a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

new multi sample nonparametric tests for panel count data this paper considers the problem of multi sample nonparametric comparison of counting processes with panel count data which arise naturally when recurrent events are considered such data frequently occur in medical follow up studies and reliability experiments for example for the problem considered we construct two new classes of nonparametric test statistics based on the accumulated weighted difierences between the rates of increase of the estimated mean functions of the counting processes over observation times wherein the nonparametric maximum likelihood approach is used to estimate the mean function instead of the nonparametric maximum pseudolikelihood the asymptotic distributions of the proposed statistics are derived and their flnite sample properties are examined through monte carlo simulations the simulation results show that the proposed methods work quite well and are more powerful than the existing test procedures two real data sets are analyzed and presented as illustrative examples 1 introduction consider a study that concerns some recurrent event and suppose that each subject in the study gives rise to a counting process n t denoting the total number of occurrences of the event of interest up to time t also suppose that for each subject observations include only the values of n t at discrete observation times or the numbers of occurrences of the event between the observation times such data are usually referred to as panel count data sun and kalb eisch 13 wellner and zhang 17 our focus here will be on the situation when such a study involves k 2 groups let l t denote the mean function of n t corresponding to the lth group for l 1 k the problem of interest is then to test the hypothesis h0 1 t k t a number of authors have discussed the analysis of recurrent event data when each subject in the study is observed continuously over an interval or when the exact times of occurrences of the recurrent event are known for example the book by andersen borgan gill and keiding 1 presents

degradation in common dynamic environments abstractdegradation studies are often used to assess reliability of products subject to degradation induced soft failures because of limited test resources several test subjects may have to share a test rig and have their degradation measured by the same operator the common environments experienced by subjects in the same group introduce significant interindividual correlations in their degradation which is known as the block effect in the present article the wiener process is used to model product degradation and the group specific random environments are captured using a stochastic time scale both semiparametric and parametric estimation procedures are developed for the model maximum likelihood estimations of the model parameters for both the semiparametric and parametric models are obtained with the help of the em algorithm performance of the maximum likelihood estimators is validated through large sample asymptotics and small sample simulations the proposed models are illustrated by an appl

modelling dependence within joint tail regions standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max stability a particular form of joint tail dependence we develop joint tail models based on a broader class of dependence structure which provides a natural link between max stable models and weaker forms of dependence including independence and negative association this approach overcomes many of the problems that are encountered with standard methods and is the basis for a poisson process representation that generalizes existing bivariate results we apply the new techniques to simulated and environmental data and demonstrate the marked advantage that the new approach offers for joint tail extrapolation

an inverse gaussian process model for degradation data this paper studies the maximum likelihood estimation of a class of inverse gaussian process models for degradation data both the subject to subject heterogeneity and covariate information can be incorporated into the model in a natural way the em algorithm is used to obtain the maximum likelihood estimators of the unknown parameters and the bootstrap is used to assess the variability of the maximum likelihood estimators simulations are used to validate the method the model is fitted to laser data and corresponding goodness of fit tests are carried out failure time distributions in terms of degradation level passages are calculated and illustrated the supplemental materials for this article are available online

estimation of the mean function with panel count data using monotone polynomial splines we study nonparametric likelihood based estimators of the mean function of counting processes with panel count data using monotone polynomial splines the generalized rosen algorithm proposed by zhang jamshidian 2004 is used to compute the estimators we show that the proposed spline likelihood based estimators are consistent and that their rate of convergence can be faster than n 1 3 simulation studies with moderate samples show that the estimators have smaller variances and mean squared errors than their alternatives proposed by wellner zhang 2000 a real example from a bladder tumour clinical trial is used to illustrate this method

bayesian modeling of multiple lesion onset and growth from interval censored data summary in studying rates of occurrence and progression of lesions or tumors it is typically not possible to obtain exact onset times for each lesion instead data consist of the number of lesions that reach a detectable size between screening examinations along with measures of the size severity of individual lesions at each exam time this interval censored data structure makes it difficult to properly adjust for the onset time distribution in assessing covariate effects on rates of lesion progression this article proposes a joint model for the multiple lesion onset and progression process motivated by cross sectional data from a study of uterine leiomyoma tumors by using a joint model one can potentially obtain more precise inferences on rates of onset while also performing onset time adjusted inferences on lesion severity following a bayesian approach we propose a data augmentation markov chain monte carlo algorithm for posterior computation

a pseudolikelihood method for analyzing interval censored data summary we introduce a method based on a pseudolikelihood ratio for estimating the distribution function of the survival time in a mixed case interval censoring model in a mixed case model an individual is observed a random number of times and at each time it is recorded whether an event has happened or not one seeks to estimate the distribution of time to event we use a poisson process as the basis of a likelihood function to construct a pseudolikelihood ratio statistic for testing the value of the distribution function at a fixed point and show that this converges under the null hypothesis to a known limit distribution that can be expressed as a functional of different convex minorants of a two sided brownian motion process with parabolic drift construction of confidence sets then proceeds by standard inversion the computation of the confidence sets is simple requiring the use of the pool adjacent violators algorithm or a standard isotonic regression algorithm we also illustrate the superiority of the proposed method over competitors based on resampling techniques or on the limit distribution of the maximum pseudolikelihood estimator through simulation studies and illustrate the different methods on a dataset involving time to hiv seroconversion in a group of haemophiliacs

on the exceedance point process for a stationary sequence it is known that the exceedance points of a high level by a stationary sequence are asymptotically poisson as the level increases under appropriate long range and local dependence conditions when the local dependence conditions are relaxed clustering of exceedances may occur based on poisson positions for the clusters in this paper a detailed analysis of the exceedance point process is given and shows that under wide conditions any limiting point process for exceedances is necessarily compound poisson more generally the possible random measure limits for normalized exceedance point processes are characterized sufficient conditions are also given for the existence of a point process limit the limiting distributions of extreme order statistics are derived as corollaries

markov chain models for threshold exceedances in recent research on extreme value statistics there has been an extensive development of threshold methods first in the univariate case and subsequently in the multivariate case as well in this paper an alternative methodology for extreme values of univariate time series is developed by assuming that the time series is markovian and using bivariate extreme value theory to suggest appropriate models for the transition distributions a new likelihood representation for threshold methods is presented which we apply to a markovian time series an important motivation for developing this kind of theory is the possibility of calculating probability distributions for functionals of extreme events we address this issue by showing how a theory of compound poisson limits for additive functionals can be combined with simulation to obtain numerical solutions for problems of practical interest the methods are illustrated by application to temperature data

semiparametric estimation methods for panel count data using monotone b splines we study semiparametric likelihood based methods for panel count data with proportional mean model e t z 0 t exp 0tz where z is a vector of covariates and 0 t is the baseline mean function we propose to estimate 0 t and 0 jointly with 0 t approximated by monotone b splines and to compute the estimators using generalized rosen algorithm proposed by jamshidian 2004 we show that the proposed spline based likelihood estimators of 0 t are consistent with a possibly better than n1 3 convergence rate if 0 t is sufficiently smooth the normality of the estimators of 0 is also established comparisons between the proposed estimators and their alternatives studied in wellner and zhang 2007 are made through simulations studies regarding their finite sample performance and computational complexity a real example from a bladder tumor clinical trial is used to illustrate the methods

on the zeros of a polynomial and its derivatives if p z is univariate polynomial with complex coefficients having all its zeros inside the closed unit disk then the gauss lucas theorem states that all zeros of p z lie in the same disk we study the following question what is the maximum distance from the arithmetic mean of all zeros of p z to a nearest zero of p z we obtain bounds for this distance depending on degree we also show that this distance is equal to 1 for polynomials of degree 3 and polynomials with real zeros

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

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

likelihood based inference for current status data on a grid a boundary phenomenon and an adaptive inference procedure in this paper we study the nonparametric maximum likelihood estimator npmle for an event time distribution function at a point in the current status model with observation times supported on a grid of potentially unknown sparsity and with multiple subjects sharing the same observation time this is of interest since observation time ties occur frequently with current status data the grid resolution is specified ascn withc 0 being a scaling constant and 0 regulating the sparsity of the grid relative to the number of subjects n the asymptotic behavior falls into three cases depending on regular normal type asymptotics obtain for 1 3 and 1 3 serves as a boundary at which the transition happens the limit distribution at the boundary is different from either of the previous cases and converges weakly to those obtained with 2 0 1 3 and 2 1 3 1 asc goes to1 and 0 respectively this weak convergence allows us to develop an adaptive procedure to construct confidence intervals for the value of the event time distribution at a point of interest without needing to know or estimate which is of enormous advantage from the perspective of inference a simulation study of the adaptive procedure is presented

limit theorems for empirical processes of cluster functionals let x n i 1 i n m is an element of n be a triangular array of row wise stationary r d valued random variables we use a blocks method to define clusters of extreme values the rows of x n i are divided into m n blocks y n j and if a block contains at least one extreme value the block is considered to contain a cluster the cluster starts at the first extreme value in the block and ends at the last one the main results are uniform central limit theorems for empirical processes z n f 1 root nv n sigma mn j 1 f y n y j ef y n y j for v n p x n x i not equal 0 and f belonging to classes of cluster functionals that is functions of the blocks y n y j which only depend on the cluster values and which are equal to 0 if y n y j does not contain a cluster conditions for finite dimensional convergence include beta mixing suitable lindeberg conditions and convergence of covariances to obtain full uniform convergence we use either bracketing entropy or bounds on covering numbers with respect to a random semi metric the latter makes it possible to bring the powerful vapnik cervonenkis theory to bear applications include multivariate tail empirical processes and empirical processes of cluster values and of order statistics in clusters although our main field of applications is the analysis of extreme values the theory can be applied more generally to rare events occurring for example in nonparametric curve estimation

a semiparametric pseudolikelihood estimation method for panel count data in this paper we study panel count data with covariates a semiparametric pseudolikelihood estimation method is proposed based on the assumption that given a covariate vector z the underlying counting process is a nonhomogeneous poisson process with the conditional mean function given by e n t z 0 t exp 0 z the proposed estimation method is shown to be robust in the sense that the estimator converges to its true value regardless of whether or not n t is a conditional poisson process given z an iterative numerical algorithm is devised to compute the semiparametric maximum pseudolikelihood estimator of 0 0 the algorithm appears to be attractive especially when 0 is a high dimensional regression parameter some simulation studies are conducted to validate the method finally the method is applied to a real dataset from a bladder tumour study

a semiparametric likelihood based method for regression analysis of mixed panel count data panel count data arise when each study subject is observed only at discrete time points in a recurrent event study and only the numbers of the event of interest between observation time points are recorded sun and zhao 2013 however sometimes the exact number of events between some observation times is unknown and what we know is only whether the event of interest has occurred in this article we will refer this type of data to as mixed panel count data and propose a likelihood based semiparametric regression method for their analysis by using the nonhomogeneous poisson process assumption however we establish the asymptotic properties of the resulting estimator by employing the empirical process theory and without using the poisson assumption also we conduct an extensive simulation study which suggests that the proposed method works well in practice finally the method is applied to a childhood cancer survivor study that motivated this study

statistics for near independence in multivariate extreme values we propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence we examine inference under the model and develop tests for independence of extremes of the marginal variables both when the thresholds are fixed and when they increase with the sample size motivated by results obtained from this model we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases a new parameter which governs the form of dependence is of fundamental importance to this characterisation by estimating this parameter we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models the methods are demonstrated through simulation and by analysing two previously published data sets

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

two estimators of the mean of a counting process with panel count data we study two estimators of the mean function of a countingprocess based on panel count data the setting for panel count data is one in which n independent subjects each with a counting process with common mean function are observed at several possibly different times duringa study following a model proposed by schick and yu we allow the number of observation times and the observation times themselves to be random variables our goal is to estimate the mean function of the counting process we show that the estimator of the mean function proposed by sun and kalbfleisch can be viewed as a pseudo maximum likelihood estimator when a non homogeneous poisson process model is assumed for the counting process we establish consistency of both the nonparametric pseudo maximum likelihood estimator of sun and kalbfleisch and the full maximum likeli hood estimator even if the underlying counting process is not a poisson process we also derive the asymptotic distribution of both estimators at a fixed time t and compare the resulting theoretical relative efficiency with finite sample relative efficiency by way of a limited monte carlo study

regression analysis of panel count data with dependent observation times panel count data often occur in long term studies that concern occurrence rate of a recurrent event methods have been proposed for regression analysis of panel count data but most of the existing research focuses on situations where observation times are independent of longitudinal response variables and therefore rely on conditional inference procedures given the observation times this article considers a different situation where the independence assumption may not hold that is the observation times and the response variable may be correlated for inference estimating equation approaches are proposed for estimation of regression parameters and both large and finite sample properties of the proposed estimates are established an illustrative example from a cancer study is provided

estimating a unimodal distribution from interval censored data in this article we consider three nonparametric maximum likelihood estimators based on mixed case interval censored data apart from the unrestricted estimator we consider estimators under the assumption that the underlying distribution function of event times is concave or unimodal characterizations of the estimates are derived and algorithms are proposed for their computation the estimators are shown to be asymptotically consistent and the benefits of additional constraints are illustrated through simulations finally the estimators are used as an ingredient in a nonparametric comparison of two samples

stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise in this work we introduce a new method to prove the existence and uniqueness of a variational solution to the stochastic nonlinear diffusion equation rm d x t rm div left frac nabla x t nabla x t right rm d t x t rm d w t rm in 0 infty times mathcal o where mathcal o is a bounded and open domain in mathbb r n n geqq 1 and w t is a wiener process of the form w t sum infty k 1 mu k e k beta k t e k in c 2 overline mathcal o cap h 1 0 mathcal o and beta k k in mathbb n are independent brownian motions this is a stochastic diffusion equation with a highly singular diffusivity term one main result established here is that for all initial conditions in l 2 mathcal o it is well posed in a class of continuous solutions to the corresponding stochastic variational inequality thus one obtains a stochastic version of the minimal total variation flow the new approach developed here also allows us to prove the finite time extinction of solutions in dimensions 1 leqq n leqq3 which is another main result of this work

extreme values for stationary and markov sequences soit x n n 1 2 une suite strictement stationnaire de variables aleatoires a valeurs reelles soit m i j max x i 1 x j et m n m 0 n soit c n une suite de nombres reels on montre sous des circonstances generales que p m n c n p x 1 c n np mu 1 u u p u n cu n xu 1 cu n o pour toute suite pn satisfaisant certaines conditions de taux de croissance

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

meta analysis of studies with bivariate binary outcomes a marginal beta binomial model approach when conducting a meta analysis of studies with bivariate binary outcomes challenges arise when the within study correlation and between study heterogeneity should be taken into account in this paper we propose a marginal beta binomial model for the meta analysis of studies with binary outcomes this model is based on the composite likelihood approach and has several attractive features compared with the existing models such as bivariate generalized linear mixed model chu and cole 2006 and sarmanov beta binomial model chen et al 2012 the advantages of the proposed marginal model include modeling the probabilities in the original scale not requiring any transformation of probabilities or any link function having closed form expression of likelihood function and no constraints on the correlation parameter more importantly because the marginal beta binomial model is only based on the marginal distributions it does not suffer from potential misspecification of the joint distribution of bivariate study specific probabilities such misspecification is difficult to detect and can lead to biased inference using currents methods we compare the performance of the marginal beta binomial model with the bivariate generalized linear mixed model and the sarmanov beta binomial model by simulation studies interestingly the results show that the marginal beta binomial model performs better than the sarmanov beta binomial model whether or not the true model is sarmanov beta binomial and the marginal beta binomial model is more robust than the bivariate generalized linear mixed model under model misspecifications two meta analyses of diagnostic accuracy studies and a meta analysis of case control studies are conducted for illustration

computational methods for multiplicative intensity models using weighted gamma processes proportional hazards marked point processes and panel count data we develop computational procedures for a class of bayesian nonparametric and semiparametric multiplicative intensity models incorporating kernel mixtures of spatial weighted gamma measures a key feature of our approach is that explicit expressions for posterior distributions of these models share many common structural features with the posterior distributions of bayesian hierarchical models using the dirichlet process using this fact along with an approximation for the weighted gamma process we show that with some care one can adapt efficient algorithms used for the dirichlet process to this setting we discuss blocked gibbs sampling procedures and polya urn gibbs samplers we illustrate our methods with applications to proportional hazard models poisson spatial regression models recurrent events and panel count data

inference on the tail process with application to financial time series modeling abstract to draw inference on serial extremal dependence within heavy tailed markov chains drees et al 2015 proposed nonparametric estimators of the spectral tail process the methodology can be extended to the more general setting of a stationary regularly varying time series the large sample distribution of the estimators is derived via empirical process theory for cluster functionals the finite sample performance of these estimators is evaluated via monte carlo simulations moreover two different bootstrap schemes are employed which yield confidence intervals for the pre asymptotic spectral tail process the stationary bootstrap and the multiplier block bootstrap the estimators are applied to stock price data to study the persistence of positive and negative shocks

proof of the sendov conjecture for polynomials of degree at most eight abstract the well known sendov conjecture asserts that if all the zeros of a polynomialplie in the closed unit disk then there must be a critical point ofpwithin unit distance of each zero a method is presented which proves this conjecture for polynomials of degreen 8 or for arbitrary degreenif there are at most eight distinct zeros

statistics of heteroscedastic extremes we extend classical extreme value theory to non identically distributed observations when the tails of the distribution are proportional much of extreme value statistics remains valid the proportionality function for the tails can be estimated non parametrically along with the common extreme value index for a positive extreme value index joint asymptotic normality of both estimators is shown they are asymptotically independent we also establish asymptotic normality of a forecasted high quantile and develop tests for the proportionality function and for the validity of the model we show through simulations the good performance of the procedures and also present an application to stock market returns a main tool is the weak convergence of a weighted sequential tail empirical process

nonparametric k sample tests with panel count data we study the nonparametric k sample test problem with panel count data the asymptotic normality of a smooth functional of the nonparametric maximum pseudolikelihood estimator wellner zhang 2000 is established under some mild conditions we construct a class of easy to implement nonparametric tests for comparing mean functions of k populations based on this asymptotic normality we conduct various simulations to validate and compare the tests the simulations show that the tests perform quite well and generally have good power to detect differences among the mean functions the method is illustrated with a real life example

ito s formula in umd banach spaces and regularity of solutions of the zakai equation using the theory of stochastic integration for processes with values in a umd banach space developed recently by the authors an ito formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in umd banach spaces the abstract results are applied to prove regularity in space and time of the solutions of the zakai equation

analysis of gap times based on panel count data with informative observation times and unknown start time abstractin biomedical studies one is often interested in repeat events with longitudinal observations occurring only intermittently resulting in panel count data the first stage of labor measured through unit increments of cervical dilation in pregnant women provides such an example obstetricians are interested in assessing the gap time distribution of per unit increments of cervical dilation for better management of labor process typically only intermittent medical examinations for cervical dilation occur after already dilated women get admitted to hospital the observation frequency is very likely correlated to how fast slow she dilates thus one could view such data as panel count data with informative observation times and unknown start time here we propose semiparametric proportional rate models for the event process and the observation process with a multiplicative subject specific frailty variable capturing the correlation between the two processes inference procedures for the gap ti

marginal analysis of panel counts through estimating functions we develop nonparametric estimation procedures for the marginal mean function of a counting process based on periodic observations using two types of self consistent estimating equations the first is derived from the likelihood studied in wellner zhang 2000 assuming a poisson counting process and gives a nondecreasing estimator which is the same as the nonparametric maximum likelihood estimator of wellner zhang and thus is consistent without the poisson assumption motivated by the construction of parametric generalized estimating equations the second type is a set of data adaptive quasi score functions which are likelihood estimating functions under a mixed poisson assumption we evaluate the procedures via simulation and illustrate them with the data from a bladder cancer study

stochastic nonlinear schrodinger equations abstract this paper is devoted to the well posedness of stochastic nonlinear schrodinger equations in the energy space h 1 r d and is a continuation of our recent work barbu et al 2014 we allow general complex coefficients in the noise thus covering both the conservative and non conservative case the latter being important to include quantum measurement effects in the underlying physical model we consider both focusing and defocusing nonlinearities and prove global well posedness in h 1 r d including also the pathwise continuous dependence on initial conditions with exponents of the nonlinearity in exactly the same sharp range as in the deterministic case in particular in the special conservative case this work improves earlier results in de bouard and debussche 2003 where the critical exponents could not be reached for d 6 in the defocusing and for d 4 in the focusing case respectively moreover the local existence uniqueness and blowup alternative are also established for the energy critical case the approach presented here is mainly based on the rescaling approach already used in barbu et al 2014 to study the l 2 case and also on the strichartz estimates established in marzuola et al 2008 for large perturbations of the laplacian

on inviscid limits for the stochastic navier stokes equations and related models we study inviscid limits of invariant measures for the 2d stochastic navier stokes equations as shown by kuksin j stat phys 115 1 2 469 492 2004 the noise scaling sqrt nu is the only one which leads to non trivial limiting measures which are invariant for the 2d euler equations using a moser type iteration for stochastic drift diffusion equations we show that any limiting measure mu 0 is in fact supported on bounded vorticities relationships of mu 0 to the long term dynamics of 2d euler in l infty with the weak topology are discussed we also obtain a drift independent modulus of continuity for a stationary deterministic model problem which leads us to conjecture that in fact mu 0 is supported on c 0 moreover in view of the batchelor krainchnan 2d turbulence theory we consider inviscid limits for a weakly damped stochastic navier stokes equation in this setting we show that only an order zero noise scaling with respect to leads to a nontrivial limiting measure in the inviscid limit

two likelihood based semiparametric estimation methods for panel count data with covariates we consider estimation in a particular semiparametric regression model for the mean of a counting process with panel count data the basic model assumption is that the conditional mean function of the counting process is of the form efn t jzg exp fl t z 0 t where z is a vector of covariates and 0 is the baseline mean function the panel count observation scheme involves observation of the counting processn for an individual at a random number k of random time points both the number and the locations of these time points may difier across individuals we study semiparametric maximum pseudo likelihood and maximum likelihood estimators of the unknown parameters fl0 0 derived on the basis of a nonhomogeneous poisson process assumption the pseudo likelihood estimator is fairly easy to compute while the maximum likelihood estimator poses more challenges from the computational perspective we study asymptotic properties of both estimators assuming that the proportional mean model holds but dropping the poisson process assumption used to derive the estimators in particular we establish asymptotic normality for the estimators of the regression parameter fl0 under appropriate hypotheses the results show that our estimation procedures are robust in the sense that the estimators converge to the truth regardless of the underlying counting process

analysing panel count data with informative observation times in this paper we study panel count data with informative observation times we assume nonparametric and semiparametric proportional rate models for the underlying event process where the form of the baseline rate function is left unspecified and a subject specific frailty variable inflates or deflates the rate function multiplicatively the proposed models allow the event processes and observation times to be correlated through their connections with the unobserved frailty moreover the distributions of both the frailty variable and observation times are considered as nuisance parameters the baseline rate function and the regression parameters are estimated by maximising a conditional likelihood function of observed event counts and solving estimation equations large sample properties of the proposed estimators are studied numerical studies demonstrate that the proposed estimation procedures perform well for moderate sample sizes an application to a bladder tumour study is presented

robust nonparametric estimation of monotone regression functions with interval censored observations nonparametric estimation of monotone regression functions is a classical problem of practical importance robust estimation of monotone regression functions in situations involving interval censored data is a challenging yet unresolved problem herein we propose a nonparametric estimation method based on the principle of isotonic regression using empirical process theory we show that the proposed estimator is asymptotically consistent under a specific metric we further conduct a simulation study to evaluate the performance of the estimator in finite sample situations as an illustration we use the proposed method to estimate the mean body weight functions in a group of adolescents after they reach pubertal growth spurt

bivariate threshold methods for extremes summary an extension of the threshold method for extreme values is developed to consider the joint distribution of extremes of two variables the methodology is based on the point process representation of bivariate extremes both parametric and nonparametric models are considered the simplest case to handle is that in which both marginal distributions are known for the more realistic case in which the marginal distributions are unknown a mixed parametric nonparametric method is proposed the techniques are illustrated with data on sulphate and nitrate levels taken from a major study of acid rain

a hybrid algorithm for computation of the nonparametric maximum likelihood estimator from censored data abstract we present a hybrid algorithm for nonparametric maximum likelihood estimation from censored data when the log likelihood is concave the hybrid algorithm uses a composite algorithmic mapping combining the expectation maximization em algorithm and the modified iterative convex minorant icm algorithm global convergence of the hybrid algorithm is proven the iterates generated by the hybrid algorithm are shown to converge to the nonparametric maximum likelihood estimator npmle unambiguously numerical simulations demonstrate that the hybrid algorithm converges more rapidly than either of the em or the naive icm algorithm for doubly censored data the speed of the hybrid algorithm makes it possible to accompany the npmle with bootstrap confidence bands

regression analysis of panel count data with covariate dependent observation and censoring times panel count data often occur in a long term study where the primary end point is the time to a specific event and each subject may experience multiple recurrences of this event furthermore suppose that it is not feasible to keep subjects under observation continuously and the numbers of recurrences for each subject are only recorded at several distinct time points over the study period moreover the set of observation times may vary from subject to subject in this paper regression methods which are derived under simple semiparametric models are proposed for the analysis of such longitudinal count data especially we consider the situation when both observation and censoring times may depend on covariates the new procedures are illustrated with data from a well known cancer study

a large deviations approach to limit theory for heavy tailed time series in this paper we propagate a large deviations approach for proving limit theory for generally multivariate time series with heavy tails we make this notion precise by introducing regularly varying time series we provide general large deviation results for functionals acting on a sample path and vanishing in some neighborhood of the origin we study a variety of such functionals including large deviations of random walks their suprema the ruin functional and further derive weak limit theory for maxima point processes cluster functionals and the tail empirical process one of the main results of this paper concerns bounds for the ruin probability in various heavy tailed models including garch stochastic volatility models and solutions to stochastic recurrence equations

inverse spectral problem for normal matrices and the gauss lucas theorem we establish an analog of the cauchy poincare interlacing theorem for normal matrices in terms of majorization and we provide a solution to the corresponding inverse spectral problem using this solution we generalize and extend the gauss lucas theorem and prove the old conjecture of de bruijn springer on the location of the roots of a complex polynomial and its derivative and an analog of rolle s theorem conjectured by schoenberg

mixed poisson likelihood regression models for longitudinal interval count data summary in many longitudinal studies it is desired to estimate and test the rate over time of a particular recurrent event often only the event counts corresponding to the elapsed time intervals between each subject s successive observation times and baseline covariate data are available the intervals may vary substantially in length and number between subjects so that the corresponding vectors of counts are not directly comparable a family of poisson likelihood regression models incorporating a mixed random multiplicative component in the rate function of each subject is proposed for this longitudinal data structure a related empirical bayes estimate of random effect parameters is also described these methods are illustrated by an analysis of dyspepsia data from the national cooperative gallstone study

likelihood based inference for monotone response models the behavior of maximum likelihood estimates mles and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied this class of problems differs radically from the usual parametric or semiparametric situations in that the mle of the monotone function at a point converges to the truth at rate n 1 3 slower than the usual n rate with a non gaussian limit distribution a framework for likelihood based estimation of monotone functions is developed and limit theorems describing the behavior of the mles and the likelihood ratio statistic are established in particular the likelihood ratio statistic is found to be asymptotically pivotal with a limit distribution that is no longer 2 but can be explicitly characterized in terms of a functional of brownian motion applications of the main results are presented and potential extensions discussed

stochastic nonlinear schrodinger equations no blow up in the non conservative case abstract this paper is devoted to the study of noise effects on blow up solutions to stochastic nonlinear schrodinger equations it is a continuation of our recent work 2 where the local well posedness is established in h 1 also in the non conservative critical case here we prove that in the non conservative focusing mass super critical case by adding a large multiplicative gaussian noise with high probability one can prevent the blow up on any given bounded time interval 0 t 0 t moreover in the case of spatially independent noise the explosion even can be prevented with high probability on the whole time interval 0 the noise effects obtained here are completely different from those in the conservative case studied in 5

the analysis of current status data on point processes abstract this article considers the analysis of event count data in which each subject is observed at only one time point and no information is available on subjects between their entry time and observation points this type of data often referred to as current status data arises frequently for example in demography epidemiology and reliability studies statistical methods for the analysis of current status data from point processes are proposed specifically a statistic for testing the equality of the mean functions of point processes is presented and its asymptotic distribution obtained for illustration the proposed method is used to analyze multiple tumor data from a tumorgenicity experiment with focus on the comparison of tumor growth rates in male and female rats the adequacy of the asymptotic distribution of the test statistic is evaluated in a small simulation study power comparisons with the usual parametric model are also obtained finally some possible directions for further research

extremes and local dependence in stationary sequences extensions of classical extreme value theory to apply to stationary sequences generally make use of two types of dependence restriction a a weak mixing condition restricting long range dependence b a local condition restricting the clustering of high level exceedances

likelihood ratio tests for monotone functions we study the problem of testing for equality at a fixed point in the setting of nonparametric estimation of a monotone function the likelihood ratio test for this hypothesis is derived in the particular case of interval censoring or current status data and its limiting distribution is obtained the limiting distribution is that of the integral of the difference of the squared slope processes corresponding to a canonical version of the problem involving brownian motion t 2 and greatest convex minorants thereof inversion of the family of tests yields pointwise confidence intervals for the unknown distribution function we also study the behavior of the statistic under local and fixed alternatives 1 introduction we shall consider likelihood ratio tests and the corresponding confidence intervals in a class of problems involving nonparametric estimation of a monotone function the problem in each case involves testing the null hypothesis h 0 that the monotone function has a particular value at afixed point t 0 in the domain of the function of course with each testing problem there is a related problem of finding confidence intervals here are some examples of the problems we have in mind

maximal polynomials and the ilieff sendov conjecture in this paper we consider those complex polynomials which have all their roots in the unit disk one fixed root and all the roots of their first derivatives as far as possible from a fixed point we conjecture that any such polynomial has all the roots of its derivative on a circle centered at the fixed point and as many of its own roots as possible on the unit circle we prove a part of this conjecture and use it to define an algorithm for constructing some of these polynomials with this algorithm we investigate the 1962 conjecture of sendov and the 1969 conjecture of goodman rahman and ratti and independently schmeisser obtaining counterexamples of degrees 6 8 10 and 12 for the latter

ito s formula for the lp norm of stochastic w 1 _ p valued processes we prove ito s formula for the lp norm of a stochastic w 1 p valued processes appearing in the theory of spdes in divergence form

nonparametric comparison for panel count data with unequal observation processes summary this article considers nonparametric comparison of several treatment groups based on panel count data which often occur in among others medical follow up studies and reliability experiments concerning recurrent events for the problem most of the existing procedures require that observation processes are identical across different treatment groups among other requirements we propose a new class of nonparametric test procedures that allow different observation processes the new test statistics are constructed based on the integrated weighted differences between the estimated mean functions of the underlying recurrent event processes the asymptotic distributions of the proposed test statistics are established and their finite sample properties are examined through monte carlo simulations which indicate that the proposed approach works well for practical situations an illustrative example is provided

a semiparametric model for regression analysis of interval censored failure time data left right and interval censored response time data arise in a variety of settings including the analyses of data from laboratory animal carcinogenicity experiments clinical trials and longitudinal studies for such incomplete data the usual regression techniques such as the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model are inapplicable in this paper we present a method for regression analysis which accommodates interval censored data we present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy a small animal tumorigenicity study and a clinical trial

a quadratic approximation to the sendov radius near the unit circle define s n to be the set of complex polynomials of degree n 2 with all roots in the unit disk and at least one root at for a polynomial p define p to be the distance between and the closest root of the derivative p finally define r n sup p p e s n in this notation a conjecture of bl sendov claims that r n 1 in this paper we investigate sendov s conjecture near the unit circle by computing constants c 1 and c 2 depending only on n such that r n 1 c 1 1 c 2 1 2 for near 1 we also consider some consequences of this approximation including a hint of where one might look for a counterexample to sendov s conjecture

a structural break test for extremal dependence in β mixing random vectors summarywe derive a structural break test for extremal dependence in beta mixing possibly high dimensional random vectors with either asymptotically dependent or asymptotically independent components existing tests require serially independent observations with asymptotically dependent components to avoid estimating a long run variance we use self normalization which obviates the need to estimate the coefficient of tail dependence when components are asymptotically independent simulations show favourable empirical size and power of the test which we apply to s p 500 and dax log returns we find evidence for one break in the coefficient of tail dependence for the upper and lower joint tail at the beginning of the 2007 08 financial crisis leading to more extremal co movement

models for the extremes of markov chains the modelling of extremes of a time series has progressed from the assumption of independent observations to more realistic forms of temporal dependence in this paper we focus on markov chains deriving a class of models for their joint tail which allows the degree of clustering of extremes to decrease at high levels overcoming a key limitation in current methodologies theoretical aspects of the model are examined and a simulation algorithm is developed through which the stochastic properties of summaries of the extremal txhaviour of the chain are evaluated the approach is illustrated through a simulation study of extremal events of gaussian autoregressive processes and an application to temperature data