a class of semiparametric regressions for the accelerated failure time model in this paper a general class of nonparametric test statistics which includes both linear and nonlinear rank tests for the accelerated failure time model is inverted into estimating equations for multiple regression for right censored data this general class of semiparametric regression procedures includes the linear rank estimators of tsiatis 1990 extends the theil sen estimator based on kendall s to multiple regression and introduces several new families of regression methods based on inverting nonlinear rank tests these new families include the weighted generalised logrank estimators and the weighted logit rank estimators several estimators of the standard errors of the regression coefficients are given the regression coefficient estimators are consistent and asymptotically normal with variances that can be consistently estimated several linear and nonlinear rank based estimators of the regression parameters and several methods of estimating their standard errors and the corresponding confidence intervals are compared in a small sample simulation in settings with and without outliers among the covariates in these simulations the generalised logrank estimators performed well as compared to the logrank estimators when there was no outlier among the covariates and had less bias than the logrank estimators when covariate outliers existed

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

words and forbidden factors given a finite or infinite word v we consider the set m v of minimal forbidden factors of v we show that the set m v is of fundamental importance in determining the structure of the word v in the case of a finite word w we consider two parameters that are related to the size of m w the first counts the minimal forbidden factors of w and the second gives the length of the longest minimal forbidden factor of w we derive sharp upper and lower bounds for both parameters we prove also that the second parameter is related to the minimal period of the word w we are further interested to the algorithmic point of view indeed we design linear time algorithm for the following two problems i given w construct the set m w and conversely ii given m w reconstruct the word w in the case of an infinite word x we consider the following two functions gx that counts for each n the allowed factors of x of length n and fx that counts for each n the minimal forbidden factors of x of length n we address the following general problem what information about the structure of x can be derived from the pair gx fx we prove that these two functions characterize up to the automorphism exchanging the two letters the language of factors of each single infinite sturmian word

the accelerated failure time model under biased sampling chen 2009 biometrics studies the semi parametric accelerated failure time model for data that are size biased chen considers only the uncensored case and uses hazard based estimation methods originally developed for censored observations however for uncensored data a simple linear regression on the log scale is more natural and provides better estimators

semiparametric estimation of an accelerated failure time model with time dependent covariates summary a class of semiparametric accelerated failure time models is introduced that are useful for modelling the relationship of survival distributions to time dependent covariates a class of semiparametric rank estimators is derived for the parameters in this model when the survival data are right censored these estimates are shown to be consistent and asymptotically normal with variances that can be consistently estimated it is also shown that estimators within this class achieve the semiparametric efficiency bound we consider an accelerated failure time model for time to event data in which the survival distribution is scaled by a factor which may be a function of time dependent covariates these models directly model the effect of covariates on the length of survival this is in contrast to the more commonly used proportional hazards model which models the hazard rate itself in some applications it may be easier to visualize the concept that a treatment intervention or exposure to an environmental contaminant increases or decreases the length of survival by a certain proportion as compared to the concept that the hazard rate is changed for time independent covariates say z z1 zp the class of accelerated failure time models assumes that the survival distribution at time t given a set of covariates z z is given by f t i z f0 h z t the proportionality constant h z can be interpreted as the scale factor by which lifetime is decreased as a function of the covariates z often h z is taken to be log linear or h z exp b z in such cases if z 0 we can interpret fo t as the baseline survival distribution or the survival distribution for individuals with covariates all equal to zero a useful way of envisioning this model is to consider a hypothetical random variable u that corresponds to an individual s survival time if that individual had covariate values all equal to zero this baseline failure time u would be modified for values of the covariate different than zero for example if we denote the actual survival time by t then for an individual with covariate value z we have t e zu the parameters b in this model have a direct interpretation in terms of the increase or decrease in lifespan as a function of the covariates the assumption that u is independent of z in this hypothetical construct induces the probabilistic model

regression with censored data summary there are four regression techniques currently available for use with censored data which do not assume particular parametric families of survival distributions they are due to i cox 1972 ii miller 1976 iii buckley james 1979 and iv koul susarla van ryzin 1981 these four methods are described and their performances compared on the updated stanford heart transplant data conclusions on the usefulness of the four procedures are drawn

convergence of luo and tsai s iterative algorithm for estimation in proportional likelihood ratio models luo tsai 2012 biometrika introduced the proportional likelihood ratio model they proposed an iterative algorithm for the estimation of the baseline distribution function but did not establish its convergence here we provide a proof of convergence copyright 2013 oxford university press

temporal aggregation of garch processes the authors derive low frequency say weekly models implied by high frequency say daily arma models with symmetric garch errors they show that low frequency models exhibit conditional heteroskedasticity of the garch form as well the parameters in the conditional variance equation of the low frequency model depend upon mean variance and kurtosis parameters of the corresponding high frequency model moreover strongly consistent estimators of the parameters in the high frequency model can be derived from low frequency data the common assumption in applications that rescaled innovations are independent is disputable since it depends upon the available data frequency copyright 1993 by the econometric society

simple and fast overidentified rank estimation for right censored length biased data and backward recurrence time summary length biased survival data subject to right censoring are often collected from a prevalent cohort however informative right censoring induced by the sampling design creates challenges in methodological development while certain conditioning arguments could circumvent the problem of informative censoring related rank estimation methods are typically inefficient because the marginal likelihood of the backward recurrence time is not ancillary under a semiparametric accelerated failure time model an overidentified set of log rank estimating equations is constructed based on the left truncated right censored data and backward recurrence time efficient combination of the estimating equations is simplified by exploiting an asymptotic independence property between two sets of estimating equations a fast algorithm is studied for solving non smooth non monotone estimating equations simulation studies confirm that the overidentified rank estimator can have a substantially improved estimation efficiency compared to just identified rank estimators the proposed method is applied to a dementia study for illustration

fixed point theorems for discontinuous mapping we prove a generalization of brouwer s famous fixed point theorem to discontinuous maps the main result shows that for discontinuous functions on a compact convex domainx one can always find a pointx x such that x f x is less than a certain measure of discontinuity applications to artificial neural nets economic equilibria and analysis are given

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

efficient estimation for the accelerated failure time model the accelerated failure time model provides a natural formulation of the effects of covariates on potentially censored response variable the existing semiparametric estimators are computationally intractable and statistically inefficient in this article we propose an approximate nonparametric maximum likelihood method for the accelerated failure time model with possibly time dependent covariates we estimate the regression parameters by maximizing a kernel smoothed profile likelihood function the maximization can be achieved through conventional gradient based search algorithms the resulting estimators are consistent and asymptotically normal the limiting covariance matrix attains the semiparametric efficiency bound and can be consistently estimated we also provide a consistent estimator for the error distribution extensive simulation studies demonstrate that the asymptotic approximations are accurate in practical situations and the new estimators are considerably more efficient than the existing o

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

minimal forbidden factors of circular words minimal forbidden factors are a useful tool for investigating properties of words and languages two factorial languages are distinct if and only if they have different antifactorial sets of minimal forbidden factors there exist algorithms for computing the minimal forbidden factors of a word as well as of a regular factorial language conversely crochemore et al ipl 1998 gave an algorithm that given the trie recognizing a finite antifactorial language m computes a dfa of the language having m as set of minimal forbidden factors in the same paper they showed that the obtained dfa is minimal if the input trie recognizes the minimal forbidden factors of a single word we generalize this result to the case of a circular word we also discuss combinatorial properties of the minimal forbidden factors of a circular word finally we characterize the minimal forbidden factors of the circular fibonacci words

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

word assembly through minimal forbidden words we give a linear time algorithm to reconstruct a finite word w over a finite alphabet a of constant size starting from a finite set of factors of w verifying a suitable hypothesis we use combinatorics techniques based on the minimal forbidden words which have been introduced in previous papers this improves a previous algorithm which worked under the assumption of stronger hypothesis

marginalization and contemporaneous aggregation in multivariate garch processes abstract we first of all show that contemporaneous aggregation of independent univariate garch processes yields a weak garch process as introduced by drost and nijman 1993 subsequently we analyze the dependence of the parameters in the aggregate on the parameters in the underlying models and show that the variance parameters after aggregation depend on the underlying variance and kurtosis parameters then we generalize the results by showing that a linear combination of variables generated by a multivariate garch process will also be weak garch finally we derive the marginal weak garch processes implied by several multivariate garch processes

non parametric tests for right censored data with biased sampling testing the equality of two survival distributions can be difficult in a prevalent cohort study when non random sampling of subjects is involved due to the biased sampling scheme independent censoring assumption is often violated although the issues about biased inference caused by length biased sampling have been widely recognized in statistical epidemiological and economical literature there is no satisfactory solution for efficient two sample testing we propose an asymptotic most efficient nonparametric test by properly adjusting for length biased sampling the test statistic is derived from a full likelihood function and can be generalized from the two sample test to a k sample test the asymptotic properties of the test statistic under the null hypothesis are derived using its asymptotic independent and identically distributed representation we conduct extensive monte carlo simulations to evaluate the performance of the proposed test statistics and compare them with the conditional test and the standard logrank test for different biased sampling schemes and right censoring mechanisms for length biased data empirical studies demonstrated that the proposed test is substantially more powerful than the existing methods for general left truncated data the proposed test is robust still maintains accurate control of type i error rate and is also more powerful than the existing methods if the truncation patterns and right censoring patterns are the same between the groups we illustrate the methods using two real data examples

some combinatorial properties of sturmian words abstract in this paper we give a characterization of finite sturmian words by palindrome words which generalizes a property of the fibonacci words we prove that the set st of finite sturmian words coincides with the set of the factors of all the words w such that w ab cxy with a b c palindromes x y a b and x y moreover using this result we prove that st is equal to the set of the factors of all words w having two periods p and q which are coprimes and such that w p q 2 several other combinatorial properties concerning special and bispecial elements of st are shown as a consequence we give a new and purely combinatorial proof of the enumeration formula of st

multiplicative censoring renewal processes deconvolution and decreasing density nonparametric estimation on donne un estimateur du maximum de vraisemblance non parametrique pour une distribution de durees de vie il est base sur un modele d observations censurees de facon multiplicative et il generalise des problemes statistiques courants tels que l estimation d une fonction de repartition sous une contrainte de densite decroissante la deconvolution non parametrique d une variable aleatoire exponentielle ou un probleme d estimation dans les processus de renouvellement

linear transformations of vector arma processes abstract linear transformations of stochastic processes are used in many ways in economic analyses for example when linear aggregates or subprocesses are considered it is demonstrated that a linear transformation of a vector arma process is again an arma process and conditions for stationarity are given three different predictors for a linearly transformed process are compared forecasting the original process and transforming the predictions is superior to forecasting the transformed process directly and to transforming univariate predictions of the components of the original process conditions for equality of the three different forecasts are provided

alignment free sequence comparison using absent words abstract sequence comparison is a prerequisite to virtually all comparative genomic analyses it is often realised by sequence alignment techniques which are computationally expensive this has led to increased research into alignment free techniques which are based on measures referring to the composition of sequences in terms of their constituent patterns these measures such as q gram distance are usually computed in time linear with respect to the length of the sequences in this paper we focus on the complementary idea how two sequences can be efficiently compared based on information that does not occur in the sequences a word is an absent word of some sequence if it does not occur in the sequence an absent word is minimal if all its proper factors occur in the sequence here we present the first linear time and linear space algorithm to compare two sequences by considering all their minimal absent words in the process we present results of combinatorial interest and also extend the proposed techniques to compare circular sequences we also present an algorithm that given a word x of length n computes the largest integer for which all factors of x of that length occur in some minimal absent word of x in time and space o n finally we show that the known asymptotic upper bound on the number of minimal absent words of a word is tight

semiparametric regression in size biased sampling size biased sampling arises when a positive valued outcome variable is sampled with selection probability proportional to its size in this article we propose a semiparametric linear regression model to analyze size biased outcomes in our proposed model the regression parameters of covariates are of major interest while the distribution of random errors is unspecified under the proposed model we discover that regression parameters are invariant regardless of size biased sampling following this invariance property we develop a simple estimation procedure for inferences our proposed methods are evaluated in simulation studies and applied to two real data analyses

transducers and repetitions the factor transducer of a word associates to each of its factors or subwords their first occurrence optimal bounds on the size of minimal factor transducers together with an algorithm for building them are given analogue results and a simple algorithm are given for the case of subsequential suffix transducers algorithms are applied to repetition searching in words le transducteur des facteurs d un mot associe a chacun de ses facteurs leur premiere occurrence on donne des bornes optimales sur la taille du transducteur minimal d un most ainsi qu un algorithme pour sa construction on donne des resultats analogues et un algorithme simple dans le cas du transducteur sous sequentiel des suffixes d un mot on donne une application a la detection de repetitions dans les mots

m estimation in censored linear models summary we propose a method of obtaining an m estimator in a linear model when the responses are subject to right censoring the central limit theorem for the estimator using squared error loss i e least squares is derived using counting process martingale techniques the estimation method is applied to the stanford heart transplant data for illustration

the structure of subword graphs and suffix trees of fibonacci words we use automata theoretic approach to analyze properties of fibonacci words the directed acyclic subword graph dawg is a useful deterministic automaton accepting all suffixes of the word we show that dawg s of fibonacci words have particularly simple structure our main result is a unifying framework for a large collection of relatively simple properties of fibonacci words the simple structure of dawgs of fibonacci words gives in many cases simplified alternative proofs and new interpretation of several well known properties of fibonacci words in particular the structure of lengths of paths corresponds to a number theoretic characterization of occurrences of any subword using the structural properties of dawg s it can be easily shown that for a string we can check if is a subword of a fibonacci word in time o and o 1 space compact dawg s of fibonacci words show a very regular structure of their suffix trees and show how the suffix tree for the fibonacci word grows extending the leaves in a very simple way into the suffix tree for the next fibonacci word

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

temporal aggregation of multivariate garch processes this paper derives results for the temporal aggregation of multivariate garch 1 1 processes in the general vector specification it is shown that the class of weak multivariate garch 1 1 processes is closed under temporal aggregation fourth moment characteristics turn out to be crucial for the low frequency dynamics for both stock and flow variables in some aspects the aggregation characteristics of multivariate garch processes are shown to be different from those of vector autoregressive moving average processes a numerical example illustrates some of the results

score estimating equations from embedded likelihood functions under accelerated failure time model the semiparametric accelerated failure time aft model is one of the most popular models for analyzing time to event outcomes one appealing feature of the aft model is that the observed failure time data can be transformed to identically independent distributed random variables without covariate effects we describe a class of estimating equations based on the score functions for the transformed data which are derived from the full likelihood function under commonly used semiparametric models such as the proportional hazards or proportional odds model the methods of estimating regression parameters under the aft model can be applied to traditional right censored survival data as well as more complex time to event data subject to length biased sampling we establish the asymptotic properties and evaluate the small sample performance of the proposed estimators we illustrate the proposed methods through applications in two examples

nonparametric inference for copulas and measures of dependence under length biased sampling and informative censoring length biased data are often encountered in cross sectional surveys and prevalent cohort studies on disease durations under length biased sampling subjects with longer disease durations have great

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

large sample study of empirical distributions in a random multiplicative censoring model consider an incomplete data problem with the following specifications there are three independent samples x 1 ldots x m z 1 ldots z n and u 1 ldots u n the first two samples are drawn from a common lifetime distribution function g while the third sample is drawn from the uniform distribution over the interval 0 1 in this paper we derive the large sample properties of hat g m n the nonparametric maximum likelihood estimate of g based on the observed data x 1 ldots x m and y 1 ldots y n where y i equiv z iu i i 1 ldots n the z s and u s are unobservable in particular we show that if m and n approach infinity at a suitable rate then sup t hat g m n t g t rightarrow 0 a s sqrt m n hat g m n g converges weakly to a gaussian process and the estimate hat g m n is asymptotically efficient in a nonparametric sense

semiparametric model for bivariate survival data subject to biased sampling to better understand the relationship between patient characteristics and their residual survival after an intermediate event such as the local cancer recurrence it is of interest to identify patients with the intermediate event and then analyze their residual survival data one challenge in analyzing such data is that the observed residual survival times tend to be longer than those in the target population since patients who die before experiencing the intermediate event are excluded from the identified cohort we propose to jointly model the ordered bivariate survival data using a copula model and appropriately adjusting for the sampling bias we develop an estimating procedure to simultaneously estimate the parameters for the marginal survival functions and the association parameter in the copula model and use a two stage expectation maximization algorithm using empirical process theory we prove that the estimators have strong consistency and asymptotic normality we conduct simulations studies to evaluate the finite sample performance of the proposed method we apply the proposed method to two cohort studies to evaluate the association between patient characteristics and residual survival

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

large sample theory of empirical distributions in biased sampling models vardi 1985a introduced an s sample model for biased sampling gave conditions which guarantee the existence and uniqueness of the nonparametric maximum likelihood estimator mathbb g n of the common underlying distribution g and discussed numerical methods for calculating the estimator here we examine the large sample behavior of the npmle mathbb g n including results on uniform consistency of mathbb g n convergence of sqrt n mathbb g n g to a gaussian process and asymptotic efficiency of mathbb g n as an estimator of g the proofs are based upon recent results for empirical processes indexed by sets and functions and convexity arguments we also give a careful proof of identifiability of the underlying distribution g under connectedness of a certain graph mathbf g examples and applications include length biased sampling stratified sampling enriched stratified sampling choice based sampling in econometrics and case control studies in biostatistics a final section discusses design issues and further problems

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

special factors and the combinatorics of suffix and factor automata the suffix automaton resp factor automaton of a finite word w is the minimal deterministic automaton recognizing the set of suffixes resp factors of w we study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w we derive formulae for the number of states of these automata we also characterize the languages l s a and l f a of words having respectively suffix automaton and factor automaton with the minimal possible number of states

analyzing length biased data with semiparametric transformation and accelerated failure time models right censored time to event data are often observed from a cohort of prevalent cases that are subject to length biased sampling informative right censoring of data from the prevalent cohort within the population often makes it difficult to model risk factors on the unbiased failure times for the general population because the observed failure times are length biased in this paper we consider two classes of flexible semiparametric models the transformation models and the accelerated failure time models to assess covariate effects on the population failure times by modeling the length biased times we develop unbiased estimating equation approaches to obtain the consistent estimators of the regression coefficients large sample properties for the estimators are derived the methods are confirmed through simulations and illustrated by application to data from a study of a prevalent cohort of dementia patients

using minimal absent words to build phylogeny an absent word in a sequence is a segment that does not occur in the given sequence it is a minimal absent word if all its proper factors occur in the given sequence in this paper we review the concept of minimal absent words which includes the notion of shortest absent word we present an efficient method for computing the minimal absent words of bounded length using a trie of bounded depth representing bounded length factors this method produces the minimal absent words of given bounded length and furthermore our technique provides a linear time algorithm with less memory usage than previous solutions we also present an approach the length weighted index to distinguish sequences of different organisms using their minimal absent words the results show that we can build a phylogenetic tree based on the information collected

asymptotic behavior of the unconditional npmle of the length biased survivor function from right censored prevalent cohort data right censored survival data collected on a cohort of prevalent cases with constant incidence are length biased and may be used to estimate the length biased i e prevalent case survival function when the incidence rate is constant so called stationarity of the incidence it is more efficient to use this structure for unconditional statistical inference than to carry out an analysis by conditioning on the observed truncation times it is well known that due to the informative censoring for prevalent cohort data the kaplan meier estimator is not the unconditional npmle of the length biased survival function and the asymptotic properties of the npmle do not follow from any known result we present here a detailed derivation of the asymptotic properties of the npmle of the length biased survival function from right censored prevalent cohort survival data with follow up in particular we show that the npmle is uniformly strongly consistent converges weakly to a gaussian process and is asymptotically efficient one important spin off from these results is that they yield the asymptotic properties of the npmle of the incident case survival function see asgharian m lan and wolfson j amer stutisi assoc 97 2002 201 209 which is often of prime interest in a prevalent cohort study our results generalize those given by vardi and zhang ann statist 20 1992 1022 1039 under multiplicative censoring which we show arises as a degenerate case in a prevalent cohort setting