new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis semiparametric regression models are very useful for longitudinal data analysis the complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis in this article two new approaches are proposed for estimating the regression coefficients in a semiparametric model the asymptotic normality of the resulting estimators is established an innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models the proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters rates of convergence of the resulting estimators are established with a proper choice of regularization parameters and penalty functions the proposed variable selection procedures are shown to perform as well as an oracle estimator a robust standard error formula is derived usi

non contraction of heat flow on minkowski spaces we study contractivity properties of gradient flows for functions on normed spaces or more generally on finsler manifolds contractivity of the flows turns out to be equivalent to a new notion of convexity for the functions this is different from the usual convexity along geodesics in non riemannian finsler manifolds as an application we show that the heat flow on minkowski normed spaces other than inner product spaces is not contractive with respect to the quadratic wasserstein distance

penalized estimating equations les modeles avec penalisation comme l estimateur ridge l estimateur de stein l estimateur en pont et le lasso ont ete proposes pour prendre en compte la collineariteen regression le lasso a ete applique au modele lineaire a la regression logistique au modele des hasards proportionnels de cox et aux reseaux de neurones cet article etudie le modele avec penalisation en pont pour une penalite j j applique aux equations d estimation et applique ce modele avec penalisation aux equations d estimation generalisees gee dans des etudes longitudinales le defaut de vraisemblance jointe dans les gee est surmonte par les equations d estimation penalisees pour lesquelles aucune vraisemblance jointe n est requise on donne les resultats asymptotiques pour l estimateur sons penalite on montre par des simulations et une application que les cee avec penalisation ameliorent potentiellement les resultats de l estimateur gee et presentent les memes proprietes que les modeles lineaires penalises

doubly robust inference when combining probability and non probability samples with high dimensional data we consider integrating a non probability sample with a probability sample which provides high dimensional representative covariate information of the target population we propose a two step approach for variable selection and finite population inference in the first step we use penalized estimating equations with folded concave penalties to select important variables and show selection consistency for general samples in the second step we focus on a doubly robust estimator of the finite population mean and re estimate the nuisance model parameters by minimizing the asymptotic squared bias of the doubly robust estimator this estimating strategy mitigates the possible first step selection error and renders the doubly robust estimator root n consistent if either the sampling probability or the outcome model is correctly specified

variable selection in semiparametric linear regression with censored data summary we describe two procedures for selecting variables in the semiparametric linear regression model for censored data one procedure penalizes a vector of estimating equations and simultaneously estimates regression coefficients and selects submodels a second proce dure controls systematically the proportion of unimportant variables through forward selection and the addition of pseudorandom variables we explore both rank based statistics and buckley james statistics in the setting proposed and evaluate the performance of all methods through extensive simulation studies and one real data set

variable selection for multivariate failure time data in this paper we proposed a penalised pseudo partial likelihood method for variable selection with multivariate failure time data with a growing number of regression coefficients under certain regularity conditions we show the consistency and asymptotic normality of the penalised likelihood estimators we further demonstrate that for certain penalty functions with proper choices of regularisation parameters the resulting estimator can correctly identify the true model as if it were known in advance based on a simple approximation of the penalty function the proposed method can be easily carried out with the newton raphson algorithm we conduct extensive monte carlo simulation studies to assess the finite sample performance of the proposed procedures we illustrate the proposed method by analysing a dataset from the framingham heart study

on quotients of spaces with ricci curvature bounded below abstract let m g be a smooth riemannian manifold and g a compact lie group acting on m effectively and by isometries it is well known that a lower bound of the sectional curvature of m g is again a bound for the curvature of the quotient space which is an alexandrov space of curvature bounded below moreover the analogous stability property holds for metric foliations and submersions the goal of the paper is to prove the corresponding stability properties for synthetic ricci curvature lower bounds specifically we show that such stability holds for quotients of rcd k n spaces under isomorphic compact group actions and more generally under metric measure foliations and submetries an rcd k n space is a metric measure space with an upper dimension bound n and weighted ricci curvature bounded below by k in a generalized sense in particular this shows that if m g has ricci curvature bounded below by k r and dimension n then the quotient space is an rcd k n space additionally we tackle the same problem for the cd cd and mcp curvature dimension conditions we provide as well geometric applications which include a generalization of kobayashi s classification theorem of homogeneous manifolds to rcd k n spaces with essential minimal dimension n n a structure theorem for rcd k n spaces admitting actions by large compact groups and geometric rigidity results for orbifolds such as cheng s maximal diameter and maximal volume rigidity theorems finally in two appendices we apply the methods of the paper to study quotients by isometric group actions of discrete spaces and of super ricci flows

euclidean spaces as weak tangents of infinitesimally hilbertian metric measure spaces with ricci curvature bounded below we show that in any infinitesimally hilbertian cd k n space at almost every point there exists a euclidean weak tangent i e there exists a sequence of dilations of the space that converges to a euclidean space in the pointed measured gromov hausdorff topology the proof follows by considering iterated tangents and the splitting theorem for infinitesimally hilbertian cd 0 n spaces

large sample theory of a modified buckley james estimator for regression analysis with censored data this approach we introduce herein a slight modification of the buckley james estimator to get around the difficulties caused by the instability at the upper tail of the associated kaplan meier estimate of the underlying error distribution and show that the modified buckleyjames estimator is consistent and asymptotically normal under certain regularity conditions a simple formula for the asymptotic variance of the modified buckley james estimator is also derived and is used to study the asymptotic efficiency of the estimator extensions of these results to the multiple regression model are also given

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

penalized generalized estimating equations for high dimensional longitudinal data analysis we consider the penalized generalized estimating equations gees for analyzing longitudinal data with high dimensional covariates which often arise in microarray experiments and large scale health studies existing high dimensional regression procedures often assume independent data and rely on the likelihood function construction of a feasible joint likelihood function for high dimensional longitudinal data is challenging particularly for correlated discrete outcome data the penalized gee procedure only requires specifying the first two marginal moments and a working correlation structure we establish the asymptotic theory in a high dimensional framework where the number of covariates p n increases as the number of clusters n increases and p n can reach the same order as n one important feature of the new procedure is that the consistency of model selection holds even if the working correlation structure is misspecified we evaluate the performance of the proposed method using monte carlo simulations and demonstrate its application using a yeast cell cycle gene expression data set

convergence in distribution of random metric measure spaces λ coalescent measure trees we consider the space of complete and separable metric spaces which are equipped with a probability measure a notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all finite subspaces sampled from these spaces converge this topology is metrized following gromov s idea of embedding two metric spaces isometrically into a common metric space combined with the prohorov metric between probability measures on a fixed metric space we show that for this topology convergence in distribution follows provided the sequence is tight from convergence of all randomly sampled finite subspaces we give a characterization of tightness based on quantities which are reasonably easy to calculate subspaces of particular interest are the space of real trees and of ultra metric spaces equipped with a probability measure as an example we characterize convergence in distribution for the ultra metric measure spaces given by the random genealogies of the coalescents we show that the coalescent defines an infinite random metric measure space if and only if the so called dust free property holds

reasoning about action i a possible worlds approach abstract reasoning about change is an important aspect of commonsense reasoning and planning in this paper we describe an approach to reasoning about change for rich domains where it is not possible to anticipate all situations that might occur the approach provides a solution to the frame problem and to the related problem that it is not always reasonable to explicitly specify all of the consequences of actions the approach involves keeping a single model of the world that is updated when actions are performed the update procedure involves constructing the nearest world to the current one in which the consequences of the actions under consideration hold the way we find the nearest world is to construct proofs of the negation of the explicit consequences of the expected action and to remove a premise in each proof from the current world computationally this construction procedure appears to be tractable for worlds like our own where few things tend to change with each action or where change is regular

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

addressing issues associated with evaluating prediction models for survival endpoints based on the concordance statistic prediction models for disease risk and prognosis play an important role in biomedical research and evaluating their predictive accuracy in the presence of censored data is of substantial interest the standard concordance c statistic has been extended to provide a summary measure of predictive accuracy for survival models motivated by a prostate cancer study we address several issues associated with evaluating survival prediction models based on c statistic with a focus on estimators using the technique of inverse probability of censoring weighting ipcw compared to the existing work we provide complete results on the asymptotic properties of the ipcw estimators under the assumption of coarsening at random car and propose a sensitivity analysis under the mechanism of noncoarsening at random ncar in addition we extend the ipcw approach as well as the sensitivity analysis to high dimensional settings the predictive accuracy of prediction models for cancer recurrence after prostatectomy is assessed by applying the proposed approaches we find that the estimated predictive accuracy for the models in consideration is sensitive to ncar assumption and thus identify the best predictive model finally we further evaluate the performance of the proposed methods in both settings of low dimensional and high dimensional data under car and ncar through simulations

existence and stability for fokker planck equations with log concave reference measure we study markov processes associated with stochastic differential equations whose non linearities are gradients of convex functionals we prove a general result of existence of such markov processes and a priori estimates on the transition probabilities the main result is the following stability property if the associated invariant measures converge weakly then the markov processes converge in law the proofs are based on the interpretation of a fokker planck equation as the steepest descent flow of the relative entropy functional in the space of probability measures endowed with the wasserstein distance

sharp holder continuity of tangent cones for spaces with a lower ricci curvature bound and applications we prove a new estimate on manifolds with a lower ricci bound which asserts that the geometry of balls centered on a minimizing geodesic can change in at most a holder continuous way along the geodesic we give examples that show that the holder exponent along with essentially all the other consequences that follow from this estimate are sharp among the applications is that the regular set is convex for any non collapsed limit of einstein metrics in the general case of a potentially collapsed limit of manifolds with just a lower ricci curvature bound we show that the regular set is weakly convex and a e convex we also show two conjectures of cheeger colding one of these asserts that the isometry group of any even collapsed limit of manifolds with a uniform lower ricci curvature bound is a lie group the other asserts that the dimension of any limit space is the same everywhere

a guide to completeness and complexity for modal logics of knowledge and belief abstract we review and re examine possible worlds semantics for propositional logics of knowledge and belief with three particular points of emphasis 1 we show how general techniques for finding decision procedures and complete axiomatizations apply to models for knowledge and belief 2 we show how sensitive the difficulty of the decision procedure is to such issues as the choice of modal operators and the axiom system and 3 we discuss how notions of common knowledge and distributed knowledge among a group of agents fit into the possible worlds framework as far as complexity is concerned we show among other results that while the problem of deciding satisfiability of an s5 formula with one agent is np complete the problem for many agents is pspace complete adding a distributed knowledge operator does not change the complexity but once a common knowledge operator is added to the language the problem becomes complete for exponential time

semiparametric and nonparametric regression analysis of longitudinal data this article deals with the regression analysis of repeated measurements taken at irregular and possibly subject specific time points the proposed semiparametric and nonparametric models postulate that the marginal distribution for the repeatedly measured response variable y at time t is related to the vector of possibly time varying covariates x through the equations e y t x t 0 t 0x t and e y t x t 0 t 0 t x t where 0 t is an arbitrary function of t 0 is a vector of constant regression coefficients and 0 t is a vector of time varying regression coefficients the stochastic structure of the process y is completely unspecified we develop a class of least squares type estimators for 0 which is proven to be n consistent and asymptotically normal with simple variance estimators furthermore we develop a closed form estimator for a cumulative function of 0 t which is shown to be n consistent and on proper normalization converges weakly to a zero mean gaussian pr

bakry emery curvature dimension condition and riemannian ricci curvature bounds the aim of the present paper is to bridge the gap between the bakry emery and the lott sturm villani approaches to provide synthetic and abstract notions of lower ricci curvature bounds we start from a strongly local dirichlet form mathcal e admitting a carre du champ gamma in a polish measure space x mathfrak m and a canonical distance mathsf d mathcal e that induces the original topology of x we first characterize the distinguished class of riemannian energy measure spaces where mathcal e coincides with the cheeger energy induced by mathsf d mathcal e and where every function f with gamma f le1 admits a continuous representative in such a class we show that if mathcal e satisfies a suitable weak form of the bakry emery curvature dimension condition mathrm be k infty then the metric measure space x mathsf d mathfrak m satisfies the riemannian ricci curvature bound mathrm rcd k infty according to duke math j 163 2014 1405 1490 thus showing the equivalence of the two notions two applications are then proved the tensorization property for riemannian energy spaces satisfying the bakry emery mathrm be k n condition and thus the corresponding one for mathrm rcd k infty spaces without assuming nonbranching and the stability of mathrm be k n with respect to sturm gromov hausdorff convergence

variable selection for cox s proportional hazards model and frailty model a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in fan and li 2001a it has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance such a property is called an oracle property the proposed procedures were illustrated in the context of linear regression robust linear regression and generalized linear models in this paper the nonconcave penalized likelihood approach is extended further to the cox proportional hazards model and the cox proportional hazards frailty model two commonly used semi parametric models in survival analysis as a result new variable selection procedures for these two commonly used models are proposed it is demonstrated how the rates of convergence depend on the regularization parameter in the penalty function further with a proper choice of the regularization parameter and the penalty function the proposed estimators possess an oracle property standard error formulae are derived and their accuracies are empirically tested simulation studies show that the proposed procedures are more stable in prediction and more effective in computation than the best subset variable selection and they reduce model complexity as effectively as the best subset variable selection compared with the lasso which is the penalized likelihood method with the l 1 penalty proposed by tibshirani the newly proposed approaches have better theoretic properties and finite sample performance

l1 regularization path algorithm for generalized linear models summary we introduce a path following algorithm for l1 regularized generalized linear models the l1 regularization procedure is useful especially because it in effect selects variables according to the amount of penalization on the l1 norm of the coefficients in a manner that is less greedy than forward selection backward deletion the generalized linear model path algorithm efficiently computes solutions along the entire regularization path by using the predictor corrector method of convex optimization selecting the step length of the regularization parameter is critical in controlling the overall accuracy of the paths we suggest intuitive and flexible strategies for choosing appropriate values we demonstrate the implementation with several simulated and real data sets

a general semiparametric hazards regression model efficient estimation and structure selection we consider a general semiparametric hazards regression model that encompasses the cox proportional hazards model and the accelerated failure time model for survival analysis to overcome the nonexistence of the maximum likelihood we derive a kernel smoothed profile likelihood function and prove that the resulting estimates of the regression parameters are consistent and achieve semiparametric efficiency in addition we develop penalized structure selection techniques to determine which covariates constitute the accelerated failure time model and which covariates constitute the proportional hazards model the proposed method is able to estimate the model structure consistently and model parameters efficiently furthermore variance estimation is straightforward the proposed estimation performs well in simulation studies and is applied to the analysis of a real data set

the lasso method for variable selection in the cox model summary i propose a new method for variable selection and shrinkage in cox s proportional hazards model my proposal minimizes the log partial likelihood subject to the sum of the absolute values of the parameters being bounded by a constant because of the nature of this constraint it shrinks coe cients and produces some coe cients that are exactly zero as a result it reduces the estimation variance while providing an interpretable final model the method is a variation of the lasso proposal of tibshirani designed for the linear regression context simulations indicate that the lasso can be more accurate than stepwise selection in this setting

sharp and rigid isoperimetric inequalities in metric measure spaces with lower ricci curvature bounds we prove that if x mathsf d mathfrak m is a metric measure space with mathfrak m x 1 having in a synthetic sense ricci curvature bounded from below by k 0 and dimension bounded above by n in 1 infty then the classic levy gromov isoperimetric inequality together with the recent sharpening counterparts proved in the smooth setting by milman for any k in mathbb r n ge 1 and upper diameter bounds holds i e the isoperimetric profile function of x mathsf d mathfrak m is bounded from below by the isoperimetric profile of the model space moreover if equality is attained for some volume v in 0 1 and k is strictly positive then the space must be a spherical suspension and in this case we completely classify the isoperimetric regions finally we also establish the almost rigidity if the equality is almost attained for some volume v in 0 1 and k is strictly positive then the space must be mgh close to a spherical suspension to our knowledge this is the first result about isoperimetric comparison for non smooth metric measure spaces satisfying ricci curvature lower bounds examples of spaces fitting our assumptions include measured gromov hausdorff limits of riemannian manifolds satisfying ricci curvature lower bounds alexandrov spaces with curvature bounded from below finsler manifolds endowed with a strongly convex norm and satisfying ricci curvature lower bounds the result seems new even in these celebrated classes of spaces

a statistical view of some chemometrics regression tools chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis in addition to borrowing many techniques from the statistics and engineering literatures chemometrics itself has given rise to several new data analytical methods this article examines two methods commonly used in chemometrics for predictive modeling partial least squares and principal components regression from a statistical perspective the goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations these methods include ordinary least squares variable subset selection and ridge regression

on uniqueness of tangent cones for einstein manifolds we show that for any ricci flat manifold with euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross section similarly for any noncollapsing limit of einstein manifolds with uniformly bounded einstein constants we show that local tangent cones are unique if one tangent cone has a smooth cross section

a unified framework for explanation based generalization of partially ordered and partially instantiated plans abstract most previous work in explanation based generalization ebg of plans dealt with totally ordered plans these methods cannot be directly applied to generalizing partially ordered partially instantiated plans a class of plans that have received significant attention in planning in this paper we present a natural way of extending the explanation based generalization methods to partially ordered partially instantiated popi plans our development is based on modal truth criteria for popi plans 3 we develop explanation structures from these truth criteria and use them as a common basis to derive a variety of generalization algorithms specifically we present algorithms for precondition generalization order generalization and possible correctness generalization of popi plans the systematic derivation of the generalization algorithms from the modal truth criterion obviates the need for carrying out a separate formal proof of correctness of the ebg algorithms our development also systematically explicates the tradeoffs among the spectrum of possible generalizations for popi plans and provides an empirical demonstration of the relative utility of ebg in partial ordering as opposed to total ordering planning frameworks

fixed and random effects selection in mixed effects models summary we consider selecting both fixed and random effects in a general class of mixed effects models using maximum penalized likelihood mpl estimation along with the smoothly clipped absolute deviation scad and adaptive least absolute shrinkage and selection operator alasso penalty functions the mpl estimates are shown to possess consistency and sparsity properties and asymptotic normality a model selection criterion called the icq statistic is proposed for selecting the penalty parameters ibrahim zhu and tang 2008 journal of the american statistical association 103 1648 1658 the variable selection procedure based on icq is shown to consistently select important fixed and random effects the methodology is very general and can be applied to numerous situations involving random effects including generalized linear mixed models simulation studies and a real data set from a yale infant growth study are used to illustrate the proposed methodology

riemannian ricci curvature lower bounds in metric measure spaces with finite measure in prior work 4 of the first two authors with savare a new riemannian notion of lower bound for ricci curvature in the class of metric measure spaces x d m was introduced and the corresponding class of spaces denoted by rcd k this notion relates the cd k n theory of sturm and lott villani in the case n to the bakry emery approach in 4 the rcd k property is defined in three equivalent ways and several properties of rcd k spaces including the regularization properties of the heat flow the connections with the theory of dirichlet forms and the stability under tensor products are provided in 4 only finite reference measures m have been considered the goal of this paper is twofold on one side we extend these results to general finite spaces on the other we remove a technical assumption appeared in 4 concerning a strengthening of the cd k condition this more general class of spaces includes euclidean spaces endowed with lebesgue measure complete noncompact riemannian manifolds with bounded geometry and the pointed metric measure limits of manifolds with lower ricci curvature bounds

calculus and heat flow in metric measure spaces and applications to spaces with ricci bounds from below this paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces x mathsf d mathfrak m our main results are a general study of the relations between the hopf lax semigroup and hamilton jacobi equation in metric spaces x d the equivalence of the heat flow in l 2 x mathfrak m generated by a suitable dirichlet energy and the wasserstein gradient flow of the relative entropy functional mathrm ent mathfrak m in the space of probability measures open image in new window the proof of density in energy of lipschitz functions in the sobolev space w 1 2 x mathsf d mathfrak m a fine and very general analysis of the differentiability properties of a large class of kantorovich potentials in connection with the optimal transport problem is the fourth achievement of the paper our results apply in particular to spaces satisfying ricci curvature bounds in the sense of lott and villani ann math 169 903 991 2009 and sturm acta math 196 65 131 2006 and acta math 196 133 177 2006 and require neither the doubling property nor the validity of the local poincare inequality

local spectral convergence in rcd k n spaces abstract in this paper we give necessary and sufficient conditions for the validity of the local spectral convergence in balls in the setting of rcd spaces

variable selection for distribution free models for longitudinal zero inflated count responses zero inflated count outcomes arise quite often in research and practice parametric models such as the zero inflated poisson and zero inflated negative binomial are widely used to model such responses like most parametric models they are quite sensitive to departures from assumed distributions recently new approaches have been proposed to provide distribution free or semi parametric alternatives these methods extend the generalized estimating equations to provide robust inference for population mixtures defined by zero inflated count outcomes in this paper we propose methods to extend smoothly clipped absolute deviation scad based variable selection methods to these new models variable selection has been gaining popularity in modern clinical research studies as determining differential treatment effects of interventions for different subgroups has become the norm rather the exception in the era of patent centered outcome research such moderation analysis in general creates many explanatory variables in regression analysis and the advantages of scad based methods over their traditional counterparts render them a great choice for addressing this important and timely issues in clinical research we illustrate the proposed approach with both simulated and real study data copyright 2016 john wiley sons ltd

equivalent definitions of bv space and of total variation on metric measure spaces abstract in this paper we introduce a new definition of bv based on measure upper gradients and prove the equivalence of this definition and the coincidence of the corresponding notions of total variation with the definitions based on relaxation of l 1 norm of the slope of lipschitz functions or upper gradients as in the previous work by the first author with gigli and savare in the sobolev case the proof requires neither local compactness nor doubling and poincare

metric measure spaces with riemannian ricci curvature bounded from below in this paper we introduce a synthetic notion of riemannian ricci bounds from below for metric measure spaces x d m which is stable under measured gromov hausdorff convergence and rules out finsler geometries it can be given in terms of an enforcement of the lott sturm and villani geodesic convexity condition for the entropy coupled with the linearity of the heat flow besides stability it enjoys the same tensorization global to local and local to global properties in these spaces which we call rcd k spaces we prove that the heat flow which can be equivalently characterized either as the flow associated to the dirichlet form or as the wasserstein gradient flow of the entropy satisfies wasserstein contraction estimates and several regularity properties in particular bakry emery estimates and the l lip feller regularization we also prove that the distance induced by the dirichlet form coincides with d that the local energy measure has density given by the square of cheeger s relaxed slope and as a consequence that the underlying brownian motion has continuous paths all these results are obtained independently of poincare and doubling assumptions on the metric measure structure and therefore apply also to spaces which are not locally compact as the infinite dimensional ones

variable selection using mm algorithms variable selection is fundamental to high dimensional statistical modeling many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions optimizing the penalized likelihood function is often challenging because it may be nondifferentiable and or nonconcave this article proposes a new class of algorithms for finding a maximizer of the penalized likelihood for a broad class of penalty functions these algorithms operate by perturbing the penalty function slightly to render it differentiable then optimizing this differentiable function using a minorize maximize mm algorithm mm algorithms are useful extensions of the well known class of em algorithms a fact that allows us to analyze the local and global convergence of the proposed algorithm using some of the techniques employed for em algorithms in particular we prove that when our mm algorithms converge they must converge to a desirable point we also discuss conditions under which this convergence may be guaranteed we exploit the newton raphson like aspect of these algorithms to propose a sandwich estimator for the standard errors of the estimators our method performs well in numerical tests

a comparison of gcv and gml for choosing the smoothing parameter in the generalized spline smoothing problem the partially improper prior behind the smoothing spline model is used to obtain a generalization of the maximum likelihood gml estimate for the smoothing parameter then this estimate is compared with the generalized cross validation gcv estimate both analytically and by monte carlo methods the comparison is based on a predictive mean square error criteria it is shown that if the true unknown function being estimated is smooth in a sense to be defined then the gml estimate undersmooths relative to the gcv estimate and the predictive mean square error using the gml estimate goes to zero at a slower rate than the mean square error using the gcv estimate if the true function is rough then the gcv and gml estimates have asymptotically similar behavior a monte carlo experiment was designed to see if the asymptotic results in the smooth case were evident in small sample sizes mixed results were obtained for n 32 gcv was somewhat better than gml for n 64 and gcv was decidedly superior for n 128 in the n 32 case gcv was better for smaller sigma 2 and the comparison close for larger sigma 2 the theoretical results are shown to extend to the generalized spline smoothing model which includes the estimate of functions given noisy values of various integrals of them

alx an action logic for agents with bounded rationality abstract we propose a modal action logic that combines ideas from h a simon s bounded rationality s kripke s possible world semantics g h von wright s preference logic pratt s dynamic logic stalnaker s minimal change and more recent approaches to update semantics alx the xth action logic is sound complete and decidable making it the first complete logic for two place preference operators alx avoids important drawbacks of other action logics especially the counterintuitive necessitation rule for goals every theorem must be a goal and the equally counterintuitive closure of goals under logical implication

propositional knowledge base revision and minimal change abstract the semantics of revising knowledge bases represented by sets of propositional sentences is analyzed from a model theoretic point of view a characterization of all revision schemes that satisfy the gardenfors rationality postulates is given in terms of minimal change with respect to an ordering among interpretations revision methods proposed by various authors are surveyed and analyzed in this framework the correspondences between gardenfors like rationality postulates and minimal changes with respect to other orderings are also investigated

collapsing of riemannian manifolds and eigenvalues of laplace operator on etudie la perturbation des valeurs propres de l operateur de laplace sous des deformations des varietes qui ne conservent pas les dimensions

quantitative isoperimetry a la levy gromov on a riemannian manifold with a positive lower bound on the ricci tensor the distance of isoperimetric sets from geodesic balls is quantitatively controlled in terms of the gap between the isoperimetric profile of the manifold and that of a round sphere of suitable radius the deficit between the diameters of the manifold and of the corresponding sphere is bounded likewise these results are actually obtained in the more general context of possibly non smooth metric measure spaces with curvature dimension conditions through a quantitative analysis of the transport rays decompositions obtained by the localization method

a generalized dantzig selector with shrinkage tuning summary the dantzig selector performs variable selection and model fitting in linear regression it uses an l 1 penalty to shrink the regression coefficients towards zero in a similar fashion to the lasso while both the lasso and dantzig selector potentially do a good job of selecting the correct variables they tend to overshrink the final coefficients this results in an unfortunate trade off one can either select a high shrinkage tuning parameter that produces an accurate model but poor coefficient estimates or a low shrinkage parameter that produces more accurate coefficients but includes many irrelevant variables we extend the dantzig selector to fit generalized linear models while eliminating overshrinkage of the coefficient estimates and develop a computationally efficient algorithm similar in nature to least angle regression to compute the entire path of coefficient estimates a simulation study illustrates the advantages of our approach relative to others we apply the methodology to two datasets

on path restoration for censored outcomes summary dimension reduction model and variable selection are ubiquitous concepts in modern statistical science and deriving new methods beyond the scope of current methodology is noteworthy this article briefly reviews existing regularization methods for penalized least squares and likelihood for survival data and their extension to a certain class of penalized estimating function we show that if one s goal is to estimate the entire regularized coefficient path using the observed survival data then all current strategies fail for the buckley james estimating function we propose a novel two stage method to estimate and restore the entire dantzig regularized coefficient path for censored outcomes in a least squares framework we apply our methods to a microarray study of lung andenocarcinoma with sample size n 200 and p 1036 gene predictors and find 10 genes that are consistently selected across different criteria and an additional 14 genes that merit further investigation in simulation studies we found that the proposed path restoration and variable selection technique has the potential to perform as well as existing methods that begin with a proper convex loss function at the outset

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

penalized nonlinear mixed effects model to identify biomarkers that predict disease progression precise modeling of disease progression in neurodegenerative disorders may enable early intervention before clinical manifestation of a disease which is crucial since early intervention at the premanifest stage is expected to be more effective neuroimaging biomarkers are indicative of the underlying disease pathology and may be used to predict future disease occurrence at the premanifest stage as observed in many pivotal studies longitudinal measurements of clinical outcomes such as motor or cognitive symptoms often present nonlinear sigmoid shapes over time where the inflection points of the trajectories mark a meaningful time in disease progression therefore to identify neuroimaging biomarkers predicting disease progression we propose a nonlinear mixed effects model based on a sigmoid function to predict longitudinal clinical outcomes and associate a linear combination of neuroimaging biomarkers with subject specific inflection points based on an expectation maximization em algorithm we propose a method that can fit a nonlinear model with many potentially correlated biomarkers for random inflection points while achieving computational stability variable selection is introduced in the algorithm in order to identify important biomarkers of disease progression and to reduce prediction variability we apply the proposed method to the data from the predictors of huntington s disease study to select brain subcortical regional volumes predictive of the inflection points of the motor and cognitive function trajectories our results reveal that brain atrophy in the striatum and expansion of the ventricular system are highly predictive of the inflection points furthermore these inflection points may precede clinically defined disease onset by as early as a decade and thus may be useful biomarkers as early signs of huntington s disease onset

weak and strong convergence of derivations and stability of flows with respect to mgh convergence abstract this paper is devoted to the study of weak and strong convergence of derivations and of the flows associated to them when dealing with a sequence of metric measure structures x d m n m n weakly convergent to m in particular under curvature assumptions either only on the limit metric structure x d m or on the whole sequence of metric measure spaces we provide several stability results

extended quasi likelihood with fractional polynomials in the frame of the accelerated failure time model the accelerated failure time model is frequently used in survival analysis because of its direct physical interpretation semiparametric inference methods have been extensively investigated for this model however the accelerated failure time model and the existing inference methods assume homogeneity of the survival data after taking log transformation this assumption is not always appropriate because heterogeneous data are often encountered in practice in dealing with this heterogeneity yu yu and liu proposed a parametric quasi likelihood method by assuming a known variance function which may not be realistic for real data in this paper we extend the parametric quasi likelihood method to semiparametric via relaxing its assumption and approximating the unknown variance function by using fractional polynomials approach simulations show that this novel extension performs superior to other methods in statistical properties of unbiasedness efficiency and correct coverage probability in finite samples an application to real data set in primary biliary cirrhosis demonstrates the applicability of this new methodology

estimation in a linear regression model with censored data we consider the semiparametric linear regression model with censored data and with unknown error distribution we describe estimation equations of the buckley james type that admit n consistent and asymptotically normal solutions the derived estimator is efficient at a particular error distribution we show the equivalence between this type of estimator and an estimator based on a linear rank test suggested by tsiatis an extension to an estimator that is efficient everywhere is discussed

penalized variable selection procedure for cox models with semiparametric relative risk we study the cox models with semiparametric relative risk which can be partially linear with one nonparametric component or multiple additive or nonadditive nonparametric components a penalized partial likelihood procedure is proposed to simultaneously estimate the parameters and select variables for both the parametric and the nonparametric parts two penalties are applied sequentially the first penalty governing the smoothness of the multivariate nonlinear covariate effect function provides a smoothing spline anova framework that is exploited to derive an empirical model selection tool for the nonparametric part the second penalty either the smoothly clipped absolute deviation scad penalty or the adaptive lasso penalty achieves variable selection in the parametric part we show that the resulting estimator of the parametric part possesses the oracle property and that the estimator of the nonparametric part achieves the optimal rate of convergence the proposed procedures are shown to work well in simulation experiments and then applied to a real data example on sexually transmitted diseases

variable selection for binary spatial regression penalized quasi likelihood approach we consider the problem of selecting covariates in a spatial regression model when the response is binary penalized likelihood based approach is proved to be effective for both variable selection and estimation simultaneously in the context of a spatially dependent binary variable an uniquely interpretable likelihood is not available rather a quasi likelihood might be more suitable we develop a penalized quasi likelihood with spatial dependence for simultaneous variable selection and parameter estimation along with an efficient computational algorithm the theoretical properties including asymptotic normality and consistency are studied under increasing domain asymptotics framework an extensive simulation study is conducted to validate the methodology real data examples are provided for illustration and applicability although theoretical justification has not been made we also investigate empirical performance of the proposed penalized quasi likelihood approach for spatial count data to explore suitability of this method to a general exponential family of distributions

spectral convergence under bounded ricci curvature abstract for a noncollapsed gromov hausdorff convergent sequence of riemannian manifolds with a uniform bound of ricci curvature we establish two spectral convergence one of them is on the hodge laplacian acting on differential one forms the other is on the connection laplacian acting on tensor fields of every type which include all differential forms these are sharp generalizations of cheeger colding s spectral convergence of the laplacian acting on functions to the cases of tensor fields and differential forms these spectral convergence have two direct corollaries one of them is to give new bounds on such eigenvalues in terms of bounds on volume diameter and the ricci curvature the other is that we show the upper semicontinuity of the first betti numbers with respect to the gromov hausdorff topology and give the equivalence between the continuity of them and the existence of a uniform spectral gap on the other hand we also define measurable curvature tensors of the noncollapsed gromov hausdorff limit space of a sequence of riemannian manifolds with a uniform bound of ricci curvature which include riemannian curvature tensor the ricci curvature and the scalar curvature as fundamental properties of our ricci curvature we show that the ricci curvature coincides with the difference between the hodge laplacian and the connection laplacian and is compatible with gigli s one and lott s ricci measure moreover we prove a lower bound of the ricci curvature is compatible with a reduced riemannian curvature dimension condition we also give a positive answer to lott s question on the behavior of the scalar curvature with respect to the gromov hausdorff topology by using our scalar curvature

penalized estimating functions and variable selection in semiparametric regression models we propose a general strategy for variable selection in semiparametric regression models by penalizing appropriate estimating functions important applications include semiparametric linear regression with censored responses and semiparametric regression with missing predictors unlike the existing penalized maximum likelihood estimators the proposed penalized estimating functions may not pertain to the derivatives of any objective functions and may be discrete in the regression coefficients we establish a general asymptotic theory for penalized estimating functions and present suitable numerical algorithms to implement the proposed estimators in addition we develop a resampling technique to estimate the variances of the estimated regression coefficients when the asymptotic variances cannot be evaluated directly simulation studies demonstrate that the proposed methods perform well in variable selection and variance estimation we illustrate our methods using data from the paul coverdell stroke registry

wasserstein space over the wiener space the goal of this paper is to study optimal transportation problems and gradient flows of probability measures on the wiener space based on and extending fundamental results of feyel ustunel carrying out the program of ambrosio gigli savare we present a complete characterization of the derivative processes for certain class of absolutely continuous curves we prove existence of the gradient flow curves for the relative entropy w r t the wiener measure and identify these gradient flow curves with solutions of the ornstein uhlenbeck evolution equation

on the geometry of metric measure spaces ii we introduce a curvature dimension condition cd k n for metric measure spaces it is more restrictive than the curvature bound underline text curv left m text d m right k introduced in sturm k t 2006 on the geometry of metric measure spaces i acta math 196 65 131 which is recovered as the borderline case cd k the additional real parameter n plays the role of a generalized upper bound for the dimension for riemannian manifolds cd k n is equivalent to text ric m left xi xi right k left xi right 2 and dim m n the curvature dimension condition cd k n is stable under convergence for any triple of real numbers k n l the family of normalized metric measure spaces m d m with cd k n and diameter l is compact condition cd k n implies sharp version of the brunn minkowski inequality of the bishop gromov volume comparison theorem and of the bonnet myers theorem moreover it implies the doubling property and local scale invariant poincare inequalities on balls in particular it allows to construct canonical dirichlet forms with gaussian upper and lower bounds for the corresponding heat kernels

model selection for generalized estimating equations accommodating dropout missingness the generalized estimating equation gee has been a popular tool for marginal regression analysis with longitudinal data and its extension the weighted gee approach can further accommodate data that are missing at random mar model selection methodologies for gee however have not been systematically developed to allow for missing data we propose the missing longitudinal information criterion mlic for selection of the mean model and the mlic for correlation mlicc for selection of the correlation structure in gee when the outcome data are subject to dropout monotone missingness and are mar our simulation results reveal that the mlic and mlicc are effective for variable selection in the mean model and selecting the correlation structure respectively we also demonstrate the remarkable drawbacks of naively treating incomplete data as if they were complete and applying the existing gee model selection method the utility of proposed method is further illustrated by two real applications involving missing longitudinal outcome data

convergence of pointed non compact metric measure spaces and stability of ricci curvature bounds and heat flows aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition we propose various definitions show that all of them are equivalent and that for doubling spaces these are also equivalent to the well known measured gromov hausdorff convergence then we show that the curvature conditions cd k and rcd k are stable under this notion of convergence and that the heat flow passes to the limit as well both in the wasserstein and in the l framework we also prove the variational convergence of cheeger energies in the naturally adapted mosco sense and the convergence of the spectra of the laplacian in the case of spaces either uniformly bounded or satisfying the rcd k condition with k 0 when applied to riemannian manifolds our results allow for sequences with diverging dimensions

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

ricci curvature for metric measure spaces via optimal transport we dene a notion of a measured length space x having nonnegative n ricci curvature for n 2 1 1 or having1 ricci curvature bounded below byk fork2 r the denitions are in terms of the displacement convexity of certain functions on the associated wasserstein metric space p2 x of probability measures we show that these properties are preserved under measured gromov hausdor limits we give geometric and analytic consequences this paper has dual goals one goal is to extend results about optimal transport from the setting of smooth riemannian manifolds to the setting of length spaces a second goal is to use optimal transport to give a notion for a measured length space to have ricci curvature bounded below we refer to 11 and 44 for background material on length spaces and optimal transport respectively further bibliographic notes on optimal transport are in appendix f in the present introduction we motivate the questions that we address and we state the main results to start on the geometric side there are various reasons to try to extend notions of curvature from smooth riemannian manifolds to more general spaces a fairly general setting is that of length spaces meaning metric spaces x d in which the distance between two points equals the inmum of the lengths of curves joining the points in the rest of this introduction we assume that x is a compact length space alexandrov gave a good notion of a length space having curvature bounded below by k with k a real number in terms of the geodesic triangles in x in the case of a riemannian manifold m with the induced length structure one recovers the riemannian notion of having sectional curvature bounded below by k length spaces with alexandrov curvature bounded below by k behave nicely with respect to the gromovhausdor topology on compact metric spaces modulo isometries they form

linear regression analysis for multivariate failure time observations abstract in this article we consider the case that each patient in a longitudinal study may experience two or more distinct failures the corresponding failure times which are possible censored are recorded for each patient the logarithm of each marginal failure time is assumed to be linearly related to its covariates however the distributional form of the error term in the model does not have to be specified in the analysis furthermore no specific structure of dependence among the distinct failure times on each subject has to be imposed various linear regression methods for analyzing multivariate failure time observations are proposed our procedures do not involve the unstable nonparametric hazard function estimation extensive numerical studies are conducted to evaluate the new proposals recommendations are also made for their practical usage

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

localization and tensorization properties of the curvature dimension condition for metric measure spaces abstract this is an addendum to the paper k bacher k t sturm localization and tensorization properties of the curvature dimension condition for metric measure spaces j funct anal 259 2010 28 56 we prove the tensorization property for the curvature dimension condition add some detailed calculations including explicit dependence of constants and comment on assumptions and conjectures concerning the local to global statement in bacher and sturm 2010 1 and villani 2009 6 respectively