stallings foldings and subgroups of free groups we re cast in a more combinatorial and computational form the topological approach of j stallings to the study of subgroups of free groups

some properties of the kaplan meier estimator for independent nonidentically distributed random variables in this paper we study the kaplan meier estimator in the case where survival and censoring times are not all i i d we prove several results which are analogous to those shown by van zuijlen in the complete data case

the asymptotic properties of nonparametric tests for comparing survival distributions the asymptotic distribution under alternative hypotheses is derived for a class of statistics used to test the equality of two survival distributions in the presence of arbitrary and possibly unequal right censoring the test statistics include equivalents to the log rank statistic the modified wilcoxon statistic and the class of rank invariant test procedures introduced by peto peto when there are equal censoring distributions and the hazard functions are proportional the sample size formula for the f test used to compare exponential samples is shown to be valid for the log rank test in certain situations the power of the log rank test falls as the amount of censoring decreases

sofic groups and direct finiteness abstract we construct an analogue of von neumann s affiliated algebras for sofic group algebras over arbitrary fields consequently we settle kaplansky s direct finiteness conjecture for sofic groups

algebras and groups defined by permutation relations of alternating type the class of finitely presented algebras over a field k with a set of generators a1 an and defined by homogeneous relations of the form a1a2 an a 1 a 2 a n where runs through altn the alternating group of degree n is considered the associated group defined by the same group presentation is described a description of the jacobson radical of the algebra is found it turns out that the radical is a finitely generated ideal that is nilpotent and it is determined by a congruence on the underlying monoid defined by the same presentation

a general class of nonparametric tests for survival analysis tarone and ware 1977 biometrika 64 156 160 developed a general class of s sample test statistics for right censored survival data that includes the log rank and modified wilcoxon procedures subsequently many authors have considered two and s sample classes in detail in this paper a family of nonparametric statistics is shown to unify existing and generate new test statistics for the s greater than or equal to 2 sample s sample trend and single continuous covariate problems

testing for a treatment effect in the presence of nonresponders good 1979 biometrics 35 483 489 introduced a new randomization test for the two sample problem where a proportion 1 p of the treatment group does not respond to the treatment and suggested that the wilcoxon test is not effective for this situation we show to the contrary that the wilcoxon test is quite useful when p greater than or equal to 6 and point out an error in his definition of a one tailed randomization test

asymptotic properties of censored linear rank tests a conjecture of prentice is established which states that for censored linear rank test exact scores based on conditional expectations can be replaced by approximate scores obtained by evaluating the score function at an estimate of the survival function we show that under minimal conditions asymptotically equivalent tests are obtained when either the kaplan meier altshuler or moment estimator of the survival function is used asymptotic normality is also established for a general random censorship model under the null hypothesis and for contiguous alternatives this is used to calculate efficacies and when the censoring times are i i d an expression for the asymptotic relative efficiency is given which is a natural generalization of the one for classical uncensored linear rank tests 1 introduction prentice 1978 has constructed a general class of linear rank tests for a regression model with censored data his approach was to specify a score function for a classical linear rank test in the absence of censoring chernoff and savage 1958 hajek and sidak 1967 to construct all possible rankings of the unobserved uncensored values which were consistent with observed censored sample and then to assign to each observation the average of all possible scores it could have received in the absence of censoring giving equal weighting to each possible uncensored ranking except for a few special scoring functions notably logarithmic or power law scores these averages are unwieldy when there is appreciable censoring and prentice suggested that asymptotically equivalent tests might arise if the score function was evaluated at some suitable estimate of the survivor function this is well known to be true for uncensored data but requires further justification when censoring is present because the estimate of the survivor function is more complicated in this work we show that prentice s conjecture is true under minimal conditions and also we show that it remains true if prentice s moment estimator of the survivor function is replaced by either the kaplan meier estimator or altshuler s estimator asymptotic normality of these tests is established under a random censorship model for the null hypothesis and contiguous alternatives by martingale methods this is used to compute efficacies for a general random censorship model and asymptotic relative efficiencies for i i d potential censoring times where fully efficient linear rank tests exist asymptotic normality for general alternatives has been established in cuzick 1982 by more complicated methods

explained variation in survival analysis several measures of explained variation have been suggested for the cox proportional hazards regression model we have categorized these measures into three classes which correspond to three different definitions of multiple r2 of the general linear model in an empirical study we compared the performance of these measures and classified them by their adherence to a set of criteria which we think should be met by a measure of explained variation for survival data we suggest that currently there is no uniformly superior measure particularly as the concepts of either uncensored or censored populations may lead to different choices for uncensored populations a measure by kent and o quigley and the squared rank correlation between survival time and the predictor from a cox regression model appear recommendable choices for the latter censored survival times are terminated using a very recent data augmentation algorithm for multiple imputation under proportional hazards with censored populations schemper s measure v2 could be considered we give an introductory example discuss aspects of application and stress the desirability of routinely evaluating explained variation in studies of survival

on asymptotically hereditarily aspherical groups we undertake a systematic study of asymptotically hereditarily aspherical aha groups the class of groups introduced by tadeusz januszkiewicz and the second author as a tool for exhibiting exotic properties of systolic groups we provide many new examples of aha groups also in high dimensions we relate the aha property with the topology at infinity of a group and deduce in this way some new properties of weakly systolic groups we also exhibit an interesting property of boundaries at infinity for a few classes of aha groups

on estimation of partially linear transformation models we study a general class of partially linear transformation models which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis a new martingale based estimating equation approach consisting of both global and kernel weighted local estimation equations is developed for estimating the parametric and nonparametric covariate effects in a unified manner we show that with a proper choice of the kernel bandwidth parameter one can obtain the consistent and asymptotically normal parameter estimates for the linear effects asymptotic properties of the estimated nonlinear effects are established as well we further suggest a simple resampling method to estimate the asymptotic variance of the linear estimates and show its effectiveness to facilitate the implementation of the new procedure an iterative algorithm is developed numerical examples are given to illustrate the finite sample performance of the procedure supplementary materials are available online

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

estimating subject specific dependent competing risk profile with censored event time observations in a longitudinal study suppose that the primary endpoint is the time to a specific event this response variable however may be censored by an independent censoring variable or by the occurrence of one of several dependent competing events for each study subject a set of baseline covariates is collected the question is how to construct a reliable prediction rule for the future subject s profile of all competing risks of interest at a specific time point for risk benefit decision makings in this paper we propose a two stage procedure to make inferences about such subject specific profiles for the first step we use a parametric model to obtain a univariate risk index score system we then estimate consistently the average competing risks for subjects which have the same parametric index score via a nonparametric function estimation procedure we illustrate this new proposal with the data from a randomized clinical trial for evaluating the efficacy of a treatment for prostate cancer the primary endpoint for this study was the time to prostate cancer death but had two types of dependent competing events one from cardiovascular death and the other from death of other causes

repeated significance testing in survival analysis using a litter matched design this paper shows that asymptotically a general class of linear rank procedures in a litter matched design form a gauss markov process over time this result is used to develop a procedure for repeated significance testing for time to response differences in litter matched studies in addition an important class of two sample linear rank procedures is shown to have uncorrelated increments over time an example is given using a litter matched cancer study empirical indications of the accuracy of a method for approximating multivariate normal critical values are also given

on bootstrap accuracy with censored data in survival analysis with censored data we consider three closely related survival function estimators the kaplan meier nelson and moment estimators we derive the edgeworth expansions for these three estimators with studentization edgeworth expansions for the corresponding bootstrap statistics are also given it is found that the bootstrap approximation is better than the normal approximation for the studentized kaplan meier and nelson estimators but not so for the studentized moment estimator with these results we construct bootstrap based confidence intervals with better coverage probabilities we also include some simulations which show strong agreement with our theoretical findings

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

a relationship between two forms of linear rank procedures for censored data summary this paper gives a useful relationship between two popular classes of linear rank statistics for arbitrarily right censored data the relationship allows a linear rank procedure with certain optimal properties to be transformed into the form of a procedure having established asymptotic properties under proportional hazards alternatives

genericity the arzhantseva ol shanskii method and the isomorphism problem for one relator groups we show that the isomorphism problem is solvable in at most exponential time for a class of one relator groups which is exponentially generic in the sense of ol shanskii this is obtained by applying the arzhantseva ol shanskii graph minimization method to prove the general result that for fixed integers m 2 and n 1 there is an exponentially generic class of non free m generator n relator groups with the property that there is only one nielsen equivalence class of m tuples which generate a non free subgroup in particular every m generated subgroup in such a generic group g is either free or is equal to g itself and such groups are thus co hopfian these results are obtained by elementary methods without using the deep results of sela about co hopficity and the isomorphism problem for torsion free hyperbolic groups

small cancellation theory over burnside groups abstract we develop a version of small cancellation theory in the variety of burnside groups more precisely we show that there exists a critical exponent n 0 such that for every odd integer n n 0 the well known classical c 1 6 small cancellation theory as well as its graphical generalization and its version for free products produce examples of infinite n periodic groups our result gives a powerful tool for producing uncountable collections of examples of n periodic groups with prescribed properties it can be applied without any prior knowledge in the subject of n periodic groups as applications we show the undecidability of markov properties in classes of n periodic groups we produce n periodic groups whose cayley graph contains an embedded expander graphs and we give an n periodic version of the rips construction we also obtain simpler proofs of some known results like the existence of uncountably many finitely generated n periodic groups and the sq universality in the class of n periodic groups of free burnside groups

weighted log rank statistics for comparing two distributions summary the derivation of locally most powerful rank statistics for comparing two censored samples against parametric alternatives is reformulated for more general classes of alternatives a particular class is considered which includes the case of two weibull distributions differing in shape parameter

sequential analysis for censored regression data abstract motivated by buckley and james modification of the least squares procedure for censored regression data we derive a score process that incorporates the time evolution and handles staggered entry data in a natural way by censored regression data we mean that the responses are subject to a possible right censorship such cases often arise from clinical trials and industrial life tests the score process can be interpreted as a weighted comparison of transformed survival times this is especially suitable for the accelerated failure time regression model by expressing it in an appropriate form so that the counting process and its associate martingale theory can be applied we show that the score process is approximated by a mean 0 multidimensional gaussian process a consistent estimator of its covariance matrix function is provided based on the covariance matrix estimator and the sequential test of slud and wei a repeated significance test is then proposed usefulness of the procedure is il

sample size calculation for cluster randomization trials with a time to event endpoint cluster randomization trials randomize groups called clusters of subjects called subunits between intervention arms and observations are collected from each subject in this case subunits within each cluster share common frailties so that the observations from subunits of each cluster tend to be correlated oftentimes the outcome of a cluster randomization trial is a time to event endpoint with censoring in this article we propose a closed form sample size formula for weighted rank tests to compare the marginal survival distributions between intervention arms under cluster randomization with possibly variable cluster sizes extensive simulation studies are conducted to evaluate the performance of our sample size formula under various design settings real study examples are taken to demonstrate our method

when is a controller optimal in the sense of spl hscr sub spl infin loop shaping in this paper we characterize the controllers which are possible solutions of a certain spl hscr sub spl infin control design problem the problem considered is the optimal robustness problem for weighted normalized coprime factor gap metric uncertainty which is the basis for the glover mcfarlane spl hscr sub spl infin loop shaping design method given a plant p and a corresponding controller c we ask if c can be obtained from the optimization procedure for some choice of weighting function this paper considers single input single output systems and gives necessary and sufficient conditions for optimality which involve right half plane pole zero counts and a certain winding number test based on the nyquist diagram of pc the results give a characterization of this class of spl hscr sub spl infin optimal designs in the language of classical control

estimation and inference of quantile regression for survival data under biased sampling abstractbiased sampling occurs frequently in economics epidemiology and medical studies either by design or due to data collecting mechanism failing to take into account the sampling bias usually leads to incorrect inference we propose a unified estimation procedure and a computationally fast resampling method to make statistical inference for quantile regression with survival data under general biased sampling schemes including but not limited to the length biased sampling the case cohort design and variants thereof we establish the uniform consistency and weak convergence of the proposed estimator as a process of the quantile level we also investigate more efficient estimation using the generalized method of moments and derive the asymptotic normality we further propose a new resampling method for inference which differs from alternative procedures in that it does not require to repeatedly solve estimating equations it is proved that the resampling method consistently estimates the asymptoti

nonparametric analysis of a duration model with stochastic unobserved heterogeneity abstract this paper develops nonparametric identification and estimation results for a single spell hazard model where the unobserved heterogeneity is specified as a levy subordinator the identification approach solves a nonlinear volterra integral equation of the first kind with an unknown kernel function both the kernel of the integral operator which models the distribution of the unobserved heterogeneity and the functions that enter it are identified given regularity conditions and minimal variation in the observed covariates the paper proposes a shape constrained nonparametric two step sieve minimum distance estimator rates of convergence are derived and monte carlo experiments show the finite sample performance of the estimator

optimal robustness in the gap metric the application of the gap metric to robust stabilization of feedback systems is considered in particular a solution to the problem of robustness optimization in the gap metric is presented the problem of robust stabilization under simultaneous plant controller perturbations is addressed and the least amount of combined plant controller uncertainty measured by the gap metric that can cause instability of a nominally stable feedback system is determined included are a detailed summary of the main properties of the gap metric and the introduction of a dual metric called the t gap metric a key contribution of this study is to show that the problem of robustness optimization in the gap metric is equivalent to robustness optimization for normalized coprime factor perturbations this settles the question as to whether maximizing allowable coprime factor uncertainty corresponds to tolerating the largest ball of uncertainty in a well defined metric

partly functional temporal process regression with semiparametric profile estimating functions summary marginal mean models of temporal processes in event time data analysis are gaining more attention for their milder assumptions than the traditional intensity models recent work on fully functional temporal process regression tpr offers great flexibility by allowing all the regression coefficients to be nonparametrically time varying the existing esti mation procedure however prevents successive goodness of fit test for covariate coefficients in comparing a sequence of nested models this article proposes a partly functional tpr model in the line of marginal mean models some covari ate effects are time independent while others are completely unspecified in time this class of models is very rich includ ing the fully functional model and the semiparametric model as special cases to estimate the parameters we propose semiparametric profile estimating equations which are solved via an iterative algorithm starting at a consistent estimate from a fully functional model in the existing work no smoothing is needed in contrast to other varying coefficient meth ods the weak convergence of the resultant estimators are developed using the empirical process theory successive tests of time varying effects and backward model selection procedure can then be carried out the practical usefulness of the methodology is demonstrated through a simulation study and a real example of recurrent exacerbation among cystic fibrosis patients

an alternative approach to confidence interval estimation for the win ratio statistic summary pocock et al 2012 european heart journal 33 176 182 proposed a win ratio approach to analyzing composite endpoints comprised of outcomes with different clinical priorities in this article we establish a statistical framework for this approach we derive the null hypothesis and propose a closed form variance estimator for the win ratio statistic in all pairwise matching situation our simulation study shows that the proposed variance estimator performs well regardless of the magnitude of treatment effect size and the type of the joint distribution of the outcomes

on the unit conjecture for supersoluble group algebras abstract we introduce structure theorems for the study of the unit conjecture for group algebras of torsion free supersoluble groups motivated by work of p m cohn we introduce the class of x y n group algebras kg and following d s passman we define an induced length function l k g n using the fact that g has the infinite dihedral group as a homomorphic image we develop splitting theorems for x y n group algebras and as an application show that if k g is a unit then l l 1 we extend our analysis of splittings to obtain a canonical reduced split form for all units in x y n group algebras this leads to the study of group algebras of virtually abelian groups and their representations as subalgebras of suitable matrix rings where we develop a determinant condition for units in such group algebras we apply our results to the fours group x y x y 2 x 1 y 2 y x 2 y 1 x 2 and show that over any field k the group algebra k has no non trivial unit of small l length using this and the fact that l is equivariant under all k automorphisms obtained k linearly from automorphisms we prove that no subset of the promislow set p is the support of a non trivial unit in k for any field k in particular this settles a long standing question and shows that the promislow set is itself not the support of a unit in k we then give an introduction to the theory of consistent chains toward a preliminary analysis of units of higher l length in k we conclude our work showing that units in torsion free supersoluble group algebras are bounded in that the supports of units and their inverses are related through a property u and the induced length function l

semiparametric transformation models for causal inference in time to event studies with all or nothing compliance we consider causal inference in randomized survival studies with right censored outcomes and all or nothing compliance using semiparametric transformation models to estimate the distribution of survival times in treatment and control groups conditional on covariates and latent compliance type estimands depending on these distributions for example the complier average causal effect cace the complier effect on survival beyond time t and the complier quantile effect are then considered maximum likelihood is used to estimate the parameters of the transformation models using a specially designed expectation maximization em algorithm to overcome the computational difficulties created by the mixture structure of the problem and the infinite dimensional parameter in the transformation models the estimators are shown to be consistent asymptotically normal and semiparametrically efficient inferential procedures for the causal parameters are developed a simulation study is conducted to evaluate the finite sample performance of the estimated causal parameters we also apply our methodology to a randomized study conducted by the health insurance plan of greater new york to assess the reduction in breast cancer mortality due to screening

partially linear additive hazards regression with varying coefficients please see the supplementary materials for a correction to this article to explore the nonlinear interactions between some covariates and an exposure variable we propose the partially linear additive hazards model for survival data in a semiparametric setting we construct a local pseudoscore function to estimate the varying and constant coefficients and establish the asymptotic normality of the proposed estimators moreover we develop the weak convergence property for the local estimator of the baseline cumulative hazard function we conduct simulation studies to empirically examine the finite sample performance of the proposed methods and use real data from a breast cancer study for illustration

evaluating prediction rules for t year survivors with censored regression models suppose that we are interested in establishing simple but reliable rules for predicting future t year survivors through censored regression models in this article we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate sensitivity and specificity and positive and negative predictive values specifically under various working models we derive consistent estimators for the above measures through substitution and cross validation estimation procedures furthermore we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified confidence intervals for example for the difference of the precision measures between two competing rules can then be constructed all of the proposals are illustrated with real examples and their finite sample properties are evaluated through a simulation study

construction of a two unique product semigroup defined by permutation relations of quaternion type abstract for a regular representation h sym n of the generalized quaternion group of order n 4 k with k 2 the monoid s n h presented with generators a 1 a 2 a n and with relations a 1 a 2 a n a 1 a 2 a n for all h is investigated it is shown that s n h has the two unique product property as a consequence for any field k the monoid algebra k s n h is a domain with trivial units which is semiprimitive

conditions for optimality over h the fundamental optimization problem in worst case frequency domain design where stability is the key constraint is left text opt a n right qquad begin array 20 c text given gamma text a text map text from mathbb t times mathbb c n text to mathbb r text find gamma 0 text and f in a n text such text that gamma mathop inf limits f in a n mathop sup limits theta gamma left e i theta f left e i theta right right mathop sup limits theta gamma left e i theta f left e i theta right right end array here a n denotes the mathbb c n valued functions on the unit circle mathbb t with analytic continuation to the unit disk mathbb d that are continuous on the closed unit disk the special case where the sublevel sets of gamma in z are disks in mathbb c n is the main mathematical problem in the area called h

a note on the relation between two forms of linear rank statistics for right censored and grouped data we show that two forms of linear rank statistics for right censored and grouped data are equivalent in the case of no tied value among uncensored observations we provide some intuition about the equivalence

a class of rank test procedures for censored survival data summary a class of linear rank statistics is proposed for the k sample problem with rightcensored survival data the class contains as special cases the log rank test mantel 1966 cox 1972 and a test essentially equivalent to peto peto s 1972 generalization of the wilcoxon test martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses a class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution some monte carlo results are displayed which present small sample behaviour

graphical methods for assessing violations of the proportional hazards assumption in cox regression a major assumption of the cox proportional hazards model is that the effect of a given covariate does not change over time if this assumption is violated the simple cox model is invalid and more sophisticated analyses are required this paper describes eight graphical methods for detecting violations of the proportional hazards assumption and demonstrates each on three published datasets with a single binary covariate i discuss the relative merits of these methods smoothed plots of the scaled schoenfeld residuals are recommended for assessing ph violations because they provide precise usable information about the time dependence of the covariate effects

a monte carlo study of some two sample rank tests with censored data abstract the powers of several nonparametric tests for the two sample problem with censored data are compared by simulation the tests studied include gehan s efron s and peto s and prentice s generalized wilcoxon tests along with the logrank test the test with the greatest power changes with the sample sizes censoring mechanism and distribution of the random variables the test that performed the best overall was the peto prentice generalized wilcoxon statistic with an asymptotic variance estimate

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

a sieve m theorem for bundled parameters in semiparametric models with application to the efficient estimation in a linear model for censored data in many semiparametric models that are parameterized by two types of parameters a euclidean parameter of interest and an infinite dimensional nuisance parameter the two parameters are bundled together i e the nuisance parameter is an unknown function that contains the parameter of interest as part of its argument for example in a linear regression model for censored survival data the unspecified error distribution function involves the regression coefficients motivated by developing an efficient estimating method for the regression parameters we propose a general sieve m theorem for bundled parameters and apply the theorem to deriving the asymptotic theory for the sieve maximum likelihood estimation in the linear regression model for censored survival data the numerical implementation of the proposed estimating method can be achieved through the conventional gradient based search algorithms such as the newton raphson algorithm we show that the proposed estimator is consistent and asymptotically normal and achieves the semiparametric efficiency bound simulation studies demonstrate that the proposed method performs well in practical settings and yields more efficient estimates than existing estimating equation based methods illustration with a real data example is also provided

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

kazhdan groups with infinite outer automorphism group for each countable group q we produce a short exact sequence 1 to n to g to q to 1 where g is f g and has a graphical frac16 presentation and n is f g and satisfies property t as a consequence we produce a group n with property t such that out n is infinite using the tools developed we are also able to produce examples of nonhopfian and non cohopfian groups with property t one of our main tools is the use of random groups to achieve certain properties

linear rank tests for the nonresponders problem with censored data summary in a two sample setting a two parameter mixture model is postulated for the treated patients where a proportion of the patients improve and the remaining proportion of nonresponders behave like the control patients the response is subject to random censoring censored data versions of linear rank statistics are developed in order to detect improvement due to treatment the tests are compared to standard tests such as the logrank test in terms of asymptotic relative efficiency empirical power and performance on real data

two sample rank tests for detecting changes that occur in a small proportion of the treated population in the course of studying a biological phenomenon thought to be a precursor to chromosome breakage researchers have found that treatments sometimes produce a higher proportion of outliers than do controls our examples pertain to smokers and patients undergoing chemotherapy although the statistical methods developed here would apply to subjects exposed to any other health hazard we formulate the problem in a nonparametric setting locally most powerful rank tests are obtained for mixture alternatives in one instance the approximate scores test has the simple form of counting the number of treatment responses above a combined sample percentile our test statistics are compared to the wilcoxon and normal scores tests using empirical power studies and asymptotic efficiencies

rips segev torsion free groups without the unique product property abstract we generalize the graphical small cancellation theory of gromov to a graphical small cancellation theory over the free product we extend gromov s small cancellation theorem to the free product we explain and generalize rips segev s construction of torsion free groups without the unique product property by viewing these groups as given by graphical small cancellation presentations over the free product our graphical small cancellation theorem then provides first examples of gromov hyperbolic groups without the unique product property we construct uncountably many non isomorphic torsion free groups without the unique product property we show that the presentations of generalized rips segev groups are not generic among finite presentations of groups

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

competing risks quantile regression quantile regression has emerged as a significant extension of traditional linear models and its potential in survival applications has recently been recognized in this paper we study quantile regression with competing risks data formulating the model based on conditional quantiles defined using the cumulative incidence function which includes as a special case an analog to the usual accelerated failure time model the proposed competing risks quantile regression model provides meaningful physical interpretations of covariate effects and moreover relaxes the constancy constraint on regression coefficients thereby providing a useful perhaps more flexible alternative to the popular subdistribution proportional hazards model we derive an unbiased monotone estimating equation for regression parameters in the quantile model the uniform consistency and weak convergence of the resulting estimators are established across a quantile continuum we develop inferences including covariance estimation second

a new test for asphericity and diagrammatic reducibility of group presentations we present a new test for studying asphericity and diagrammatic reducibility of group presentations our test can be applied to prove diagrammatic reducibility in cases where the classical weight test fails we use this criterion to generalize results of j howie and s m gersten on asphericity of lots and of adian presentations and derive new results on solvability of equations over groups we also use our methods to investigate a conjecture of s v ivanov related to kaplansky s problem on zero divisors we strengthen ivanov s result for locally indicable groups and prove a weak version of the conjecture

nonparametric association analysis of exchangeable clustered competing risks data summary the work is motivated by the cache county study of aging a population based study in utah in which sibship associations in dementia onset are of interest complications arise because only a fraction of the population ever develops dementia with the majority dying without dementia the application of standard dependence analyses for independently right censored data may not be appropriate with such multivariate competing risks data where death may violate the independent censoring assumption nonparametric estimators of the bivariate cumulative hazard function and the bivariate cumulative incidence function are adapted from the simple nonexchangeable bivariate setup to exchangeable clustered data as needed with the large sibships in the cache county study time dependent association measures are evaluated using these estimators large sample inferences are studied rigorously using empirical process techniques the practical utility of the methodology is demonstrated with realistic samples both via simulations and via an application to the cache county study where dementia onset clustering among siblings varies strongly by age

partially linear hazard regression for multivariate survival data this article studies estimation of partially linear hazard regression models for multivariate survival data a profile pseudo partial likelihood estimation method is proposed under the marginal hazard model framework the estimation on the parameters for the linear part is accomplished by maximization of a pseudo partial likelihood profiled over the nonparametric part this enables us to obtain consistent estimators of the parametric component asymptotic normality is obtained for the estimates of both the linear and nonlinear parts the new technical challenge is that the nonparametric component is indirectly estimated through its integrated derivative function from a local polynomial fit an algorithm of fast implementation of our proposed method is presented consistent standard error estimates using sandwich type ideas are also developed which facilitates inferences for the model it is shown that the nonparametric component can be estimated as well as if the parametric components were known and the

rank tests for survival analysis a comparison by analogy with games several commonly used two sample linear rank tests for censored data have been shown to be closely linked in mathematical structure this pedagogical paper elucidates the relationships among the tests by introducing a videogame played between a boys team and a girls team with different rules of payment by the consecutive losers considered depending on the rule of payment the total amount of money the girls win as a team becomes the wilcoxon statistic the savage statistic or their generalizations under censoring

the durations of recession and prosperity what distribution do they follow abstract i study the duration of periods of prosperity and recessions from twenty one leading economies and determine what distribution is a reasonable and plausible fit for these duration data the earlier literature has focused on the power law and exponential distributions for these duration data i consider these two distributions as well as two alternative distributions however unlike earlier papers i use a maximum likelihood framework that estimates and evaluates the fit of each of these candidate distributions as well as allowing for model comparison tests to compare a particular distribution against competing distributions

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

a mixture cure rate model for responses and response times in time limit tests many large scale standardized tests are intended to measure skills related to ability rather than the rate at which examinees can work time limits imposed on these tests make it difficult to distinguish between the effect of low proficiency and the effect of lack of time this paper proposes a mixture cure rate model approach to address this issue maximum likelihood estimation is proposed for parameter and variance estimation for three cases when examinee parameters are to be estimated given precalibrated item parameters when item parameters are to be calibrated given known examinee parameters and when item parameters are to be estimated without assuming known examinee parameters large sample properties are established for the cases under suitable regularity conditions simulation studies suggest that the proposed approach is appropriate for inferences concerning model parameters in addition not distinguishing between the effect of low proficiency and the effect of lack of time is shown to have considerable consequences for parameter estimation a real data example is presented to demonstrate the new model choice of survival models for the latent power times is also discussed

on least squares regression with censored data summary the semiparametric accelerated failure time model relates the logarithm of the failure time linearly to the covariates while leaving the error distribution unspecified the present paper describes simple and reliable inference procedures based on the least squares principle for this model with right censored data the proposed estimator of the vector valued regression parameter is an iterative solution to the buckley james estimating equation with a preliminary consistent estimator as the starting value the estimator is shown to be consistent and asymptotically normal a novel resampling procedure is developed for the estimation of the limiting covariance matrix extensions to marginal models for multivariate failure time data are considered the performance of the new inference procedures is assessed through simulation studies illustrations with medical studies are provided

weights determine stability of sensitivity optimal controllers abstract it is shown that the weight determines the stability of the h optimal controller for weighted sensitivity minimization problems for a large class of scalar plants and weights necessary and sufficient interpolation conditions on the weight are given in order for the optimal controller to be stable an easily evaluated formula for the optimal controller is provided when the interpolation conditions are met it is also shown that for many scalar plants it is possible to choose the weights for weighted mixed sensitivity minimization so that the optimal controller is stable and minimum phase 1997 elsevier science ltd

the problem of a covariate time qualitative interaction in a survival study we introduce a test for the equality of two survival distributions against the specific alternative of crossing hazards although this kind of alternative is somewhat rare designing a test specifically aimed at detecting such departures from the null hypothesis in this direction leads to powerful procedures upon which we can call in those few cases where such departures are suspected furthermore the proposed test and an approximate version of the test are seen to suffer only moderate losses in power when compared with their optimal counterparts should the alternative be one of proportional hazards our interest in the problem is motivated by clinical studies on the role of acute graft versus host disease as a risk factor in leukemic children and we discuss the analysis of this study in detail the model we use in this work is a special case of the one introduced by anderson and senthilselvan 1982 applied statistics 31 44 51 we propose overcoming an inferential problem stemming from their model by using the methods of davies 1977 biometrika 64 247 254 1987 biometrika 74 33 43 backed up by resampling techniques we also look at an approach relying directly on resampling techniques the distributional aspects of this approach under the null hypothesis are interesting but practically its behaviour is such that its use cannot be generally recommended outlines of the necessary asymptotic theory are presented and for this we use the tools of martingale theory

score tests for association under response dependent sampling designs for expensive covariates this is a pre copyedited author produced pdf of an article accepted for publication in biometrika following peer review the version of record derkach a lawless j f and sun l 2015 score tests for association under response dependent sampling designs for expensive covariates biometrika 102 4 988 994 is available online at http biomet oxfordjournals org content 102 4 988 full pdf html doi 10 1093 biomet asv038

uncertainty in the weighted gap metric a geometric approach the stability of control systems is studied in the context of weighted input output signal spaces necessary and sufficient conditions for a controller to stabilize a plant are given in terms of geometric notions these geometric quantities can be calculated by solving h optimization problems maximally stabilizing controllers in a weighted signal space are introduced and characterized in terms of nehari extensions the robustness properties of maximally stabilizing controllers are analysed in terms of weighted coprime factor uncertainty necessary and sufficient conditions are established for a controller of a given plant to be the maximally stabilizing controller of the plant with respect to a weight an upper bound for the mixed sensitivity of a control system is given where the controller is the maximally stabilizing controller of the plant

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

testing for monotone trend in recurrent event processes tests for the presence of monotone trends in recurrent event processes have been proposed and studied by many authors however a general concept of trend is elusive and the dependence of the behavior of tests on the assumed definitions of no trend and trend and on the observation periods for the processes has been largely ignored we discuss these issues and study them through analytical results and simulation studies the article also presents robust tests for trend across multiple processes extends them to deal with interval censored event times and compares them and other well known trend tests with respect to the issues mentioned

maximum likelihood estimation for semiparametric regression models with multivariate interval censored data interval censored multivariate failure time data arise when there are multiple types of failure or there is clustering of study subjects and each failure time is known only to lie in a certain interval we investigate the effects of possibly time dependent covariates on multivariate failure times by considering a broad class of semiparametric transformation models with random effects and we study nonparametric maximum likelihood estimation under general interval censoring schemes we show that the proposed estimators for the finite dimensional parameters are consistent and asymptotically normal with a limiting covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood in addition we develop an em algorithm that converges stably for arbitrary datasets finally we assess the performance of the proposed methods in extensive simulation studies and illustrate their application using data derived from the atherosclerosis risk in communities study

linear rank statistics for truncated data summary motivated by prentice s 1978 generalization of linear rank statistics for censored data we introduce a similar kernel for deriving linear rank statistics for truncated data they take very similar forms to those of prentice s statistics moreover we also show that they can be expressed equivalently in weighted log rank type forms thus providing natural variance estimators explicit forms corresponding to wilcoxon and log rank tests are obtained extensions to data subject to both left truncation and right censoring are provided

on estimands arising from misspecified semiparametric rate based analysis of recurrent episodic conditions marginal rate based analyses are widely used for the analysis of recurrent events in clinical trials in many areas of application the events are not instantaneous but rather signal the onset of a symptomatic episode representing a recurrent infection respiratory exacerbation or bout of acute depression in rate based analyses it is unclear how to best handle the time during which individuals are experiencing symptoms and hence are not at risk we derive the limiting value of the nelson aalen estimator and estimators of the regression coefficients under a semiparametric rate based model in terms of an underlying two state process we investigate the impact of the distribution of the episode durations heterogeneity and dependence on the asymptotic and finite sample properties of standard estimators we also consider the impact of these features on power in trials designed to test intervention effects on rate functions an application to a trial of individuals with herpes simplex virus is given for illustration

functional laws of the iterated logarithm for the product limit estimator of a distribution function under random censorship or truncation functional laws of the iterated logarithm are established for a modified version of the classical product limit estimator of a distribution function when the data are subject to random censorship or truncation making use of stochastic integral representations and empirical process theory strong approximations involving i i d continuous parameter martingales are developed for the product limit estimator and these strong approximations are then applied to derive the functional laws

three classes of censored data rank tests strengths and weaknesses under censoring summary nonparametric tests are useful when definite parametric alternatives are not available the behaviour under censoring of extensions of the tests is used to delineate three distinct classes of censored data rank tests asymptotically efficient approximately distribution free and approximately unbiased section 2 gives qualitative comparisons 3 gives some representative numerical comparisons the pitman efficiencies approximated by lee desu gehan 1975 from simulations with 50 observations in each group are shown to agree with asymptotic calculations 1 weighted log rank tests it is assumed that two samples of randomly censored observations are available that is that the true lifetimes yij have cumulative distribution functions f y i oj for j 1 n i i 1 2 that the censoring times cij have cumulative distribution functions h y i of and that the observable quantities are xij min yij c and dij xij yij where a denotes the indicator function of the set a it is assumed that 01 0 that f t 1 0 is continuous in 0 and that the null hypothesis is 61 02 0 the true value of 02 will be denoted by 0 and the functions f t i 0 and h t i 0 will be abbreviated to f and h survival distributions will be denoted by a bar so that f t 1 f t the hazard rates of f and f t 10 will be denoted by a and ao respectively the test statistics studied are functions of di t the number of deaths observed before time t in the ith sample ri t the number at risk at time t in the ith sample and aj an estimator of the cumulative hazard function for the ith sample these functions are defined formally by n i n i