on the tolerance approach to sensitivity analysis in linear programming abstract the tolerance approach to sensitivity analysis in linear programming aims at finding a unique numerical value tolerance representing the maximum absolute perturbation which can be applied simultaneously and independently on each right hand side or objective coefficient without affecting the optimality of the given basis some extensions have been proposed in the literature which allow for individual tolerances for each coefficient thus enlarging the tolerance region in this paper we review the main results concerning the approach giving new and simpler proofs and we propose an efficient geometric algorithm returning a tolerance region that is maximal with respect to inclusion we compare our method with the existing ones on two examples showing how a priori information can be naturally exploited by our algorithm to further enlarge individual tolerances

weak convergence of a self consistent estimator of the survival function with doubly censored data double censoring often occurs in collecting lifetime data and accordingly self consistent estimators are widely employed for estimating the survival functions in this paper we prove the weak convergence of self consistent estimators using classical results on the fredholm integral equation also a method of calculating the asymptotic variance is presented

interval censoring identifiability and the constant sum property the constant sum property given in oller et al 2004 for censoring models justifies the use of a simplified likelihood to obtain the nonparametric maximum likelihood estimator of the lifetime distribution in this paper we study the relevance of the constant sum property in the identifiability of the lifetime distribution we show that the lifetime distribution is not identifiable outside the class of constant sum models we also show that the lifetime probabilities assigned to the observable intervals are identifiable inside the class of constant sum models we illustrate all these notions with several examples

algorithms for computing self consistent and maximum likelihood estimators with doubly censored data sce and the nonparametric maximum likelihood estimator npmle for doubly censored data an explicit sufficient and necessary condition for an sce to be the npmle is given based on this algorithms for computing the sce and the npmle are provided the relation between our algorithms and the em algorithm is studied

weighted empirical likelihood in some two sample semiparametric models with various types of censored data in this article the weighted empirical likelihood is applied to a general setting of two sample semiparametric models which includes biased sampling models and case control logistic regression models as special cases for various types of censored data such as right censored data doubly censored data interval censored data and partly interval censored data the weighted empirical likelihood based semiparametric maximum likelihood estimator n fn for the underlying parameter 0 and distribution f0 is derived and the strong consistency of n fn and the asymptotic normality of n are established under biased sampling models the weighted empirical log likelihood ratio is shown to have an asymptotic scaled chi squared distribution for censored data aforementioned for right censored data doubly censored data and partly interval censored data it is shown that sqrt n tilde f n f 0 weakly converges to a centered gaussian process which leads to a consistent goodness of fit test for the case control logistic regression models

a class of estimators of the survival function from interval censored data a model of interval censorship of a failure time t is considered when there is only one inspection time y the observable data are n independent copies of the pair y where t y we construct a class of self consistent estimators of the survival function of t defined implicitly through two equations and show their strong consistency under certain conditions the properties of the nonparametric maximum likelihood estimator are also investigated

semiparametric likelihood ratio inference likelihood ratio tests and related confidence intervals for a real parameter in the presence of an infinite dimensional nuisance parameter are considered in all cases the estimator of the real parameter has an asymptotic normal distribution however the estimator of the nuisance parameter may not be asymptotically gaussian or may converge to the true parameter value at a slower rate than the square root of the sample size nevertheless the likelihood ratio statistic is shown to possess an asymptotic chi squared distribution the examples considered are tests concerning survival probabilities based on doubly censored data a test for presence of heterogeneity in the gamma frailty model a test for significance of the regression coefficient in cox s regression model for current status data and a test for a ratio of hazards rates in an exponential mixture model in both of the last examples the rate of convergence of the estimator of the nuisance parameter is less than the square root of the sample size

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

using bounds on the data in linear programming the tolerance approach to sensitivity analysis in contrast to traditional sensitivity analysis in linear programming the tolerance approach considers simultaneous and independent variations in a number of parameters a primary focus of this approach is to determine a maximum tolerance percentage for selected right hand side terms in which the same basis is optimal as long as each term is accurate to within that percentage of its estimated value similarly the approach yields a maximum tolerance percentage for selected objective function coefficients this paper shows how the tolerance approach can exploit information on the range of possible values over which terms and coefficients can vary to yield larger maximum tolerance percentages

type ii sensitivity analysis of cost coefficients in the degenerate transportation problem abstract this paper focuses on sensitivity analysis of the degenerate transportation problem dtp when perturbation occurs on one cost coefficient the conventional type i sensitivity analysis of the transportation problem tp determines the perturbation ranges for the invariant optimal basis due to different degenerate optimal basic solutions yielding different type i ranges the type i range is misleading for the dtp type ii sensitivity analysis which determines the perturbation ranges for the invariant shipping pattern is more practical for the dtp however it is too tedious to obtain type ii ranges by enumerating all optimal basic solutions and all primal optimal basic solutions while getting the union of each corresponding type i ranges here we propose two labeling algorithms to determine the type ii ranges of the cost coefficient besides three lemmas are provided for obtaining the upper bound or lower bound of the type ii ranges of the cost coefficient directly under specific conditions of the dtp a numerical example is given to demonstrate the procedure of the proposed labeling algorithms and computational results have been provided

maximal and supremal tolerances in multiobjective linear programming abstract let a multiobjective linear programming problem and any efficient solution be given tolerance analysis aims to compute interval tolerances for possibly all objective function coefficients such that the efficient solution remains efficient for any perturbation of the coefficients within the computed intervals the known methods either yield tolerances that are not the maximal possible ones or they consider perturbations of weights of the weighted sum scalarization only we focus directly on perturbations of the objective function coefficients which makes the approach independent on a scalarization technique used in this paper we propose a method for calculating the supremal tolerance the maximal one need not exist the main disadvantage of the method is the exponential running time in the worst case nevertheless we show that the problem of determining the maximal supremal tolerance is np hard so an efficient polynomial time procedure is not likely to exist we illustrate our approach on examples and present an application in transportation problems since the maximal tolerance may be small we extend the notion to individual lower and upper tolerances for each objective function coefficient an algorithm for computing maximal individual tolerances is proposed

possibilistic linear regression with fuzzy data tolerance approach with prior information abstract we introduce the tolerance approach to the construction of fuzzy regression coefficients of a possibilistic linear regression model with fuzzy data both input and output the method is very general the only assumption is that cuts of the fuzzy data are efficiently computable we take into account possible prior restrictions of the parameters space we assume that the restrictions are given by linear and quadratic constraints the method for construction of the possibilistic regression coefficients is in a reduction of the fuzzy valued model to an interval valued model on a given cut which is further reduced to a linear time method i e running in time o n p computing with endpoints of the intervals here n is the number of observations and p is the number of regression parameters the speed of computation makes the method applicable for huge datasets unlike various approaches based on mathematical programming formulations the tolerance based construction preserves central tendency of the resulting regression coefficients in addition we prove further properties if inputs are crisp and outputs are fuzzy then the construction preserves piecewise linearity and convex shape of fuzzy numbers we derive an o n 2 p algorithm for enumeration of breakpoints of the membership function of the estimated coefficients similar results are also derived for the fuzzy input and output model we illustrate the theory for the case of triangular and asymmetric gaussian fuzzy inputs and outputs of an inflation consumption model

the tolerance approach to sensitivity analysis in linear programming in constrast to ordinary sensitivity analysis in linear programming the tolerance approach considers simultaneous and independent changes in the objective function coefficients and in the right hand side terms this approach yields a maximum tolerance percentage such that as long as selected coefficients or terms are accurate to within that percentage of their estimated values the same basis is optimal in particular if the objective function coefficients are accurate to within the maximum tolerance percentage of their specified values then the same solution is optimal

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

enlarging the radius of stability and stability regions in data envelopment analysis abstract this paper extends fundamental results on metric sensitivity in data envelopment analysis specifically it shows how to obtain a larger radius of stability for a decision making unit dmu by exploiting knowledge about its variability and how to enlarge a dmu s region of stability to a nonsymmetric hyperbox

linear models random censoring and synthetic data summary estimators for the linear model in the presence of censoring are available a new extension of the least squares estimator to censored data is equivalent to applying the ordinary least squares estimator to synthetic times time constructed by magnifying the gaps between successive order statistics under suitable regularity conditions the synthetic data estimator is fisher consistent and asymptotically normal examples facilitate com parison of the synthetic data estimator with estimators proposed by buckley james 1979 and by koul susarla van ryzin 1981 the entire lifetime of a person a machine a plant or an animal is not always observable some lifetimes may be censored in that only a lower bound for the lifetime is recorded statisticians are often interested in modelling the distribution of the true lifetimes as a function of covariates when censoring is present a proportional hazards model is often used when there is no censoring linear models are often used for ad hoc modelling of dependent variables miller halpern 1982 survey the methods that have been proposed for the linear model in the presence of censoring this paper describes a closed form method which is consistent and asymptotically normal this method incorporates censor ing in a natural way section 2 formulates classical least squares estimation in a manner that generalizes to accommodate random right censoring section 3 gives some theoretical results for the simplest nontrivial linear model the two sample case section 4 contains examples and the final section discusses the role of this estimator the covariate vector of the ith person will be denoted by xi and usually includes one as the first component the true lifetime yi follows a linear model if its conditional distribution given xi is

linear regression with doubly censored data linear regression with doubly censored responses is considered buckley james ritov type estimators are proposed semiparametric information and projective scores are discussed an expansion of the estimating equations is obtained under fairly general assumptions sufficient conditions are given for the asymptotic consistency and normality of the estimators

functional jackknifing rationality and general asymptotics on considere une technique de jackknife a deux niveaux pour l estimation de la variance et des representations de distributions asymptotiques du second ordre pour les estimateurs du jackknife classiques

stochastic calculus as a tool in survival analysis a review this paper gives a brief survey of the uses of stochastic calculus in survival analysis the role played by martingale central limit theory in deriving asymptotic distributions of estimators and test statistics is described the nelson aalen estimator the kaplan meier estimator cox s proportional hazards model aalen s additive risk model and a goodness of fit test for cox s model are discussed sketches of the proofs of the main results are included

construction of the largest sensitivity region for general linear programs this paper develops an alternative approach to post optimality analysis for general linear program models which provides the largest sensitivity region of any single or simultaneous change of right hand side of constraints and the coefficients of decision variables in the objective function the goal is a theoretical unification of various types of sensitivity analyses as well as advancement in the practical implementation of post optimality analysis we extend our proposed approach in the construction of sensitivity region to maintain the degenerate vertex for models with degenerate optimal solution as well as maintaining the multiple solutions for the models with non unique optimal solutions as a by product the paper resolves the paradoxical situation known as the more for less less for more situations the proposed method is based on the given optimal solution s therefore it is easy to understand easy to implement and provides useful information to the decision makers the methodology and their computational algorithms are presented and discussed in the context of some illustrative numerical examples

a missing information principle and m estimators in regression analysis with censored and truncated data a general missing information principle is proposed for constructing mestimators of regression parameters in the presence of left truncation and right censoring on the observed responses by making use of martingale central limit theorems and empirical process theory the asymptotic normality of m estimators is established under certain assumptions asymptotically efficient m estimators are also developed by using data dependent score functions in addition robustness properties of the estimators are discussed and formulas for their influence functions are derived for the robustness analysis