continuous right inverses for the asymptotic borel map in ultraholomorphic classes via a laplace type transform abstract a new construction of linear continuous right inverses for the asymptotic borel map is provided in the framework of general carleman ultraholomorphic classes in narrow sectors such operators were already obtained by v thilliez by means of whitney extension results for non quasianalytic ultradifferentiable classes due to j chaumat and a m chollet but our approach is completely different resting on the introduction of a suitable truncated laplace type transform this technique is better suited for a generalization of these results to the several variables setting moreover it closely resembles the classical procedure in the case of gevrey classes so indicating the way for the introduction of a concept of summability which generalizes k summability theory as developed by j p ramis

summable solutions of some partial differential equations and generalised integral means abstract we describe partial differential operators for which we can construct generalised integral means satisfying pizzetti type formulas using these formulas we give a new characterisation of summability of formal power series solutions to some multidimensional partial differential equations in terms of holomorphic properties of generalised integral means of the cauchy data

estimation of covariate effects in generalized linear mixed models with informative cluster sizes in standard regression analyses of clustered data one typically assumes that the expected value of the response is independent of cluster size however this is often false for example in studies of surgical interventions investigators have frequently found surgery volume and outcomes to be related to the skill level of the surgeons this paper examines the effect of ignoring response dependent informative cluster sizes on standard analytical methods such as mixed effects models and conditional likelihood methods using analytic calculations simulation studies and an example from a study of periodontal disease we consider the case in which cluster sizes and responses share random effects which we assume to be independent of the covariates our focus is on maximum likelihood methods that ignore informative cluster sizes and we show that they exhibit little bias in estimating covariate effects that are uncorrelated with the random effects associated with cluster sizes however estimation of covariate effects that are associated with the random effects can be biased in particular for models with random intercepts only ignoring informative cluster sizes can yield biased estimators of the intercept but little bias in estimation of all covariate effects

summability of divergent solutions of the n dimensional heat equation abstract the cauchy problem for n dimensional complex heat equation is considered the borel summability of formal solutions is characterized in terms of analytic continuation with an appropriate growth condition of the spherical mean of the cauchy data

weighted logrank tests for interval censored data when assessment times depend on treatment we consider weighted logrank tests for interval censored data when assessment times may depend on treatment and for each individual we only use the two assessment times that bracket the event of interest it is known that treating finite right endpoints as observed events can substantially inflate the type i error rate under assessment treatment dependence atd but the validity of several other implementations of weighted logrank tests score tests permutation tests multiple imputation tests has not been studied in this situation with a bounded number of unique assessment times the score test under the grouped continuous model retains the type i error rate asymptotically under atd however although the approximate permutation test based on the permutation central limit theorem is not asymptotically valid under every atd scenario we show through simulation that in many atd scenarios it retains the type i error rate better than the score test we show a case where the approximate permutation test retains the type i error rate when the exact permutation test does not we study and modify the multiple imputation logrank tests of huang lee and yu 2008 statistics in medicine 27 3217 3226 showing that the distribution of the rank like scores asymptotically does not depend on the assessment times we show through simulations that our modifications of the multiple imputation logrank tests retain the type i error rate in all cases studied even with atd and a small number of individuals in each treatment group simulations were performed using the interval r package us government work in the public domain

summability in general carleman ultraholomorphic classes a definition of summability is put forward in the framework of general carleman ultraholomorphic classes in sectors so generalizing k summability theory as developed by j p ramis departing from a strongly regular sequence of positive numbers we construct an associated analytic proximate order and corresponding kernels which allow us to consider suitable laplace and borel type transforms both formal and analytic whose behavior closely resembles that of the classical ones in the gevrey case an application to the study of the summability properties of the formal solutions to some moment partial differential equations is included

strongly regular sequences and proximate orders abstract summability methods for ultraholomorphic classes in sectors defined in terms of a strongly regular sequence m m p p n 0 have been put forward by a lastra s malek and the second author 28 we study several open questions related to the existence of kernels of summability constructed by means of analytic proximate orders in particular we give a simple condition that allows us to associate a proximate order with a strongly regular sequence under this assumption and through the characterization of strongly regular sequences in terms of so called regular variation we show that the growth index m defined by v thilliez 54 and the order of quasianalyticity m introduced by the second author 50 are the same

marginal analyses of clustered data when cluster size is informative we propose a new approach to fitting marginal models to clustered data when cluster size is informative this approach uses a generalized estimating equation gee that is weighted inversely with the cluster size we show that our approach is asymptotically equivalent to within cluster resampling hoffman sen and weinberg 2001 biometrika 73 13 22 a computationally intensive approach in which replicate data sets containing a randomly selected observation from each cluster are analyzed and the resulting estimates averaged using simulated data and an example involving dental health we show the superior performance of our approach compared to unweighted gee the equivalence of our approach with wcr for large sample sizes and the superior performance of our approach compared with wcr when sample sizes are small

helices on del pezzo surfaces and tilting calabi yau algebras we study tilting for a class of calabi yau algebras associated to helices on fano varieties we do this by relating the tilting operation to mutations of exceptional collections for helices on del pezzo surfaces the algebras are of dimension three and using an argument of herzog together with results of kuleshov and orlov we obtain a complete description of the tilting process in terms of quiver mutations

on the multisummability of divergent solutions of linear partial differential equations with constant coefficients abstract we consider the cauchy problem for general linear partial differential equations in two complex variables with constant coefficients we obtain necessary and sufficient conditions for the multisummability of formal solutions in terms of analytic continuation properties and growth estimates of the cauchy data

tests for informative cluster size using a novel balanced bootstrap scheme clustered data are often encountered in biomedical studies and to date a number of approaches have been proposed to analyze such data however the phenomenon of informative cluster size ics is a challenging problem and its presence has an impact on the choice of a correct analysis methodology for example dutta and datta 2015 biometrics presented a number of marginal distributions that could be tested depending on the nature and degree of informativeness of the cluster size these marginal distributions may differ as do the choices of the appropriate test in particular they applied their new test to a periodontal data set where the plausibility of the informativeness was mentioned but no formal test for the same was conducted we propose bootstrap tests for testing the presence of ics a balanced bootstrap method is developed to successfully estimate the null distribution by merging the re sampled observations with closely matching counterparts relying on the assumption of exchangeability within clusters the proposed procedure performs well in simulations even with a small number of clusters at different distributions and against different alternative hypotheses thus making it an omnibus test we also explain how to extend the ics test to a regression setting and thereby enhancing its practical utility the methodologies are illustrated using the periodontal data set mentioned earlier copyright 2017 john wiley sons ltd

informative cluster sizes for subcluster level covariates and weighted generalized estimating equations williamson et al 2003 s cluster weighted generalized estimating equations cwgee are effective at adjusting for bias due to informative cluster sizes for cluster level covariates we show that cwgee may not perform well however for covariates that can take different values within a cluster if the numbers of observations at each covariate level are informative on the other hand inverse probability of treatment weighting accounts for informative treatment propensity but not for informative cluster size motivated by evaluating the effect of a binary exposure in presence of such types of informativeness we propose several weighted generalized estimating equation estimators with weights related to the size of a cluster as well as the distribution of the binary exposure within the cluster choice of the weights depends on the population of interest and the nature of the exposure through simulation studies we demonstrate the superior performance of the new estimators compared to existing estimators such as from gee cwgee and inverse probability of treatment weighted gee we demonstrate the use of our method using an example examining covariate effects on the risk of dental caries among small children

summability of formal solutions of linear partial differential equations with divergent initial data abstract we study the cauchy problem for a general homogeneous linear partial differential equation in two complex variables with constant coefficients and with divergent initial data we state necessary and sufficient conditions for the summability of formal power series solutions in terms of properties of divergent cauchy data we consider both the summability in one variable t with coefficients belonging to some banach space of gevrey series with respect to the second variable z and the summability in two variables t z the results are presented in the general framework of moment pdes

within cluster resampling for multilevel models under informative cluster size a within cluster resampling method is proposed for fitting a multilevel model in the presence of informative cluster size our method is based on the idea of removing the information in the cluster sizes by drawing bootstrap samples which contain a fixed number of observations from each cluster we then estimate the parameters by maximising an average over the bootstrap samples of a suitable composite log likelihood the consistency of the proposed estimator is shown 15 and does not require that the correct model for cluster size is specified we give an estimator of the covariance matrix of the proposed estimator and a test for the non informativeness of the cluster sizes a simulation study shows as in neuhaus mcculloch 2011 that the standard maximum likelihood estimator exhibits little bias for some regression coefficients however for those parameters which exhibit non negligible bias the proposed method is successful in cor 20 recting for this bias

cohomological characterization of vector bundles on multiprojective spaces abstract we show that horrocks criterion for the splitting of vector bundles on p n can be extended to vector bundles on multiprojective spaces and to smooth projective varieties with the weak cm property see definition 3 11 as a main tool we use the theory of n blocks and beilinson type spectral sequences cohomological characterizations of vector bundles are also showed

the frobenius morphism in invariant theory abstract let r be the homogeneous coordinate ring of the grassmannian g gr 2 n defined over an algebraically closed field of characteristic p 0 in this paper we give a completely characteristic free description of the decomposition of r considered as a graded r p module into indecomposables frobenius summands as a corollary we obtain a similar decomposition for the frobenius pushforward of the structure sheaf of g and we obtain in particular that this pushforward is almost never a tilting bundle on the other hand we show that r provides a noncommutative resolution for r p when p n 2 generalizing a result known to be true for toric varieties in both the invariant theory and the geometric setting we observe that if the characteristic is not too small the frobenius summands do not depend on the characteristic in a suitable sense in the geometric setting this is an explicit version of a general result by bezrukavnikov and mirkovic on frobenius decompositions for partial flag varieties we are hopeful that it is an instance of a more general p uniformity principle

a covariate specific time dependent receiver operating characteristic curve for correlated survival data several studies for the clinical validity of circulating tumor cells ctcs in metastatic breast cancer were conducted showing that it is a prognostic biomarker of overall survival in this work we consider an individual patient data meta analysis for nonmetastatic breast cancer to assess the discrimination of ctcs regarding the risk of death data are collected in several centers and present correlated failure times for subjects of the same center however although the covariate specific time dependent receiver operating characteristic roc curve has been widely used for assessing the performance of a biomarker there is no methodology yet that can handle this specific setting with clustered censored failure times we propose an estimator for the covariate specific time dependent roc curves and area under the roc curve when clustered failure times are detected we discuss the assumptions under which the estimators are consistent and their interpretations we assume a shared frailty model for modeling the effect of the covariates and the biomarker on the outcome in order to account for the cluster effect a simulation study was conducted and it shows negligible bias for the proposed estimator and a nonparametric one based on inverse probability censoring weighting while a semiparametric estimator ignoring the clustering is markedly biased finally in our application to breast cancer data the estimation of the covariate specific area under the curves illustrates that the ctcs discriminate better patients with inflammatory tumor than patients with noninflammatory tumor with respect to their risk of death

efficiency of regression estimates for clustered data statistical methods for clustered data such as generalized estimating equations gee and generalized least squares gls require selecting a correlation or convariance structure to specify the dependence between observations within a cluster valid regression estimates can be obtained that do not depend on correct specification of the true correlation but inappropriate specifications can result in a loss of efficiency we derive general expressions for the asymptotic relative efficiency of gee and gls estimators under nested correlation structures efficiency is shown to depend on the covariate distribution the cluster sizes the response variable correlation and the regression parameters the results demonstrate that efficiency is quite sensitive to the between and within cluster variation of the covariates and provide useful characterizations of models for which upper and lower efficiency bounds are attained efficiency losses for simple working correlation matrices such as independence can be large even for small to moderate correlations and cluster sizes

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

t structures on some local calabi yau varieties abstract let z be a smooth fano variety satisfying the condition that the rank of the grothendieck group of z is one more than the dimension of z let z denote the total space of the canonical line bundle of z considered as a non compact calabi yau variety we use the theory of exceptional collections to describe t structures on the derived category of coherent sheaves on z the combinatorics of these t structures is determined by a natural action of an affine braid group closely related to the well known action of the artin braid group on the set of exceptional collections on z

consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models generalized linear models are used for regression analysis in a number of cases including categorical responses where the classical assumptions are violated the statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator we present mild general conditions which respectively assure weak or strong consistency or asymptotic normality most of the previous work has been concerned with natural link functions in this case our normality condition though obtained by a different approach is closely related to a condition of haberman 1977a examples show how the general conditions reduce to weak requirements for special exponential families further for regressors with a compact range sufficient conditions are given which do not involve the unknown parameter and are therefore easy to check in practice responses with a bounded range e g categorical responses and stochastic regressors also are treated

bootstrapping clustered data summary various bootstraps have been proposed for bootstrapping clustered data from one way arrays the simulation results in the literature suggest that some of these methods work quite well in practice the theoretical results are limited and more mixed in their conclusions for example mccullagh reached negative conclusions about the use of non parametric bootstraps for one way arrays the purpose of this paper is to extend our understanding of the issues by discussing the effect of different ways of modelling clustered data the criteria for successful bootstraps used in the literature and extending the theory from functions of the sample mean to include functions of the between and within sums of squares and non parametric bootstraps to include model based bootstraps we determine that the consistency of variance estimates for a bootstrap method depends on the choice of model with the residual bootstrap giving consistency under the transformation model whereas the cluster bootstrap gives consistent estimates under both the transformation and the random effect model in addition we note that the criteria based on the distribution of the bootstrap observations are not really useful in assessing consistency

multisummability of formal power series solutions of partial differential equations with constant coefficients we study gevrey properties and summability of power series in two variables that are formal solutions of a cauchy problem for general linear partial differential equations with constant coefficients in doing so we extend earlier results in two articles of balser and lutz miyake and schafke for the complex heat equation as well as in a paper of balser and miyake who have investigated the same questions for a certain class of linear pde with constant coefficients subject to some restrictive assumptions moreover we also present an example of a pde where the formal solution of the cauchy problem is not k summable for whatever value of k but instead is multisummable with two levels under corresponding conditions upon the cauchy data that this can occur has not been observed up to now

analysis of clustered binary outcomes using within cluster paired resampling summary conditional logistic regression clr is useful for analyzing clustered binary outcome data when interest lies in estimating a cluster specific exposure parameter while treating the dependency arising from random cluster effects as a nuisance clr aggregates unmeasured cluster specific factors into a cluster specific baseline risk and is invalid in the presence of unmodeled heterogeneous covariate effects or within cluster dependency we propose an alternative resampling based method for analyzing clustered binary outcome data within cluster paired resampling wcpr which allows for within cluster dependency not solely due to baseline heterogeneity for example dependency may be in part caused by heterogeneity in response to an exposure across clusters due to unmeasured cofactors when both clr and wcpr are valid our simulations suggest that the two methods perform comparably when clr is invalid wcpr continues to have good operating characteristics for illustration we apply both wcpr and clr to a periodontal data set where there is heterogeneity in response to exposure across clusters

a rank sum test for clustered data when the number of subjects in a group within a cluster is informative the wilcoxon rank sum test is a popular nonparametric test for comparing two independent populations groups in recent years there have been renewed attempts in extending the wilcoxon rank sum test for clustered data one of which datta and satten 2005 journal of the american statistical association 100 908 915 addresses the issue of informative cluster size i e when the outcomes and the cluster size are correlated we are faced with a situation where the group specific marginal distribution in a cluster depends on the number of observations in that group i e the intra cluster group size we develop a novel extension of the rank sum test for handling this situation we compare the performance of our test with the datta satten test as well as the naive wilcoxon rank sum test using a naturally occurring simulation model of informative intra cluster group size we show that only our test maintains the correct size we also compare our test with a classical signed rank test based on averages of the outcome values in each group paired by the cluster membership while this test maintains the size it has lower power than our test extensions to multiple group comparisons and the case of clusters not having samples from all groups are also discussed we apply our test to determine whether there are differences in the attachment loss between the upper and lower teeth and between mesial and buccal sites of periodontal patients

analysis of failure time data with multilevel clustering with application to the child vitamin a intervention trial in nepal we consider the problem of estimating covariate effects in the marginal cox proportional hazard model and multilevel associations for child mortality data collected from a vitamin a supplementation trial in nepal where the data are clustered within households and villages for this purpose a class of multivariate survival models that can be represented by a functional of marginal survival functions and accounts for hierarchical structure of clustering is exploited based on this class of models an estimation strategy involving a within cluster resampling procedure is proposed and a model assessment approach is presented the asymptotic theory for the proposed estimators and lack of fit test is established the simulation study shows that the estimates are approximately unbiased and the proposed test statistic is conservative under extremely heavy censoring but approaches the size otherwise the analysis of the nepal study data shows that the association of mortality is much greater within households than within villages

the borel summable solutions of heat operators on a real analytic manifold abstract we study heat type equations t u u where the operator is given by a sum of squares of commuting real analytic vector fields acting on a real analytic manifold we give necessary and sufficient conditions for convergence and borel summability of formal power series solutions in terms of generalized integral means of the initial data the results are also valid for affine perturbations of

multisummability of formal solutions to the cauchy problem for some linear partial differential equations abstract the paper considers the cauchy problem for linear partial differential equations of non kowalevskian type in the complex domain it is shown that if the cauchy data are entire functions of a suitable order the problem has a formal solution which is multisummable the precise bound of the admissible order of entire functions is described in terms of the newton polygon of the equation

within cluster resampling within cluster resampling is proposed as a new method for analysing clustered data although the focus of this paper is clustered binary data the within cluster resampling asymptotic theory is general for many types of clustered data within cluster resampling is a simple but computationally intensive estimation method its main advantage over other marginal analysis methods such as generalised estimating equations liang zeger 1986 zeger liang 1986 is that it remains valid when the risk for the outcome of interest is related to the cluster size which we term nonignorable cluster size we present theory for the asymptotic normality and provide a consistent variance estimator for the within cluster resampling estimator simulations and an example are developed that assess the finite sample behaviour of the new method and show that when both methods are valid its performance is similar to that of generalised estimating equations

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

mean estimating equation approach to analysing cluster correlated data with nonignorable cluster sizes most methods for analysing cluster correlated biological data implicitly assume the ignorability of cluster sizes when this assumption fails the resulting inferences may be asymptotically invalid hoffman et al 2001 proposed a simple but computationally intensive method based on a large number of within cluster resamples and associated separate estimating equations that leads to asymptotically valid inferences whether the cluster sizes are ignorable or not we study a simple method based on a single inverse cluster size weighted estimating equation that avoids resampling and yet leads to asymptotically valid inferences simulation results are presented to assess the performance of the proposed method we also propose wald tests for ignorability of cluster sizes