a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

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

reduced solutions of douglas equations and angles between subspaces in this paper we study some particular solutions of douglas type equations by means of generalized inverses and angles we apply this result to characterize positive solutions and some special projections which are symmetrizable for a semidefinited positive bounded linear operator

new extremal characterizations of generalized inverses of linear operators abstract in 1956 r penrose studied best approximate solutions of the matrix equation ax b he proved that a b where a is the moore penrose inverse is the unique matrix of minimal frobenius norm among all matrices which minimize the frobenius norm of ax b in particular a is the unique best approximate solution of ax i the vector version of penrose s result that is the fact that the vector a b is the best approximate solution in the euclidean norm of the vector equation ax b has long been generalized to infinite dimensional hilbert spaces in this paper an infinite dimensional version of penrose s full result is given we show that a straightforward generalization is not possible and provide new extremal characterizations in terms of the hermitian order of a and of the classes of generalized inverses associated with minimal norm solutions of consistent operator equations or with least squares solutions for a certain class of operators we can phrase our characterizations in terms of a whole class of norms including the hilbert schmidt and the trace norms thus providing new extremal characterizations even in the matrix case we treat both operators with closed range and with not necessarily closed range finally we characterize a as the unique inner inverse of minimal hilbert schmidt norm if a 2

semiparametric estimation in the proportional hazard model accounting for a misclassified cause of failure summary misclassified causes of failures are a common phenomenon in competing risks survival data such as cancer mortality we propose new estimating equations for a semiparametric proportional hazards ph model with misattributed causes of failures unlike other methods the estimator does not require any parametric assumptions on baseline cause specific hazard rates it is shown that the estimators for regression coefficients are consistent and asymptotically normal simulation results support the theoretical analysis in finite samples the methods are applied to analyze prostate cancer survival

explicit exponential stability conditions for linear differential equations with several delays abstract new explicit conditions of exponential stability are obtained for the nonautonomous linear equation x t k 1 m a k t x h k t 0 where k 1 m a k t 0 h k t t by comparing this equation with a nonoscillatory exponentially stable equation of the form x t k i a k t x g k t 0 where i 1 m g k t t every comparison result gives 2 m 1 different stability conditions due to the a priori choice of a subset i

inference based on imputed failure times for the proportional hazards model with interval censored data abstract we propose an approach to the proportional hazards model for interval censored data in which parameter estimates are obtained by solving estimating equations that are the partial likelihood score equations for the full data proportional hazards model averaged over all rankings of imputed failure times consistent with the observed censoring intervals imputed failure times are generated using a parametric estimate of the baseline distribution the parameters of the baseline distribution are estimated simultaneously with the proportional hazards regression parameters although a parametric form for the baseline distribution must be specified simulation studies show that the method performs well even when the baseline distribution is misspecified the estimating equations are solved using monte carlo techniques we present a recursive stochastic approximation scheme that converges to the zero of the estimating equations the solution has a random error that is asymptotically normally distributed w

preservation of stability in delay equations under delay perturbations we consider a class of linear delay equations with perturbed time lags and present conditions which guarantee that the asymptotic stability of the trivial solution of the equation at hand is preserved under these perturbations as an example we show how our results can be used to obtain an estimate on the maximum allowable sampling interval in the stabilization of a hybrid system with feedback delays we also present applications of our perturbation theorem to obtain stability conditions for delay equations with multiple delays

factorizations of linear relations abstract given two linear relations a and b we characterize the existence of a linear relation operator c such that a b c respectively a c b these factorizations extend and improve well known results by douglas and sebestyen

weighted least squares solutions of the equation axb c 0 abstract let h be a hilbert space l h the algebra of bounded linear operators on h and w l h a positive operator such that w 1 2 is in the p schatten class for some 1 p given a b l h with closed range and c l h we study the following weighted approximation problem analyze the existence of 0 1 m i n x l h a x b c p w where x p w w 1 2 x p we also study the related operator approximation problem analyze the existence of 0 2 m i n x l h a x b c w a x b c where the order is the one induced in l h by the cone of positive operators in this paper we prove that the existence of the minimum of 0 2 is equivalent to the existence of a solution of the normal equation a w a x b c 0 we also give sufficient conditions for the existence of the minimum of 0 1 and we characterize the operators where the minimum is attained

asymptotic representation of solutions of equationẏ t β t y t y t τ t abstract in this paper the equation t t y t y t t is considered where c i 1 r i 1 t 1 r 0 t t is an increasing function on i 1 t t i 1 0 c i 1 r results about asymptotic structure and behavior of the solutions of this equation are proved a connection with the equation t c t x t t and the asymptotic representation of its solutions is obtained

solution estimates for linear differential equations with delay abstract in this paper we give explicit exponential estimates x t m e t t 0 where t t0 m 0 for solutions of a linear scalar delay differential equation x t k 1 m b k t x h k t f t t t 0 x t t t t 0 we consider two different cases when 0 corresponding to exponential stability and the case of in the first case together with the exponential estimate we also obtain an exponential stability test in the second case we get estimation for solution growth here both the coefficients and the delays are measurable not necessarily continuous

large sample theory for parametric multiple imputation procedures we consider the asymptotic behaviour of various parametric multiple imputation procedures which include but are not restricted to the proper imputation procedures proposed by rubin 1978 the asymptotic variance structure of the resulting estimators is provided this result is used to compare the relative efficiencies of different imputation procedures it also provides a basis to understand the behaviour of two monte carlo iterative estimators stochastic em celeux diebolt 1985 wei tanner 1990 and simulated em ruud 1991 we further develop properties of these estimators when they stop at iteration k with imputation size m an application to a mcasurement error problem is used to illustrate the results

operator theoretic and computational approaches to ill posed problems with applications to antenna theory a general framework for regularization and approximation methods for ill posed problems is developed three levels in the resolution processes are distinguished and emphasized philosophy of resolution regularization approximation schema and regularization algorithms dilemmas and methodologies of resolution of ill posed problems and their numerical implementations are examined in this framework with particular reference to the problem of finding numerically minimum weighted norm least squares solutions of first kind integral equations and more generally of linear operator equations with nonclosed range a common problem in all these methods is delineated each method reduces the problem of resolution to a nonstandard minimization problem involving an unknown critical parameter whose optimal value is crucial to the numerical realization and amenability of the method the nonstandardness results from the fact that one does not have explicitly or a priori the function to be minimized it has to built up using additional information convergence rate estimates and robustness conditions etc several results are developed that complement recent advances in numerical analysis and regularization of inverse and ill posed identification and pattern synthesis problems an emphasis is placed on the role of constraints function space methods the role of generalized inverses and reproducing kernels in the regularization and stable computational resolution of these problems the results will be applied specifically to problems of antenna synthesis and identification however the thrust of the paper is devoted to the interdisciplinary character of operator theoretic and numerical methods for ill posed problems

multiple imputation methods for nonparametric inference on cumulative incidence with missing cause of failure we propose a nonparametric approach for cumulative incidence estimation when causes of failure are unknown or missing for some subjects under the missing at random assumption we estimate the cumulative incidence function using multiple imputation methods we develop asymptotic theory for the cumulative incidence estimators obtained from multiple imputation methods we also discuss how to construct confidence intervals for the cumulative incidence function and perform a test for comparing the cumulative incidence functions in two samples with missing cause of failure through simulation studies we show that the proposed methods perform well the methods are illustrated with data from a randomized clinical trial in early stage breast cancer

semiparametric estimators for the regression coefficients in the linear transformation competing risks model with missing cause of failure summary we consider the problem of estimating the regression coefficients in a competing risks model where the relationship between the cause specific hazard for the cause of interest and covariates is described using linear transformation models and when cause of failure is missing at random for a subset of individuals using the theory of robins et al 1994 for missing data problems and the approach of chen et al 2002 for estimating regression coefficients for linear transformation models we derive augmented inverse probability weighted complete case estimators for the regression coefficients that are doubly robust simulations demonstrate the relevance of the theory in finite samples

multiple imputation after 18 years abstract multiple imputation was designed to handle the problem of missing data in public use data bases where the data base constructor and the ultimate user are distinct entities the objective is valid frequency inference for ultimate users who in general have access only to complete data software and possess limited knowledge of specific reasons and models for nonresponse for this situation and objective i believe that multiple imputation by the data base constructor is the method of choice this article first provides a description of the assumed context and objectives and second reviews the multiple imputation framework and its standard results these preliminary discussions are especially important because some recent commentaries on multiple imputation have reflected either misunderstandings of the practical objectives of multiple imputation or misunderstandings of fundamental theoretical results then criticisms of multiple imputation are considered and finally comparisons are made to alt

nonparametric analysis of competing risks data with event category missing at random summary in competing risks setup the data for each subject consist of the event time censoring indicator and event category however sometimes the information about the event category can be missing as for example in a case when the date of death is known but the cause of death is not available in such situations treating subjects with missing event category as censored leads to the underestimation of the hazard functions we suggest nonparametric estimators for the cumulative cause specific hazards and the cumulative incidence functions which use the nadaraya watson estimator to obtain the contribution of an event with missing category to each of the cause specific hazards we derive the propertied of the proposed estimators optimal bandwidth is determined which minimizes the mean integrated squared errors of the proposed estimators over time the methodology is illustrated using data on lung infections in patients from the united states cystic fibrosis foundation patient registry

weighted procrustes problems abstract let h be a hilbert space l h the algebra of bounded linear operators on h and w l h a positive operator such that w 1 2 is in the p schatten class for some 1 p given a l h with closed range and b l h we study the following weighted approximation problem analyze the existence of m i n x l h a x b p w where x p w w 1 2 x p in this paper we prove that the existence of this minimum is equivalent to a compatibility condition between r b and r a involving the weight w and we characterize the operators which minimize this problem as w inverses of a in r b

asymptotic integration of nonautonomous delay differential systems we prove existence theorems and asymptotic formulas for the solutions of a class of delay differential equations with time state dependent lag

quantum enveloping algebras with von neumann regular cartan like generators and the pierce decomposition quantum bialgebras derivable from uq sl2 which contain idempotents and von neumann regular cartan like generators are introduced and investigated various types of antipodes invertible and von neumann regular on these bialgebras are constructed which leads to a hopf algebra structure and a von neumann hopf algebra structure respectively for them explicit forms of some particular r matrices also invertible and von neumann regular are presented and the latter respects the pierce decomposition

multiple imputation methods for estimating regression coefficients in the competing risks model with missing cause of failure we propose a method to estimate the regression coefficients in a competing risks model where the cause specific hazard for the cause of interest is related to covariates through a proportional hazards relationship and when cause of failure is missing for some individuals we use multiple imputation procedures to impute missing cause of failure where the probability that a missing cause is the cause of interest may depend on auxiliary covariates and combine the maximum partial likelihood estimators computed from several imputed data sets into an estimator that is consistent and asymptotically normal a consistent estimator for the asymptotic variance is also derived simulation results suggest the relevance of the theory in finite samples results are also illustrated with data from a breast cancer study

analysis of competing risks survival data when some failure types are missing we propose a method to analyse competing risks survival data when failure types are missing for some individuals our approach is based on a standard proportional hazards structure for each of the failure types and involves the solution to estimating equations we present consistent and asymptotically normal estimators of the regression coefficients and related score tests an appealing feature is that individuals with known failure types make the same contributions as they would to a standard proportional hazards analysis contributions of individuals with unknown failure types are weighted according to the probability that they failed from the cause of interest efficiency and robustness are discussed results are illustrated with data from a breast cancer trial

on the stability region of scalar delay differential equations on considere l equation differentielle scalaire a retard x t x t x t q ou r et q 0 on definit les regions de stabilite des solutions