common hermitian solutions to some operator equations on hilber c modules abstract we establish necessary and sufficient conditions for the existence of the general common hermitian solution to the equations a 1 x c 1 xb 1 c 2 a 3 xa 3 c 3 a 4 xa 4 c 4 for adjointable operators between hilbert c modules and present an expression for the common hermitian solution to the equations in terms of moore penrose inverse of operators when the solvability conditions are satisfied the findings of this paper extend some known results in the literature

a szego limit formula for conjugates of ψ do s by hecke operators let tg be a hecke operator and let op a be a do on l2 b further let be the projection onto span uj uj juj tguj j g uj j we will determine the szego limit measure g a for the operators tg op a tg xkd g a x lim 1 rank tr t g op a tg k comparison of g a with the szego limit measure of op tga shows that tg op a tg is quite remote spectrally from op tga

the analysis of transformed data abstract recently it was suggested bickel and doksum 1981 that when data are used to select a transformation the post transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection we argue that common sense and the work of box and cox 1964 point to a contrary conclusion our argument is based on considerations of parameter interpretation and subsequent bayesian analysis within the context of fitting normal error linear models numerical examples are used to illustrate the main points

representations for weighted moore penrose inverses of partitioned adjointable operators abstract for two positive definite adjointable operators m and n and an adjointable operator a acting on a hilbert c module some properties of the weighted moore penrose inverse a mn are established if a a ij is 1 2 or 2 2 partitioned then general representations for a mn in terms of the individual blocks of a ij are studied in the case when a is 1 2 partitioned a unified representation for a mn is presented in the 2 2 partitioned case an approach to the construction of the moore penrose inverse from the non weighted case to the weighted case is provided some results known for matrices are extended to the general setting of operators on hilbert c modules

a nonparametric test for panel count data summary panel count data arise when a recurrent event is under investigation and each study subject is observed only at discrete time points in this situation observed data include only the numbers of occurrences of the event of interest between observation time points and no information is available on subjects between their observation time points we propose a nonparametric test for comparing the point processes characterising the recurrent event when only panel count data are available the asymptotic distribution of the test statistic is derived and a simulation study is conducted to evaluate its performance the method is illustrated using data from a medical follow up study

fitting semi markov models to interval censored data with unknown initiation times in a semi markov model the hazard of making a transition between stages depends on the time spent in the current stage but is independent of time spent in other stages if the initiation time time of entry into the network is not known for some persons and if transition time data are interval censored i e if transition times are not known exactly but are known only to have occurred in some interval then the length of time these persons spent in any stage is not known we show how a semi markov model can still be fit to interval censored data with missing initiation times for the special case of models in which all persons enter the network at the same initial stage and proceed through the same succession of stages to a unique absorbing stage we present discrete time nonparametric maximum likelihood estimators of the waiting time distributions for this type of data

the analysis of panel data under a markov assumption abstract methods for the analysis of panel data under a continuous time markov model are proposed we present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models and for other process characteristics such as mean sojourn times and equilibrium distributions generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented and an example based on a longitudinal study of the smoking habits of school children is discussed questions of embeddability and estimation are examined

the gamma frailty poisson model for the nonparametric estimation of panel count data summary in this article we study nonparametric estimation of the mean function of a counting process with panel observations we introduce the gamma frailty variable to account for the intracorrelation between the panel counts of the counting process and construct a maximum pseudo likelihood estimate with the frailty variable three simulated examples are given to show that this estimation procedure while preserving the robustness and simplicity of the computation improves the efficiency of the nonparametric maximum pseudo likelihood estimate studied in wellner and zhang 2000 annals of statistics28 779 814 a real example from a bladder tumor study is used to illustrate the method

pseudo differential analysis on hyperbolic surfaces soit d le disque unite psu 1 1 un sous groupe discret et x d une surface hyperbolique on considere le comportement asymptotique des valeurs propres et des fonctions propres de sur x on presente un calcul d operateur pseudo differentiel pour obtenir ce resultat

discrete time nonparametric estimation for semi markov models of chain of events data subject to interval censoring and truncation chain of events data are longitudinal observations on a succession of events that can only occur in a prescribed order one goal in an analysis of this type of data is to determine the distribution of times between the successive events this is difficult when individuals are observed periodically rather than continuously because the event times are then interval censored chain of events data may also be subject to truncation when individuals can only be observed if a certain event in the chain e g the final event has occurred we provide a nonparametric approach to estimate the distributions of times between successive events in discrete time for data such as these under the semi markov assumption that the times between events are independent this method uses a self consistency algorithm that extends turnbull s algorithm 1976 journal of the royal statistical society series b 38 290 295 the quantities required to carry out the algorithm can be calculated recursively for improved computational efficiency two examples using data from studies involving hiv disease are used to illustrate our methods

analysis of repeated ordered categorical outcomes with possibly missing observations and time dependent covariates abstract this article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome the method which allows both time dependent covariates and missing observations consists of two analytic steps in the first step the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by mccullagh 1980 the joint asymptotic distribution of the estimates of these occasion specific regression coefficients and a consistent estimator of their asymptotic covariance matrix are obtained without imposing any parametric model of dependence on the repeated observations in the second step this asymptotic distribution together with appropriate simultaneous inference procedures is used to characterize the overall difference between groups and the variation in group differences over time the missing data process may differ between gro

semi markov models with phase type sojourn distributions continuous time multistate models are widely used for categorical response data particularly in the modeling of chronic diseases however inference is difficult when the process is only observed at discrete time points with no information about the times or types of events between observation times unless a markov assumption is made this assumption can be limiting as rates of transition between disease states might instead depend on the time since entry into the current state such a formulation results in a semi markov model we show that the computational problems associated with fitting semi markov models to panel observed data can be alleviated by considering a class of semi markov models with phase type sojourn distributions this allows methods for hidden markov models to be applied in addition extensions to models where observed states are subject to classification error are given the methodology is demonstrated on a dataset relating to development of bronchiolitis obliterans syndrome in post lung transplantation patients

a smoothed em approach to indirect estimation problems with particular reference to stereology and emission tomography there are many practical problems where the observed data are not drawn directly from the density g of real interest but rather from another distribution derived from g by the application of an integral operator the estimation of g then entails both statistical and numerical difficulties a natural statistical approach is by maximum likelihood conveniently implemented using the em algorithm but this provides unsatisfactory reconstructions of g in this paper we modify the maximum likelihood em approach by introducing a simple smoothing step at each em iteration in our experience this algorithm converges in relatively few iterations to good estimates of g that do not depend on the choice of starting configuration some theoretical background is given that relates this smoothed em algorithm to a maximum penalized likelihood approach two applications are considered in detail the first is the classical stereology problem of determining particle size distributions from data collected on a plane section through a composite medium the second concerns the recovery of the structure of a section of the human body from external observations obtained by positron emission tomography for this problem we also suggest several technical improvements on existing methodology

particular formulae for the moore penrose inverse of a columnwise partitioned matrix abstract an essential part of cegielski s obtuse cones and gram matrices with non negative inverse linear algebra appl 335 2001 167 181 considerations of some properties of gram matrices with nonnegative inverses which are pointed out to be crucial in constructing obtuse cones consists in developing some particular formulae for the moore penrose inverse of a columnwise partitioned matrix a a1 a2 under the assumption that it is of full column rank in the present paper these results are generalized and extended the generalization consists in weakening the assumption mentioned above to the requirement that the ranges of a1 and a2 are disjoint while the extension consists in introducing the conditions referring to the class of all generalized inverses of a

semiparametric time to event modeling in the presence of a latent progression event summary in cancer research interest frequently centers on factors influencing a latent event that must precede a terminal event in practice it is often impossible to observe the latent event precisely making inference about this process difficult to address this problem we propose a joint model for the unobserved time to the latent and terminal events with the two events linked by the baseline hazard covariates enter the model parametrically as linear combinations that multiply respectively the hazard for the latent event and the hazard for the terminal event conditional on the latent one we derive the partial likelihood estimators for this problem assuming the latent event is observed and propose a profile likelihood based method for estimation when the latent event is unobserved the baseline hazard in this case is estimated nonparametrically using the em algorithm which allows for closed form breslow type estimators at each iteration bringing improved computational efficiency and stability compared with maximizing the marginal likelihood directly we present simulation studies to illustrate the finite sample properties of the method its use in practice is demonstrated in the analysis of a prostate cancer data set

particular formulae for the moore penrose inverses of the partitioned bounded linear operators abstract for any two complex hilbert spaces h and k let bl h k be the set of bounded linear operators from h to k and h k be the direct sum of h and k given three hilbert spaces h 1 h 2 h 3 and two operators a 1 bl h 1 h 3 a 2 bl h 2 h 3 a partitioned bounded linear operator a a 1 a 2 bl h 1 h 2 h 3 can be induced where a h 1 h 2 a 1 h 1 a 2 h 2 for h i h i i 1 2 in this note we study the moore penrose inverse a of such a partitioned bounded linear operator a and generalize a recent result of j k baksalary and o m baksalary particular formulae for the moore penrose inverse of a columnwise partitioned matrix linear algebra appl 421 2007 16 23 from finite matrices to hilbert space operators

positive semi definite matrices of adjointable operators on hilbert c modules abstract let a be a c algebra h k be two hilbert a modules and b be an adjointable operator from h to k in this paper we prove that the moore penrose inverse of b exists if and only if b has closed range in addition some known results about the moore penrose inverses acting on hilbert spaces as well as in c algebras are extended in the context of hilbert c modules as an application a characterization of positive semi definite matrices of adjointable operators with respect to an orthogonal pair of a hilbert c module is given

a note on nonparametric estimation of the distribution function from interval censored and truncated observations this paper is concerned with the nonparametric estimation of the distribution function f from interval censored and truncated data as discussed by turnbull it is observed that turnbun s characterization of f the maximum likelihood estimator of f is not applicable in general when the data are interval censored and truncated it is shown however that turnbull s characterization can be easily modified to obtain the appropriate characterization of f

on the hermitian solutions to a system of adjointable operator equations we establish necessary and sufficient conditions for the existence of a hermitian solution to the system of equations a1x1 c1 x1b1 d1 a2x2 c2 x2b2 d2 a3x1a3 a4x2a4 c5 for adjointable operators between hilbert c modules and provide an expression for the general hermitian solution to the system we present necessary and sufficient conditions for the existence of a unique hermitian solution to the systems a1x1 c1 x1b1 d1 and a3x1a3 c5 of adjointable operators between hilbert c modules several examples are given to explain the use of the theory some of the findings of this paper extend some known results in the literature

on nonparametric maximum likelihood estimation with interval censoring and left truncation summary a graph theoretical approach is employed to describe the support set of the nonparametric maximum likelihood estimator for the cumulative distribution function given interval censored and left truncated data a necessary and sufficient condition for the existence of a nonparametric maximum likelihood estimator is then derived two previously analysed data sets are revisited

uniform distribution of eigenfunctions on compact hyperbolic surfaces on demontre que les fonctions propres k du laplacien sur une surface hyperbolique compacte x devient uniformement distribuee sur x quand k

moore penrose inverses of partitioned adjointable operators on hilbert c modules abstract let a be a c algebra h i i 1 2 3 be three hilbert a modules a 1 l h 1 h 3 and a 2 l h 2 h 3 where l h 1 h 3 resp l h 2 h 3 is the set of the adjointable operators from h 1 to h 3 resp h 2 to h 3 for such two operators a 1 and a 2 a 1 2 partitioned operator a a 1 a 2 can be induced by letting a h 1 h 2 a 1 h 1 a 2 h 2 for h i h i i 1 2 in this paper several formulae for the moore penrose inverse a of a are derived and an approach to constructing the weighted moore penrose inverse from the non weighted case is provided in particular the main result of udwadia and phohomsiri f e udwadia p phohomsiri recursive formulas for the generalized lm inverse of a matrix j optimiz theory app 131 2006 1 16 is generalized

the analysis of asthma control under a markov assumption with use of covariates in studies of disease states and their relation to evolution data on the state are usually obtained at in frequent time points during follow up moreover in many applications there are measured covariates on each individual under study and interest centres on the relationship between these covariates and the disease evolution we developed a continuous time markov model with use of time dependent covariates and a markov model with piecewise constant intensities to model asthma evolution methods to estimate the effect of covariates on transition intensities to test the assumption of time homogeneity and to assess goodness of fit are proposed we apply these methods to asthma control we consider a three state model and we discuss in detail the analysis of asthma control evolution copyright 2003 john wiley sons ltd