set choice problems with incomplete information about the preferences of the decision maker we consider the problem of selecting a predetermined number of objects from a given finite set it is assumed that the preferences of the decision maker on this set are only partially known our solution approach is based on the notions of optimal and non dominated subsets the properties of such subsets and the objects they contain are investigated the implementation of the developed approach is discussed and illustrated by various examples

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

nonparametric analysis of covariance for censored data the fully nonparametric model for nonlinear analysis of covariance proposed in akritas et al 2000 is considered in the context of censored observations under this model the distributions for each factor level combination and covariate value are not restricted to comply to any parametric or semiparametric model the data can be continuous or ordinal categorical the possibility of different shapes of covariate effect in different factor level combinations is also allowed this generality is useful whenever modelling assumptions such as additive risks proportional hazards or proportional odds appear suspect test statistics are obtained for the nonparametric hypotheses of no main effect and of no interaction effect which adjusts for the presence of a covariate they are quadratic forms based on averages over the covariate values of beran estimators of the conditional distribution of the survival time given each covariate value the derivation of the asymptotic chi 2 distribution of the test statistics uses a recently obtained asymptotic representation of the bekan estimator as average of independent random variables a real data set is analysed and results of simulation studies are reported

a semiparametric extension of the mann whitney test for randomly truncated data in many applications statistical data are frequently observed subject to a retrospective sampling criterion resulting in pure right truncated data in classical testing problems the mann whitney test is used for testing the equality of two distributions a semiparametric extension of this test is developed for the case when truncation is present we consider a model in which the truncation distribution is parameterized while the lifetime distribution is left as a nonparametric component the method is seen to be applicable to many patterns of truncation including left truncation right truncation and doubly truncated data for which no other nonparametric or semiparametric test is currently available applications of the semiparametric method are given simulation results indicate that for pure right truncated data the semiparametric test is more powerful than a recent nonparametric test

asymptotic properties of the product limit estimate under random truncation on donne une description precise du comportement asymptotique de l estimateur limite produit incluant une forme explicite simple de la structure de covariance asymptotique

a proportional hazards model for arbitrarily censored and truncated data turnbull 1976 journal of royal statistical society series b 38 290 295 proposed a method for nonparametric estimation of the distribution function when the data are incomplete because of censoring and truncation however as noted by frydman 1994 journal of royal statistical society series b 56 71 74 turnbull s method has to be modified to accommodate both truncation and censoring this paper presents a detailed correction of turnbull s method and an extension to the regression analysis a method of fitting the proportional hazards model for arbitrarily censored and truncated data is developed the method allows partial testing for zero regression coefficients the test can be performed using the likelihood ratio test or the wald test the methodology is applied to estimate the distribution of the induction time of patients diagnosed with transfusion associated aids and to estimate the distribution of time from diabetes onset to development of diabetic nephropathy for insulin dependent diabetics

properties of proportional hazards score tests under misspecified regression models the effects are investigated of misspecifying a proportional hazards regression model on the associated partial likelihood score test for comparing two randomized treatments in the presence of covariates the asymptotic efficiency of the proportional hazards score test relative to the optimal partial likelihood test declines slowly as the hazard functions for the two treatments deviate from proportionality the efficiency can be very low when the hazard functions cross or differ only at large survival times misspecification of the functional form of the regression portion of a proportional hazards model introduces a quantitative treatment covariate interaction in the situations that we examine based on a binary covariate this misspecification usually results in only a minor drop in efficiency the omission of a covariate that is balanced across treatments has a negligible effect on the size of the score test but can substantially reduce power when the covariate effect is strong the loss of power from mismodeling a balanced covariate is usually small

deconvolution of microfluorometric histograms with b splines abstract we consider the problem of estimating a probability density from observations from that density which are further contaminated by random errors we propose a method of estimation using spline functions discuss the numerical implementation of the method and prove its consistency the problem is motivated by the analysis of dna content obtained by microfluorometry and an example of such an analysis is included

metrics of negative ricci curvature one of the most natural and important topics in riemannian geometry is the relation between curvature and global structure of the underlying manifold for instance complete manifolds of negative sectional curvature are always aspherical and in the compact case their fundamental group can only contain abelian subgroups which are infinite cyclic furthermore it seemed to be a natural principle that a closed manifold cannot carry two metrics of different signed curvatures as it is a basic fact that this is true for sectional curvature but it turned out to be wrong much later and from a strongly analytic argument for the scalar curvature s since each manifold m n 3 admits a complete metric with s 1 cf aubin a and bland kalka bik hence the situation for ricci curvature ric lying between sectional and scalar curvature seemed to be quite delicate up to now the most general results concerning ric 0 were proved by gao yau gy and brooks br using thurston s theory of hyperbolic threemanifolds viz each closed three manifold admits a metric with ric 0 this is obtained from the fact that these manifolds carry hyperbolic metrics with certain singularities gao and yau resp brooks smoothed these singularities to get a regular metric with ric 0 these methods extend to three manifolds of finite type and certain hyperbolic orbifolds in any case the arguments rely on exploiting some extraordinary metric structures whose existence is neither obvious nor conceptually related to the ricci curvature problem indeed the existence depends on the assumption that the manifold is three dimensional and compact moreover this approach does not provide insight into the typical behaviour of metrics with ric 0 since one is led to very special metrics in this article we approach negative ricci curvature using a completely different and new concept which will become even more significant in l2 as we deliberately produce ric 0 actually we will prove the following results in these notes ric g resp r g denotes the ricci tensor resp curvature of a smooth metric g

utility as an additive set function foundations for additive models of subset evaluation are stated by axioms for a preference relation on a family s of subsets of x that cover x the axiomatizations include cases in which s is arbitrary s contains only finite subsets of x and s is the set of all subsets of x expected utility with subsets as outcomes is also considered

a remark on compact ricci solitons it is shown that a complete shrinking soliton is compact if and only if it is bounded and moreover in such a case it has finite fundamental group

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

nonparametric estimation from cross sectional survival data abstract in many follow up studies survival data are often observed according to a cross sectional sampling scheme data of this type are subject to left truncation in addition to the usual right censoring a number of characteristics and properties of the product limit estimate for left truncated and right censored data have been explored and found to be similar to those of the kaplan meier estimate under the stationarity assumption however it is believed that an alternative estimate has much better efficiency in this article the conditional maximum likelihood estimate mle property of the product limit estimate is visited the non parametric mle of the truncation distribution is derived use of this estimate includes testing the stationarity assumption estimating the proportion of truncated data and other applications in prevalent cohort studies the analysis of the estimation is based on a working data approach the asymptotic properties of the proposed estimates are developed through nonpar

comparison geometry for the bakry emery ricci tensor for riemannian manifolds with a measure m g edvolg we prove mean curvature and volume comparison results when the bakry emery ricci tensor is bounded from below and f is bounded or rf is bounded from below generalizing the classical ones i e when f is constant this leads to extensions of many theorems for ricci curvature bounded below to the bakry emery ricci tensor in particular we give extensions of all of the major comparison theorems when f is bounded simple examples show the bound on f is necessary for these results

testing the equality of two survival functions with right truncated data to compare the survival functions based on right truncated data lagakos et al proposed a weighted logrank test based on a reverse time scale this is in contrast to bilker and wang who suggested a semi parametric version of the mann whitney test by assuming that the distribution of truncation times is known or can be estimated parametrically the approach of lagakos et al is simple and elegant but the weight function in their method depends on the underlying cumulative hazard functions even under proportional hazards models on the other hand a semi parametric test may have better efficiency but it may be sensitive to misspecification of the distribution of truncation times therefore this paper proposes a non parametric test statistic based on the integrated weighted difference between two estimated survival functions in forward time the comparative results from a simulation study are presented and the implementation of these methods to a real data set is demonstrated

on the maximum weight clique problem we introduce several new classes of graphs on which the maximum weight clique problem is solvable in polynomial time their common feature and the central idea of our algorithms is that every clique of any of our graphs is contained in some member of a polynomial sized collection of induced subgraphs that are complements of bipartite graphs

some cheeger gromov taylor type compactness theorems via m bakry emery and m modified ricci curvatures abstract we establish some new compactness criteria for complete riemannian manifolds via m bakry emery and m modified ricci curvatures in the spirit of cheeger et al 1982 our results improve and generalize previous compactness theorems for complete riemannian manifolds via m bakry emery and m modified ricci curvatures obtained by fernandez lopez and garcia rio 2008 limoncu 2010 2012 qian 1997 wei and wylie 2009 and wu 2018

estimating survival under a dependent truncation summary the product limit estimator calculated from data subject to random left truncation relies on the testable assumption of quasi independence between the failure time and the truncation time in this paper we propose a model for a truncated sample of pairs xi y satisfying 1 xi a possible dependency between the truncation time and the variable of interest is modelled with a parametric family of copulas the model also features a distribution function fx and a survival distribution sy associated with the marginal behaviours of x and y in the observable region y x semiparametric estimators for these two functions are proposed they do not make any parametric assumption about either fx or sy we derive an estimator for the copula parameter cx based on the conditional kendall s tau we generalise the copula graphic estimators of zheng klein 1995 to truncated variables the asymptotic distributions of all these estimators are then investigated the methods are illustrated with a real dataset on hiv infection by transfusion and by simulations

bivariate estimation with right truncated data abstract bivariate estimation with survival data has received considerable attention recently however most of the work has focused on random censoring models another common feature of survival data random truncation is considered in this study truncated data may arise if the time origin of the events under study precedes the observation period in a random right truncation model one observes the iid samples of y t only if y t where y is the variable of interest and t is an independent variable that prevents the complete observation of y suppose that y x is a bivariate vector of random variables where y is subject to right truncation in this study the bivariate reverse hazard vector is introduced and a nonparametric estimator is suggested an estimator for the bivariate survival function is also proposed weak convergence and strong consistency of this estimator are established via a representation by iid variables an expression for the limiting covariance function is provided and a

multinomial analysis of smoothed hiv back calculation models incorporating uncertainty in the aids incidence back calculation models developed to reconstruct the past trend of human immunodeficiency virus hiv and to project future acquired immunodeficiency syndrome incidence aids are usually and unrealistically based on the assumption that the observed aids counts are independently distributed according to a poisson process in contrast we argue that a multinomial framework is more suitable to this situation leading to a natural covariance structure the ill conditioned nature of the problem is solved by modelling the hiv parameters according to a cubic spline function to reduce the dimensionality of the parameter space and obtain smoother parameter estimates we applied a regression spline technique which yields to a computationally stable basis incorporating the incubation period in the new design matrix we directly incorporate the reporting delay distribution in the aids incidence data leading to a more complex formulation of the variance and covariance model that is adapted to the iteratively reweighted least square irls algorithm in this case we obtain more accurate estimates of the standard error of the hiv incidence especially in the most recent time our model which uses a cubic spline reparameterization based on a multinomial probability distribution is applied to the aids epidemic data in italy

semiparametric profile likelihood estimation for continuous outcomes with excess zeros in a random threshold damage resistance model continuous outcome data with a proportion of observations equal to zero often referred to as semicontinuous data arise frequently in biomedical studies typical approaches involve two part models with one part a logistic model for the probability of observing a zero and some parametric continuous distribution for modeling the positive part of the data we propose a semiparametric model based on a biological system with competing damage manifestation and resistance processes this allows us to derive a closed form profile likelihood based on the retro hazard function leading to a flexible procedure for modeling continuous data with a point mass at zero a simulation study is presented to examine the properties of the method in finite samples we apply the method to a data set consisting of pulmonary capillary hemorrhage area in lab rats subjected to diagnostic ultrasound copyright 2017 john wiley sons ltd

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

nonparametric analysis of truncated survival data with application to aids summary one source of data for the induction distribution of aids arises from persons infected by the aids virus from contaminated blood transfusions analyses of these data are complicated because the number of individuals infected by transfusion is unknown information is available only for those who are infected and develop aids within a certain chronologic time interval the statistical problem is one of making inferences about a stochastic process of infection and disease for which realizations are right truncated in chronologic time by considering the process in reverse time we transform the problem to one of analysing survival data that are left truncated in internal time we develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions of several groups an important feature of the natural history and population dynamics of aids is the induction period between infection with the aids virus and the onset of clinical aids this time is sometimes referred to as the latency period or incubation period follow up studies of individuals at risk of being infected will provide direct observations from the induction distribution but most of these studies will not be completed for several years one alternative source of information arises from persons infected with the aids virus from a contaminated blood transfusion of persons infected in this way only those who develop aids by a certain date can be identified the total number who are infected is not known a similar sampling distribution arises in the study of pediatric aids children who contract aids as a result of being infected in utero or at birth can be identified but the total number infected in this way is unknown the statistical problem is one of making inferences about a stochastic process of infection and subsequent disease in which realizations are right truncated in chronologic time by considering the process in reverse time the problem can be transformed to one of survival data that are left truncated in internal time we use this relationship to develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions for

the bakry emery ricci tensor and its applications to some compactness theorems let m g be a complete and connected riemannian manifold of dimension n by using the bakry emery ricci curvature tensor on m we prove two theorems which correspond to the myers compactness theorem

a linearization procedure for quadratic and cubic mixed integer problems several techniques of linearization have appeared in the literature the technique of f glover which seems to be the most efficient linearizes a binary quadratic integer problem of n variables by introducing n new continuous variables and 4n auxiliary linear constraints the new technique proposed in this paper is not only useful in linearizing binary quadratic and cubic integer problems but also applicable to the case of quadratic and to a certain class of cubic mixed integer problems it is shown that the new technique further reduces the number of auxiliary linear constraints from 4n to n while keeping the number of new continuous variables at n for the binary quadratic integer problem of n variables and it requires in the case of a certain class of cubic mixed integer problems having 2n of 0 1 variables only 3n auxiliary linear constraints and the same number of new continuous variables the analytical superiority of the new linearization technique has also been observed in terms of the nu

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

the loss in efficiency from misspecifying covariates in proportional hazards regression models summary this note considers partial likelihood score tests for association between a covariate process and survival time based on a proportional hazards regression model we derive the asymptotic efficiency of the test based on a misspecified form of the covariate process relative to the test based on the correct form the results can be used to assess the consequences of various types of misspecification

binary interactions and subset choice abstract subset evaluation and choice problems abound in practical decision settings they are often analyzed with linear objective functions that value subsets as sums of utilities of items in the subsets this simplifies assessment and computational tasks but runs a risk of substantial suboptimality because it disregards evaluative interdependencies among items this paper examines a binary interaction model that accounts for preference interdependencies between items ordinal and cardinal versions of the model are axiomatized and compared to the simpler linear model as well as the general model that incorporates all orders of interdependence comparisons of computational complexity for standard subset choice problems are made between the linear and binary interaction models

estimating a distribution function with truncated data let mathscr p be a finite population with n geq 1 elements for each e in mathscr p let x e and y e be independent positive random variables with unknown distribution functions f and g and suppose that the pairs x e y e are i i d we consider the problem of estimating f g and n when the data consist of those pairs x e y e for which e in mathscr p and y e leq x e the nonparametric maximum likelihood estimators mles of f and g are described and their asymptotic properties as n rightarrow infty are derived it is shown that the mles are consistent against pairs f g for which f and g are continuous g 1 0 leq f 1 0 and g 1 1 leq f 1 1 sqrt n times estimation error for f converges in distribution to a gaussian process if int infty 0 1 g df infty but may fail to converge if this integral is infinite

a maximum pseudo profile likelihood estimator for the cox model under length biased sampling this paper considers semiparametric estimation of the cox proportional hazards model for right censored and length biased data arising from prevalent sampling to exploit the special structure of length biased sampling we propose a maximum pseudo profile likelihood estimator which can handle time dependent covariates and is consistent under covariate dependent censoring simulation studies show that the proposed estimator is more efficient than its competitors a data analysis illustrates the methods and theory

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

nonparametric estimation and regression analysis with left truncated and right censored data abstract in many prospective and retrospective studies survival data are subject to left truncation in addition to the usual right censoring for left truncated data without covariates only the conditional distribution of the survival time y given y can be estimated nonparametrically where is the lower boundary of the support of the left truncation variable t if the data are also right censored then the conditional distribution can be consistently estimated only at points not larger than where is the upper boundary of the support of the right censoring variable c in this article we first consider nonparametric estimation of trimmed functionals of the conditional distribution of y with the trimming inside the observable range between and we then extend the approach to regression analysis and curve fitting in the presence of left truncation and right censoring on the response variable y asymptotic normality of m estimators of the regression parameters derived from this approach is

an upper diameter bound for compact ricci solitons with application to the hitchin thorpe inequality in this article stimulated by fernandez lopez and garcia rio we shall give an upper diameter bound for compact shrinking ricci solitons in terms of the range of the scalar curvature as well as in terms of the range of the potential function as an application we shall provide some new sufficient conditions for compact four dimensional shrinking ricci solitons to satisfy the hitchin thorpe inequality