survival analysis using a scale change random effects model abstract frailty models are effective in broadening the class of survival models and inducing dependence in multivariate survival distributions in proportional hazards the random effect multiplies the hazard function the scale change model incorporates unobserved heterogeneity through a random effect that enters the baseline hazard function to change the time scale we interpret this random effect as frailty or other unobserved risks that create heterogeneity in the population this model produces a wide range of shapes for univariate survival and hazard functions we extend this model to multivariate survival data by assuming that members of a group share a common random effect this structure induces association among the survival times in a group and provides alternative association structures to the proportional hazards frailty model we present parametric and semiparametric estimation techniques and illustrate these methods with an example

a likelihood ratio test for stationarity of rating transitions abstract we study the time stationarity of rating transitions modelled by a time continuous discrete state markov process and derive a likelihood ratio test for multiple markov processes from a multiplicative intensity model maximum likelihood parameter estimates can be written as martingale transform of the processes counting transitions between the rating states so that the profile partial likelihood ratio is asymptotically 2 distributed an application to an internal rating data set reveals highly significant instationarity

numerical analysis of a nonlinear evolutionary system with applications in viscoplasticity we consider numerical approximations of a class of abstract nonlinear evolutionary systems arising in the study of quasi static frictional contact problems for elastic viscoplastic materials both semidiscrete and fully discrete schemes are analyzed strong convergence of both approximations is established under minimal solution regularity the results are applied to two particular frictional contact problems for viscoplastic bodies where the finite element method is employed to discretize the spatial domain under additional regularity assumptions on the exact solution some error estimates are derived

non parametric testing of discrete panel data models abstract the stochastic structures of the homogeneous multinomial process the heterogeneous multinomial process the markov chain and the heterogeneous markov chain are analyzed within a discrete panel data framework a general theoretical and computationally tractible framework to test the stochastic structures is proposed our testing framework is non parametric in nature and can incorporate the presence of time varying exogenous variables and can be applied to the general polychotomous response cases asymptotically optimal tests can be easily implemented the lm tests for the stochastic structures are simply to test certain orthogonality conditions with residuals

regression models for positive random variables abstract many variables in economics finance and other disciplines are positive and nonnormally distributed this paper considers a regression model with a specification of residuals which allows great flexibility for the distribution of the dependent variable these distributions include the exponential weibull gamma lognormal burr generalized gamma generalized beta type 2 and others as special cases the specification provides a general parametric form for modeling observed and unobserved heterogeneity as well as including the possibility of increasing decreasing constant and shaped hazard functions the models are used to study the distribution and hazard functions of welfare duration and the relationship between these spells and various demographic characteristics

an elastic viscoplastic quasistatic contact problem existence and uniqueness of a weak solution in this paper the contact between an elastic viscoplastic body and a deformable obstacle is studied the effect of the damage due to internal tension or compression and caused by the opening and growth of micro cracks and micro cavities is also considered the variational formulation leads to a coupled system of evolutionary equations an existence and uniqueness result is established by using approximate problems the pseudomonotone operators theory schauder fixed point theorem and a comparison result

an elastic viscoplastic quasistatic contact problem with damage abstract in this paper the contact between an elastic viscoplastic body and a deformable obstacle is studied the effect of the damage due to tension or compression is also considered the variational formulation leads to a coupled system of evolutionary equations for which an existence and uniqueness result is stated then a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are obtained and as a consequence the convergence of the algorithm is deduced finally some numerical simulations are presented to demonstrate the accuracy of the algorithm

numerical analysis and simulations of a quasistatic frictional contact problem with damage in viscoelasticity we consider a quasistatic problem which models the bilateral contact between a viscoelastic body and a foundation taking into account the damage and the friction the damage which results from tension or compression is then involved in the constitutive law and it is modelled using a nonlinear parabolic inclusion the variational problem is formulated as a coupled system of evolutionary equations for which we state the existence of a unique solution then we introduce a fully discrete scheme using the finite element method to approximate the spatial variable and the euler scheme to discretize the time derivatives error estimates are derived and under suitable regularity hypotheses the convergence of the numerical scheme obtained finally a numerical algorithm and results are presented for some two dimensional examples

random effects weibull regression model for occupational lifetime abstract with great interest we read the recent publication of sohn et al sohn s y chang i s moon t h 2007 random effects weibull regression model for occupational lifetime european journal of operational research 179 124 131 on a weibull regression model with random effects for modelling occupational lifetime we congratulate sohn and colleagues on their comprehensive and clearly written paper nevertheless we would like to comment on two points the first regarding the moments of the underlying weibull distribution the second regarding the relations of sohn s model to the class of frailty models

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance friction and damage we consider a model for quasistatic frictional contact between a viscoelastic body and a foundation the material constitutive relation is assumed to be nonlinear the mechanical damage of the material caused by excessive stress or strain is described by the damage function the evolution of which is determined by a parabolic inclusion the contact is modeled with the normal compliance condition and the associated version of coulomb s law of dry friction we derive a variational formulation for the problem and prove the existence of its unique weak solution we then study a fully discrete scheme for the numerical solutions of the problem and obtain error estimates on the approximate solutions

the design of a panel study under an alternating poisson process assumption we discuss the design of a panel study for the estimation of the average durations in the two states of an alternating poisson process two types of designs are examined the first fixes the number of follow up waves but permits the total length of follow up to vary and the second varies the number of follow up waves with fixed length simple expressions for nearly optimal designs are presented and we compare these with designs allowing for continuous observation both equilibrium and nonequilibrium cases are examined an example is given using morbidity data to illustrate how these results can be applied

the geometry of mixture likelihoods a general theory in this paper certain fundamental properties of the maximum likelihood estimator of a mixing distribution are shown to be geometric properties of the likelihood set the existence support size likelihood equations and uniqueness of the estimator are revealed to be directly related to the properties of the convex hull of the likelihood set and the support hyperplanes of that hull it is shown using geometric techniques that the estimator exists under quite general conditions with a support size no larger than the number of distinct observations analysis of the convex dual of the likelihood set leads to a dual maximization problem a convergent algorithm is described the defining equations for the estimator are compared with the usual parametric likelihood equations for finite mixtures sufficient conditions for uniqueness are given part ii will deal with a special theory for exponential family mixtures

a quasistatic contact problem for viscoelastic materials with friction and damage abstract we consider a mathematical model which describes the frictional contact between a deformable body and a foundation the process is quasistatic the material is assumed to be viscoelastic with long memory and the frictional contact is modelled with subdifferential boundary conditions the mechanical damage of the material is described by the damage function which is modelled by a nonlinear partial differential equation we derive the variational formulation of the problem which is a coupled system of a hemivariational inequality and a parabolic equation then we prove the existence of a unique weak solution to the model the proof is based on arguments of abstract stationary inclusion and a fixed point theorem

nonparametric analysis of a duration model with stochastic unobserved heterogeneity abstract this paper develops nonparametric identification and estimation results for a single spell hazard model where the unobserved heterogeneity is specified as a levy subordinator the identification approach solves a nonlinear volterra integral equation of the first kind with an unknown kernel function both the kernel of the integral operator which models the distribution of the unobserved heterogeneity and the functions that enter it are identified given regularity conditions and minimal variation in the observed covariates the paper proposes a shape constrained nonparametric two step sieve minimum distance estimator rates of convergence are derived and monte carlo experiments show the finite sample performance of the estimator

duality methods for solving variational inequalities abstract methods of maximal monotone operators are used in order to study from a general point of view duality numerical algorithms for solving variational inequalities with classical algorithms such as uzawa s method for the standard and augmented lagrangian this paper presents some new algorithms which appear to have very good numerical performances

a frictionless contact problem for elastic viscoplastic materials with normal compliance numerical analysis and computational experiments in this paper we consider a frictionless contact problem between an elastic viscoplastic body and an obstacle the process is assumed to be quasistatic and the contact is modeled with normal compliance we present a variational formulation of the problem and prove the existence and uniqueness of the weak solution using strongly monotone operators arguments and banach s fixed point theorem we also study the numerical approach to the problem using spatially semi discrete and fully discrete finite elements schemes with implicit and explicit discretization in time we show the existence of the unique solution for each of the schemes and derive error estimates on the approximate solutions finally we present some numerical results involving examples in one two and three dimensions

a frictionless contact problem for elastic viscoplastic materials with normal compliance and damage abstract we study a quasistatic frictionless contact problem with normal compliance and damage for elastic viscoplastic bodies the mechanical damage of the material caused by excessive stress or strain is described by a damage function whose evolution is modelled by an inclusion of parabolic type we provide a variational formulation for the mechanical problem and sketch a proof of the existence of a unique weak solution to the model we then introduce and study a fully discrete scheme for the numerical solutions of the problem an optimal order error estimate is derived for the approximate solutions under suitable solution regularity numerical examples are presented to show the performance of the method

convex optimization shape constraints compound decisions and empirical bayes rules estimation of mixture densities for the classical gaussian compound decision problem and their associated empirical bayes rules is considered from two new perspectives the first motivated by brown and greenshtein introduces a nonparametric maximum likelihood estimator of the mixture density subject to a monotonicity constraint on the resulting bayes rule the second motivated by jiang and zhang proposes a new approach to computing the kiefer wolfowitz nonparametric maximum likelihood estimator for mixtures in contrast to prior methods for these problems our new approaches are cast as convex optimization problems that can be efficiently solved by modern interior point methods in particular we show that the reformulation of the kiefer wolfowitz estimator as a convex optimization problem reduces the computational effort by several orders of magnitude for typical problems by comparison to prior em algorithm based methods and thus greatly expands the practical applicability of the resulting method

the natural variability of vital rates and associated statistics the first concern of this work is the development of approximations to the distributions of crude mortality rates age specific mortality rates age standardized rates standardized mortality ratios and the like for the case of a closed population or period study it is found that assuming poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate poisson distribution it is suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic poisson distribution for the number of deaths with mean proportional to the population size and an exponential function of a linear combination of the explanatories such a model is fit to mortality data for canadian females classified by age and year a dynamic variant of the model is further fit to the time series of total female deaths alone by year the models with extra poisson variation are found to lead to substantially improved fits excerpt

achieving semiparametric efficiency bounds in left censored duration models consider the estimation of unemployment duration when the statistician samples individuals from the pool of unemployed persons and later interviews them and asks how long they had been unmployed this incurs the problem of left censoring ignoring left censoring overestimates the mean duration since longer spells tend to be observed more frequently than shorter ones lancaster 1979 gives a simple and convenient solution to the problem by introducing a conditional maximum likelihood estimator mle i e analysis conditional on duration at the time of sampling here we give answers to the question whether or not such an approach is optimal in the sense that a semiparametric efficiency bound is achieved

the strict positivstellensatz for global analytic functions and the moment problem for semianalytic sets analytic functions strictly positive on a global semianalytic set x f1 0 fk 0 in rn are characterized as functions expressible as g a0 a1f1 akfk for strictly positive global analytic functions a0 ak the proof is elementary using the fact that the analytic functions are dense in c rn r in the whitney topology the same proof works for nash functions this is an improvement of the standard analytic version of stengle s positivstellensatz in two directions the hypothesis is weaker there is no requirement that x be compact and the conclusion is stronger several applications are given including i a new proof of the weak positivstellensatz for semianalytic sets and ii the solution of thek moment problem for basic closed semianalytic

the mis specification of discrete duration models with unobserved heterogeneity a monte carlo study empirical researchers usually prefer statistical models that can be easily estimated with the help of commonly available software packages sequential binary models with or without normal random effects are an example of such models that can be adopted to estimate discrete duration models with unobserved heterogeneity but an easy to implement estimation may incur a cost in this paper we conduct a monte carlo simulation to evaluate the consequences of omitting or misspecifying the unobserved heterogeneity distribution in single spell discrete duration models

the moment problem on compact semi algebraic sets in this chapter we begin the study of the multidimensional moment problem the passage to dimensions d 2 brings new difficulties and unexpected phenomena in sect 3 2 we derived solvability criteria of the moment problem on intervals in terms of positivity conditions it seems to be natural to look for similar characterizations in higher dimensions as well this leads us immediately into the realm of real algebraic geometry and to descriptions of positive polynomials on semi algebraic sets in this chapter we treat this approach for basic closed compact semi algebraic subsets of mathbb r d it turns out that for such sets there is a close interaction between the moment problem and positivstellensatze for strictly positive polynomials

archimedean operator theoretic positivstellensatze abstract we prove a general archimedean positivstellensatz for hermitian operator valued polynomials and show that it implies the multivariate fejer riesz theorem of dritschel rovnyak and positivstellensatze of ambrozie vasilescu and scherer hol we also obtain several generalizations of these and related results the proof of the main result depends on an extension of the abstract archimedean positivstellensatz for algebras that is interesting in its own right

semiparametric proportional hazards estimation of competing risks models with time varying covariates abstract recent research has focused on the class of proportional hazards models which are nonparametric with respect to the form of the baseline hazard han and hausman 1990 meyer 1986 kiefer 1987 this paper extends the previous literature on these semiparametric duration estimators in two distinct ways first i extend the regression form of the competing risks proportional hazards model to allow covariates to vary over time i demonstrate identification and asymptotic normality of the general estimator for the competing risks models with time varying covariates second i develop monte carlo simulations to assess the performance of the bivariate risk estimator for various sample sizes in the presence and absence of unobserved heterogeneity of various forms and given temporal aggregation the results indicate that the estimator performs well in finite samples but that the estimates are sensitive to misspecification of the error distribution the qualitative results are however relatively insensitive to an incorrect error assumption in contrast the effects of aggregation are potentially quite serious with parameters for the time varying variables in particular showing considerable sensitivity to the degree of aggregation

damage gradient of damage and principle of virtual power a theory of continuum damage mechanics is developed within the framework of the principle of virtual power because the damage in a solid results from microscopic movements we decided to include the power of these microscopic movements in the power of the internal forces the microscopic velocities are related to the damage rate the power of the internal forces we choose depends on the damage velocity and its gradient to take into account the interactions models issued from this theory are presented they are coherent from the mechanical and mathematical points of view the numerical computations show no mesh sensitivity they describe with good agreement the main experimental properties concrete is chosen as an example to illustrate the theory a model using two damage quantities is also presented it yields the correct description of the unilateral phenomenon observed in concrete finally an extension of the existing models is proposed to describe the fatigue damage behaviour

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

existence and uniqueness of solutions for a dynamic one dimensional damage model we consider a one dimensional dynamic model that describes the evolution of damage caused by tension in a viscoelastic material the process is modeled by a coupled set of two differential inclusions for the elastic displacement and damage fields we establish the existence of local weak solutions the existence result is derived from the a priori estimates obtained for a sequence of regularized truncated and time retarded approximations we also establish the existence of the unique weak solution of a simplified version of the model

damageable contact between an elastic body and a rigid foundation in this work the contact problem between an elastic body and a rigid obstacle is studied including the development of material damage which results from internal compression or tension the variational problem is formulated as a first kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field the existence of a unique local weak solution is stated then a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are derived on the approximate solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions finally three two dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme

positive polynomials and tame preorderings from the geometric point of view it is one of the essential merits of theartinschreier theory of ordered fields to have shed new light on certain problems concerning the behaviour of regular functions on an irreducible variety v over r this eventually led to a purely algebraic characterization of those f r v which are positive or nonnegative on v r reg a first example is provided by e artin s positive solution of hilbert s 17 th problem in the seventies classical artin schreier theory was extended to commutative rings and generalizations of artin s result were proven for the purpose of this introduction we consider only a special situation let us fix polynomials f1 fk r x r x1 xn