a modified wilcoxon rank sum test for paired data summary a function of the wilcoxon rank sum statistic is proposed for testing the equality of the marginal distributions when sampling from a bivariate population the test statistic is asymptotically nonparametric a comparison is made between the test statistic and several parametric and nonparametric tests in terms of their pitman relative efficiency and small sample performance the test statistic has power comparable to the paired t test when sampling from the bivariate normal distribution and greater power in several important cases

semiparametric inference in a model for association in bivanate survival data summary clayton s 1978 model for association in bivariate survival data is both of intrinsic importance and an interesting example of a semiparametric estimation problem that is a problem where inference about a parameter is required in the presence of nuisance functions we derive the asymptotic variance of clayton s estimator obtaining a simple explicit formula for uncensored data and indicating the modification required when the survival times are subject to arbitrary random censorship some comparisons are made with results derived by oakes 1982 for other estimators within this model in the absence of censoring the exact null variance of the score statistic corresponding to clayton s estimator is derived and compared with that of the locally most powerful rank test given by cuzick 1982

the rubin stark conjecture for imaginary abelian fields of odd prime power conductor we build upon ideas developed in 9 as well as results of greither on a strong form of brumer s conjecture 2 4 and prove rubin s integral version of stark s conjecture for imaginary abelian extensions of q of odd prime power conductor

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

testing equality of survival functions based on both paired and unpaired censored data summary we introduce two test procedures for comparing two survival distributions on the basis of randomly right censored data consisting of both paired and unpaired observations our procedures are based on generalizations of a pooled rank test statistic previously proposed for uncensored data one generalization adapts the prentice wilcoxon score while the other adapts the akritas score the use of these particular scoring systems in pooled rank tests with randomly right censored paired data has been advocated by several researchers our test procedures utilize the permutation distributions of the test statistics based on a novel manner of permuting the scores permutation versions of tests for right censored paired data and for two independent right censored samples that use the proposed scoring systems are obtained as special cases of our test procedures simulation results show that our test procedures have high power for detecting scale and location shifts in exponential and log logistic distributions for the survival times we also demonstrate the advantages of our test procedures in terms of utilizing randomly occurring unpaired observations that are discarded in test procedures for paired data the tests are applied to skin graft data previously reported elsewhere

congruences between derivatives of abelian l functions at s 0 let k k be a finite abelian extension of global fields we prove that a natural equivariant leading term conjecture implies a family of explicit congruence relations between the values at s 0 of derivatives of the dirichlet l functions associated to k k we also show that these congruences provide a universal approach to the refined abelian stark conjectures formulated by inter alia stark gross rubin popescu and tate we thereby obtain the first proofs of amongst other things the rubin stark conjecture and the refined class number formulas of both gross and tate for all extensions k k in which k is either an abelian extension of or is a function field

rank tests for association with right censored data summary rank tests for association between a time variable and a continuous covariate and between two time variables are given in the presence of censoring in the first case these tests are related to the semiparametric tests of cox 1972 and prentice 1978 but differ in that the covariate is replaced by a score computed from its rank in the second case the test statistic is again a simple inner product which in the proportional hazards model reduces to the correlation between the two vectors of log rank scores the loss of efficiency arising from incorrect score functions is also explored when there is no censoring in this paper we consider a general model for association between pairs of observations in which either variable or both variables may be right censored the aim is to develop tests based on the generalized ranks of both variables which have maximal power at alternatives which are near to the null hypothesis of independence attention will be concentrated on two special cases of interest in survival analysis tests for association between a censored survival time and a possibly censored continuous covariate and tests for association between the times to different events beginning with cox 1972 the first situation has been studied extensively in a semiparametric set up in which information based on ranks is used for the time variable but exact values are used for the covariate procedures which use only the ranks of both variables have been developed by brown hollander korwar 1974 and more recently by o brien 1978 however neither of these procedures have been developed with a particular model in mind and one of the achievements of the present paper is to derive rank tests with good local power when a particular model such as the proportional hazards model holds in the case of a proportional hazards model with a continuous covariate the present development may be preferable to the semiparametric methods when the functional form of the relation ship between the hazard and the covariate is not known in advance or when errors or outliers may exist in the observed covariate values thus significance levels may be obtained which are not inflated by multiple regroupings or transformations of the covariate data although it would be expected that parametric model building with variables found to be associated with survival would often be carried out in further analyses

signed rank tests for censored matched pairs abstract i consider the problem of testing bivariate symmetry in matched pair experiments where the observations are subject to univariate censoring thus the observable random variables are given by y 1 y 2 and 1 2 where y j min x j c and j i x j c j 1 2 here x 1 x 2 is a random pair of partially observable lifetimes and c is a fixed or random censoring variable the hypothesis to be tested is that x 1 x 2 and x 2 x 1 have the same distribution following woolson and lachenbruch 1980 i consider censored data generalizations of signed rank tests such as the sign signed wilcoxon and signed normal scores tests i derive the asymptotic distribution of these test statistics under fixed and contiguous alternatives the efficiencies of the signed rank tests are considered in a log linear model and compared with efficiencies of the paired prentice wilcoxon and log rank tests

digital pid controller design via general discrete orthogonal polynomials based on the discrete orthogonal polynomials a new computer oriented algebraic method is proposed for designing a digital pid controller the pid controller can approximately achieve an arbitrarily specified closed loop response and is determined by solving a linear equation using the least squares method an example is given to demonstrate the availability of the proposed technique

adaptation of bivariate frailty models for prediction with application to biological markers as prognostic indicators serial biological markers are often used in medicine as prognostic indicators for example elevated tumour antigen tests presage tumour recurrence rapid decrease in the cd4 cell counts of hiv individuals indicate high risk for developing aids methods for evaluating the usefulness of markers should address how the prediction of future risk is revised in a way that assists the making of decisions at the time such an indicator is observed proportional hazards modelling with time varying covariates a common approach seems unnatural for this purpose because its orientation is explanatory it addresses the question is the individual suffering a failure more likely to have had the marker and allows use of all information prior to the failure rather than the more relevant predictive question does the appearance of the marker alter the individual s subsequent risk enough to warrant intervention today frailty models do address this question but available methods for their analysis make censoring assumptions which are inappropriate in the predictive setting we adapt frailty models to relevant censoring processes and propose a predictively oriented test statistic and a related estimation procedure based on summing concurrent martingales each representing a landmark analysis

tamagawa numbers for motives with noncommutative coefficients ii we provide corroborative evidence for the equivariant tamagawa number conjecture which was formulated in the first part of this article

tests of independence for bivariate data with random censoring a contingency table approach procedures are proposed for testing the hypothesis of independence between two discrete or discretized random variables one or both of which may be randomly censored the censoring mechanisms can be either independent bivariate censoring or identical univariate censoring the proposed tests reduce to goodness of fit tests for log linear models applied to either complete or incomplete contingency tables three examples are analyzed for illustrative purposes

on the equivariant tamagawa number conjecture for tate motives let l be a finite abelian extension of and let k be any subfield of l for each integer r with r 0 we prove the equivariant tamagawa number conjecture for the pair h0 spec l r gal l k

a paired prentice wilcoxon test for censored paired data prentice 1978 biometrika 65 167 179 has provided a censored data generalization of classical linear rank statistics this paper investigates a method to generalize the prentice statistics to the analysis of censored paired data particular emphasis is given to the paired data version of the prentice wilcoxon statistic with discussion of the reasons for preferring prentice over the gehan scores the paired prentice wilcoxon ppw statistic makes use of interblock information and can be viewed as a censored data generalization of the conover iman 1981 the american statistician 35 124 129 paired t test on the ranks or of the lam longnecker 1983 biometrika 70 510 513 modified wilcoxon rank sum statistic in simulations comparing the ppw sign and generalized signed rank gsr statistics the ppw is most powerful against all but the exponential scale alternative furthermore the small advantage of the gsr over the ppw in that alternative is lost if outlier pairs are introduced when compared to the two sample prentice wilcoxon statistic the ppw is nearly as powerful in uncorrelated data and its power becomes superior as correlation between paired members increases

on galois structure invariants associated to tate motives we establish the equivalence of two definitions of invariants measuring the galois module structure of k groups of rings of integers in number fields due to chinburg et al on the one hand and the authors on the other we also make some remarks concerning the possibility of yet another such definition via lichtenbaum complexes

tests of independence for bivariate survival data we propose two test statistics based on the covariance process of the martingale residuals for testing independence of bivariate survival data the first test statistic takes the supremum over time of the absolute value of the covariance process and the second test statistic is a time weighted summary of the process we derive asymptotic properties of the two test statistics under the null hypothesis of independence in addition we derive the asymptotic distribution of the weighted test and construct optimal weights for contiguous alternatives to independence through simulations we compare the performance of the proposed tests and the inner product of the savage scores statistics of clayton and cuzick 1985 journal of the royal statistical society series a 148 82 108 these demonstrate that the supremum test is generally more powerful with comparatively little power loss relative to their test when clayton s family alternative holds and the weighted test is more powerful when the weight is appropriately chosen

a concordance test for independence in the presence of censoring an extension of the definition of kendall s coefficient of concordance is proposed for testing independence in bivariate censored survival times the test statistic counts the number of known concordances minus the number of known discordances the variance of the statistic is calculated for an random censorship model which however does not require independence of the components of the censoring distribution two examples are given

a cautionary note on applying scores in stratified data when rank tests are used to analyze stratified data three methods for assigning scores to the observations have been proposed s independently within each stratum see lehmann 1975 nonparametrics statistical methods based on ranks san francisco holden day a after aligning the observations within each stratum and then pooling the aligned observations hodges and lehmann 1962 annals of mathematical statistics 33 482 497 and p after pooling the observations across all strata that is without alignment mantel 1963 journal of the american statistical association 58 690 700 mantel and ciminera 1979 cancer research 39 4308 4315 test statistics are formed for each method by combining the stratum specific linear rank tests using the assigned scores we show that method p is sensitive to the score function used in the case of two moderately sized strata in general we recommend methods s and a for use with moderate to large sized strata

methods for bounding the marginal survival distribution for time to event data with many potential failure types one cannot uniquely determine the distribution of time to a specific event type or marginal survival distribution in the case where event types are mutually exclusive in this paper we discuss several methods for estimating functions that bound the non identifiable marginal survival distribution in the competing risks problem we compute and compare bounds for data simulated from two bivariate survival distributions results show that the methods provide a suitable estimate of the marginal survival probability when one has specified dependence correctly data from a large clinical trial for breast cancer illustrate the methods

nonparametric bivariate estimation with randomly censored data summary the estimation of a bivariate distribution function with randomly censored data is considered it is assumed that the censoring occurs independently of the lifetimes and that deaths and losses which occur simultaneously can be separated two estimators are developed a reduced sample estimator and a self consistent one it is shown that the latter estimator satisfies a nonparametric likelihood function and is unique up to the final uncensored values in any dimension it jumps at the points of double deaths in both dimensions some key word8 censored data kaplan meier estimator life table product limit estimator survival estimation

congruences between derivatives of geometric l functions we prove a natural refinement of a theorem of lichtenbaum describing the leading terms of zeta functions of curves over finite fields in terms of weil etale cohomology we then use this result to prove the validity of chinburg s 3 conjecture for all abelian extensions of global function fields to prove natural refinements and generalisations of the refined stark conjectures formulated by amongst others gross tate rubin and popescu to prove a variety of explicit restrictions on the galois module structure of unit groups and divisor class groups and to describe explicitly the fitting ideals of certain weil etale cohomology groups in an appendix coauthored with k f lai and k s tan we also show that the main conjectures of geometric iwasawa theory can be proved without using either crystalline cohomology or drinfeld modules

model reduction of digital systems using discrete walsh series this study discusses the application of discrete walsh series expansion to reduce the order of a linear time invariant digital system described by z transfer function the approach is based on matching the discrete walsh spectra to determine both the coefficients of the denominator and numerator of the reduced model the proposed method is simple for computation can preserve the dynamic characteristic of the original model satisfactorily and guarantees to have the same zero initial response as the original system

on the rubin stark conjecture for a special class of cm extensions of totally real number fields we use greither s recent results on brumer s conjecture to prove rubin s integral version of stark s conjecture up to a power of 2 for an infinite class of cm extensions of totally real number fields called nice extensions under the assumption that a certain iwasawa invariant vanishes as a consequence and under the same assumption we show that the brumer stark conjecture is true for nice extensions up to a power of 2

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

sample size formula for clustered survival data using weighted log rank statistics summary we present a simple sample size formula for weighted log rank statistics applied to clustered survival data with variable cluster sizes and arbitrary treatment assignments within clusters this formula is based on the asymptotic normality of weighted log rank statistics under certain local alternatives in the clustered data context we also provide consistent variance estimators the derived sample size formula reduces to schoenfeld s 1983 formula for cases of no clustering or independence within clusters simulation results verify control of the type i error and accuracy of the sample size formula use of the sample size formula in an event driven clinical trial design is illustrated using data from the early treatment diabetic retinopathy study

generalized stark formulae over function fields we establish formulae of stark type for the stickelberger elements in the function field setting our result generalizes a work of hayes and a conjecture of gross it is used to deduce a p adic version of rubin stark conjecture and burns conjecture

using weighted kaplan meier statistics in nonparametric comparisons of paired censored survival outcomes this research introduces methods for nonparametric testing of weighted integrated survival differences in the context of paired censored survival designs the current work extends work done by pepe and fleming 1989 biometrics 45 497 507 which considered similar test statistics directed toward independent treatment group comparisons an asymptotic closed form distribution of the proposed family of tests is presented along with variance estimates constructed under null and alternative hypotheses using nonparametric maximum likelihood estimates of the closed form quantities the described method allows for additional information from individuals with no corresponding matched pair member to be incorporated into the test statistic in sampling scenarios where singletons are not prone to selection bias simulations presented over a range of potential dependence in the paired censored survival data demonstrate substantial power gains associated with taking into account the dependence structure consequences of ignoring the paired nature of the data include overly conservative tests in terms of power and size in fact simulation results using tests for independent samples in the presence of positive correlation consistently undershot both size and power targets that would have been attained in the absence of correlation this additional worrisome effect on operating characteristics highlights the need for accounting for dependence in this popular family of tests

on the cyclotomic main conjecture for the prime 2 we complete the proof of the equivariant tamagawa number conjecture for tate motives over absolutely abelian fields by proving a refined cyclotomic main conjecture at the prime 2

a refined beilinson bloch conjecture for motives of modular forms we propose a refined version of the beilinson bloch conjecture for the motive associated with a modular form of even weight this conjecture relates the dimension of the image of the relevant p adic abel jacobi map to certain combinations of heegner cycles on kuga sato varieties we prove theorems in the direction of the conjecture and in doing so obtain higher weight analogues of results for elliptic curves due to darmon

computation of stark tamagawa units let k be a totally real number field and let l denote an odd prime number we design an algorithm which computes strong numerical evidence for the validity of the equivariant tamagawa number conjecture for the q g equivariant motive h0 spec l where l k is a cyclic extension of degree l and group g this conjecture is a very deep refinement of the classical analytic class number formula in the course of the algorithm we compute a set of special units which must be considered as a generalization of the conjecturally existing stark units associated to first order vanishing dirichlet l functions

walsh function analysis of linear and bilinear discrete time systems a technique is presented for analysing linear and bilinear discrete systems in terms of walsh functions the method replaces the solution of a dynamical difference equation with the solution of an algebraic equation in the special case of a linear system a numerically stable recursive technique is derived to solve this algebraic equation the technique is illustrated with an example

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

nonparametric estimation of the bivariate survival function with an application to vertically transmitted aids summary in this paper we propose a nonparametric estimator of the bivariate survival function when the two durations are subject to right censoring we consider the situation where the duration variables are successive and are always observed in a particular order and the censoring mechanism bears on their sum rather than on each separately thus if they are correlated the second duration is right censored by a dependent variable a nonparametric maximum likelihood estimator is derived that takes the dependent censoring into account we also derive the asymptotic variance of the estimator and show how it can be estimated the methods are applied on a vertically acquired mother to child transmission aids data set the first duration corresponds to the hiv incubation period and the second to the period of aids

simple methods for the shift transformation matrix direct product matrix and summation matrix of discrete walsh series this paper presents new easy methods for directly obtaining the shift transformation matrix direct product matrix and summation matrix of discrete walsh series the proposed methods can be conveniently implemented with a digital computer they will be very useful in the study of control systems via discrete walsh series

combined rank tests for randomly censored paired data abstract many authors have dealt with the problem of extending ordinary two sample rank tests to cases where censoring occurs albers and akritas 1987 proposed simple tests for this purpose based on the idea of making separate rankings for uncensored and censored observations and subsequently combining the resulting two rank statistics similarly some papers appeared that studied the problem of censoring for the paired data case rather than the two sample case this article indicates how the approach of albers and akritas can be adapted to the paired data case the tests involved are not based on the ranks of the differences but the differences of the ranks in the pooled sample in this way use is made of interblock information the asymptotic distribution of the new statistic is obtained under the null hypothesis and contiguous location alternatives by way of example wilcoxon and savage type scores are introduced that are optimal for logistic location and exponential scale alternatives respecti

discrete walsh operational matrices for analysis and optimal control of linear digital systems abstract by the introduction of the shift transformation matrix direct product matrix and summation matrix of the discrete walsh series the analysis of time varying digital control systems is facilitated and the approximate solution of time invariant digital optimal control problems is achieved of this study the design algorithms of digital optimal control are based on the discrete variational principle combined with the idea of penalty functions to obtain the conveniently computational formulations for evaluating the optimal control and trajectory three examples are illustrated by using the discrete walsh approach

on derivatives of artin l series we present a universal theory of refined stark conjectures we give evidence in support of these explicit and very general conjectures including a full proof in several important cases and explain the connection to previous conjectures of bloch and kato of lichtenbaum and of serre and tate we also deduce a wide range of unconditional consequences of these results concerning the annihilation as galois modules of ideal class groups by explicit elements constructed from the values of higher order derivatives of non abelian artin l series

simultaneous group sequential analysis of rank based and weighted kaplan meier tests for paired censored survival data this research sequentially monitors paired survival differences using a new class of nonparametric tests based on functionals of standardized paired weighted log rank pwlr and standardized paired weighted kaplan meier pwkm tests during a trial these tests may alternately assume the role of the more extreme statistic by monitoring pemax the maximum between the absolute values of the standardized pwlr and pwkm one combines advantages of rank based rb and non rb paired testing paradigms simulations show that monitoring treatment differences using pemax maintains type i error and is nearly as powerful as using the more advantageous of the two tests in proportional hazards ph as well as non ph situations hence pemax preserves power more robustly than individually monitored pwlr and pwkm while maintaining a reasonably simple approach to design and analysis of results an example from the early treatment diabetic retinopathy study etdrs is given

on the regression analysis of multivariate failure time data summary the paper is concerned with the analysis of regression effects when individual study subjects may experience multiple failures the proposed methods are most likely to be useful when there are a fairly large number of study subjects two general classes of regression models are considered in order to relate the hazard or intensity function to covariates and to preceding failure time history both models are of a stratified proportional hazards type one model includes baseline intensity functions that are arbitrary as a function of time from the beginning of study while the other includes baseline intensity functions that are arbitrary as a function of time from the study subject s immediately preceding failure partial likelihood functions are derived for the regression coefficients generalizations and illustrations are given

on the equivariant tamagawa number conjecture in tame cm extensions let l k be a finite galois cm extension with galois group g the equivariant tamagawa number conjecture etnc for the pair h 0 rm spec l 0 mathbb z g naturally decomposes into p parts where p runs over all rational primes if p is odd these p parts in turn decompose into a plus and a minus part let l k be tame above p we show that a certain ray class group of l defines an element in k 0 mathbb z p g mathbb q p which is determined by a corresponding stickelberger element if and only if the minus part of the etnc at p holds for this we use the lifted root number conjecture for small sets of places which is equivalent to the etnc in the number field case for abelian g we show that the minus part of the etnc at p implies the strong brumer stark conjecture at p we prove the minus part of the etnc at p for almost all primes p

explicit units and the equivariant tamagawa number conjecture let l k be a finite abelian extension of number fields of group g we study the tamagawa number t l k of h 0 spec l considered as a motive defined over k and with coefficients inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i g for a large class of extensions l k we interpret the conjectural vanishing of t l k in terms of the existence of s units in l satisfying a variety of explicit conditions these explicit conditions are in the same spirit as but are in general much finer than the conditions studied by rubin and popescu by using this approach we are able to complete the proof that t l k vanishes for all of the genus field extensions considered by frohlich in the course of proving this result we find that for certain extensions the vanishing of t l k is a refinement of the main result of solomon concerning wild euler systems