robustness of granulometric moments granulometric moments are used for classification of random sets and estimation of their parameters these moments are random variables possessing their own probability distributions for certain random sets composed of nonoverlapping grains there are expressions for the granulometric moments the moments are asymptotically normal and their asymptotic means and variances are known all representations depend on the grain sizing distributions being known for all grain primitives generating the random set this paper investigates model robustness by considering the effects of the following violations of the assumptions 1 assuming an incorrect sizing distribution 2 using erroneous parameters for the sizing distribution and 3 prior segmentation when there is modest overlapping the last situation occurs because the paper proposes segmentation prior to granulometric analysis when there is modest overlapping both nonreconstructive and reconstructive granulometries are investigated in the case of prior segmentation

a rational function preconditioner for indefinite sparse linear systems this paper introduces a rational function preconditioner for linear systems with indefinite sparse matrices a by resorting to rational functions of a the algorithm decomposes the spectrum of a into two disjoint regions and approximates the restriction of a 1 on these regions separately we show a systematic way to construct these rational functions so that they can be applied stably and inexpensively an attractive feature of the proposed approach is that the construction and application of the preconditioner can exploit two levels of parallelism moreover the proposed preconditioner can be modified at a negligible cost into a preconditioner for a nearby matrix of the form a ci which can be useful in some applications the efficiency and robustness of the proposed preconditioner are demonstrated on a few tests with challenging model problems including problems arising from the helmholtz equation in three dimensions

a dynamic approach to the statistical analysis of point processes summary an approach to the analysis of point processes based on sequential analysis of successive intervals assuming a piecewise constant intensity rate is presented bayesian inference for processes with explanatory variables is derived in terms of on line estimation filtering and prediction limiting equations for the time continuous intensity rate are obtained and solved for the no covariates case examples are provided and the approach is applied in a numerical example similar approaches include the work of koch spreij 1983 and snyder 1975 6 which also use a dynamic model with a system equation these approaches based on filtering theory for time continuous processes provide good probabilistic descriptions their main problem is the difficulty in applying the results in the presence of covariates even in simple problems the purpose of this paper is to provide tractable yet reasonable solutions to the inference problem of point processes with explanatory variables azzalini 1982 warns about the complications of exact calculations required by filtering theory even in the absence of covariates the approach is based on and to some extent generalizes work on survival data gamerman 1991 inference is considered in terms of on line and smoothed or filtered estimation of model parameters and prediction of future occurrences based on past information in 2 the model is stated and inference procedures derived in 3 the model with no covariates is considered in detail and limiting equations for any continuous rate

a projection method for generalized eigenvalue problems using numerical integration in this paper we propose a method for finding certain eigenvalues of a generalized eigenvalue problem that lie in a given domain of the complex plane the proposed method projects the matrix pencil onto a subspace associated with the eigenvalues that are located in the domain via numerical integration

a contour integral approach to the computation of invariant pairs abstract we study some aspects of the invariant pair problem for matrix polynomials as introduced by betcke and kressner 3 and by beyn and thummler 6 invariant pairs extend the notion of eigenvalue eigenvector pairs providing a counterpart of invariant subspaces for the nonlinear case we compute formulations for the condition numbers and the backward error for invariant pairs and solvents we then adapt the sakurai sugiura moment method 1 to the computation of invariant pairs including some classes of problems that have multiple eigenvalues numerical refinement via a variant of newton s method is also studied furthermore we investigate the relation between the matrix solvent problem and the triangularization of matrix polynomials

nonlinear eigenvalue problems and contour integrals in this paper beyn s algorithm for solving nonlinear eigenvalue problems is given a new interpretation and a variant is designed in which the required information is extracted via the canonical polyadic decomposition of a hankel tensor a numerical example shows that the choice of the filter function is very important particularly with respect to where it is positioned in the complex plane

an error analysis of two related quadrature methods for computing zeros of analytic functions we present an error analysis for two related quadrature methods the delves lyness method and its modification by kravanja sakurai and van barel for computing all the zeros of an analytic function that lie inside the unit circle we consider the forward as well as the backward approximation error in case the integrals are computed via the trapezoidal rule on the unit circle contrary to the delves lyness method the quadrature error that arises from the zeros located inside the unit circle does not affect the results of the approach of kravanja et al numerical experiments illustrate our main results

posterior likelihood methods for multivariate survival data this article deals with the semiparametric analysis of multivariate survival data with random block group effects survival times within the same group are correlated as a consequence of a frailty random block effect the standard approaches assume either a parametric or a completely unknown baseline hazard function this paper considers an intermediate solution that is a nonparametric function that is reasonably smooth this is accomplished by a bayesian model in which the conditional proportional hazards model is used with a correlated prior process for the baseline hazard the posterior likelihood based on data as well as the prior process is similar to the discretized penalized likelihood for the frailty model the methodology is exemplified with the recurrent kidney infections data of mcgilchrist and aisbett 1991 biometrics 47 461 466 in which the times to infections within the same patients are expected to be correlated the reanalysis of the data has shown that the estimates of the parameters of interest and the associated standard errors depend on the prior knowledge about the smoothness of the baseline hazard

the exponentially convergent trapezoidal rule it is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line the mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity it is linked with computational methods all across scientific computing including algorithms related to inverse laplace transforms special functions complex analysis rational approximation integral equations and the computation of functions and eigenvalues of matrices and operators

heterogeneous morphological granulometries abstract the most basic class of binary granulometries is composed of unions of openings by structuring elements that are homogeneously scaled by a single parameter these univariate granulometries have previously been extended to multivariate granulometries in which each structuring element is scaled by an individual parameter this paper introduces the more general class of filters in which each structuring element is scaled by a function of its sizing parameter the result being multivariate heterogeneous granulometries owing to computational considerations of particular importance are the univariate heterogeneous granulometries for which scaling is by functions of a single variable the basic morphological properties of heterogeneous granulometries are given analytic and geometric relationships between multivariate and univariate heterogeneous pattern spectra are explored and application to texture classification is discussed the homogeneous granulometric mixing theory both the representation of granulometric moments and the asymptotic theory concerning the distributions of granulometric moments is extended to heterogeneous scaling

semiparametric bayesian analysis of survival data abstract this review article investigates the potential of bayes methods for the analysis of survival data using semiparametric models based on either the hazard or the intensity function the nonparametric part of every model is assumed to be a realization of a stochastic process the parametric part which may include a regression parameter or a parameter quantifying the heterogeneity of a population is assumed to have a prior distribution with possibly unknown hyperparameters careful applications of some recently popular computational tools including sampling based algorithms are used to find posterior estimates of several quantities of interest even when dealing with complex models and unusual data structures the methodologies developed herein are motivated and aimed at analyzing some common types of survival data from different medical studies here we focus on univariate survival data in the presence of fixed and time dependent covariates multiple event time data for repeated nonfatal events

beyond automated multilevel substructuring domain decomposition with rational filtering this paper proposes a rational filtering domain decomposition technique for the solution of large and sparse symmetric generalized eigenvalue problems the proposed technique is purely algebraic an

an integral method for solving nonlinear eigenvalue problems we propose a numerical method for computing all eigenvalues and the corresponding eigenvectors of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane the method uses complex integrals of the resolvent operator applied to at least k column vectors where k is the number of eigenvalues inside the contour the theorem of keldysh is employed to show that the original nonlinear eigenvalue problem reduces to a linear eigenvalue problem of dimension k no initial approximations of eigenvalues and eigenvectors are needed the method is particularly suitable for moderately large eigenvalue problems where k is much smaller than the matrix dimension we also give an extension of the method to the case where k is larger than the matrix dimension the quadrature errors caused by the trapezoid sum are discussed for the case of analytic closed contours using well known techniques it is shown that the error decays exponentially with an exponent given by the product of the number of quadrature points and the minimal distance of the eigenvalues to the contour

a novel numerical method to determine the algebraic multiplicity of nonlinear eigenvalues we generalize the algebraic multiplicity of the eigenvalues of nonlinear eigenvalue problems neps to the rational form and give the extension of the argument principle in addition we propose a novel numerical method to determine the algebraic multiplicity of the eigenvalues of the neps in a given region by the contour integral method finally some numerical experiments are reported to illustrate the effectiveness of our method

using implicitly filtered rks for generalised eigenvalue problems the rational krylov sequence rks method can be seen as a generalisation of arnoldi s method it projects a matrix pencil onto a smaller subspace this projection results in a small upper hessenberg pencil as for the arnoldi method rks can be restarted implicitly using the qr decomposition of a hessenberg matrix this restart comes with a projection of the subspace using a rational function in this paper it is shown how the restart can be worked out in practice in a second part it is shown when the filtering of the subspace basis can fail and how this failure can be handled by deflating a converged eigenvector from the subspace using a schur decomposition

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

stable polefinding and rational least squares fitting via eigenvalues a common way of finding the poles of a meromorphic function f in a domain where an explicit expression of f is unknown but f can be evaluated at any given z is to interpolate f by a rational function pq such that r i f i at prescribed sample points i i 1l and then find the roots of q this is a two step process and the type of the rational interpolant needs to be specified by the user many other algorithms for polefinding and rational interpolation or least squares fitting have been proposed but their numerical stability has remained largely unexplored in this work we describe an algorithm with the following three features 1 it automatically finds an appropriate type for a rational approximant thereby allowing the user to input just the function f 2 it finds the poles via a generalized eigenvalue problem of matrices constructed directly from the sampled values f i in a one step fashion and 3 it computes rational approximants p q in a numerically stable manner in that p p q q f with small p q at the sample points making it the first rational interpolation or approximation algorithm with guaranteed numerical stability our algorithm executes an implicit change of polynomial basis by the qr factorization and allows for oversampling combined with least squares fitting through experiments we illustrate the resulting accuracy and stability which can significantly outperform existing algorithms

optimal linear granulometric estimation for random sets this paper addresses two pattern recognition problems in the context of random sets for the first the random set law is known and the task is to estimate the observed pattern from a feature set calculated from the observation for the second the law is unknown and we wish to estimate the parameters of the law estimation is accomplished by an optimal linear system whose inputs are features based on morphological granulometries in the first case these features are granulometric moments in the second they are moments of the granulometric moments for the latter estimation is placed in a bayesian context by assuming that there exists a prior distribution for the parameters determining the law a disjoint random grain model is assumed and the optimal linear estimator is determined by using asymptotic expressions for the moments of the granulometric moments in both cases the linear approach serves as a practical alternative to previously proposed nonlinear methods granulometric pattern estimation has previously been accomplished by a nonlinear method using full distributional knowledge of the random variables determining the pattern and granulometric features granulometric estimation of the law of a random grain model has previously been accomplished by solving a system of nonlinear equations resulting from the granulometric asymptotic mixing theorem both methods are limited in application owing to the necessity of performing a nonlinear optimization the new linear method avoids this it makes estimation possible for more complex models

posterior mode estimation by extended kalman filtering for multivariate dynamic generalized linear models abstract a family of multivariate dynamic generalized linear models is introduced as a general framework for the analysis of time series with observations from the exponential family besides common conditionally gaussian models this article deals with univariate models for counted and binary data and as the most interesting multivariate case models for nonstationary multicategorical time series for univariate responses a related yet different class of models has been introduced in a bayesian setting by west harrison and migon assuming conjugate prior posterior distributions for the natural parameter of the exponential family they derive an approximate filter for estimation of time varying states or parameters however their method raises some problems in particular in extending it to the multivariate case a different approach to filtering and smoothing is chosen in this article to avoid a full bayesian analysis based on numerical integration which becomes computationally critical for higher

numerical algorithms based on analytic function values at roots of unity let f z be an analytic or meromorphic function in the closed unit disk sampled at the n th roots of unity based on these data how can we approximately evaluate f z or f m z at a point z in the disk how can we calculate the zeros or poles of f in the disk these questions exhibit in the purest form certain algorithmic issues that arise across computational science in areas including integral equations partial differential equations and large scale linear algebra we analyze some of the possibilities and emphasize the distinction between algorithms based on polynomial or rational interpolation and those based on trapezoidal rule approximations of cauchy integrals we then show how these developments apply to the problem of computing the eigenvalues in the disk of a matrix of large dimension finally we highlight the power of rational in comparison with polynomial approximations for some of these problems

non homothetic granulometric mixing theory with application to blood cell counting a granulometry is a family of morphological openings by scaled structuring elements as the scale increases increasing image area is removed normalizing removed area by the total area yields the pattern spectrum of the image the pattern spectrum is a probability distribution function and its moments are known as granulometric moments modeling the image as a random set the pattern spectrum is a random function and its moments are random variables the original granulometric mixing theory provides closed form representation of the granulometric moments shows that the distributions of the moments are asymptotically normal and gives asymptotic expressions for the means and variances of the granulometric moments the theory applies to random set models formed as disjoint unions of randomly scaled image primitives grains the scaled grains are known as homothetics the theory can be used in a method of moments fashion to estimate the parameters governing the random scaling factors and mixture proportions application is limited by the homothetic assumption this paper drops the homothetic requirement and provides a mixing theory for a disjoint union of fully randomized primitives whereas the original asymptotic theory gives expressions for the moments themselves and is applied by taking expectations afterwards the non homothetic theory involves the granulometric size density which is the mean of the original size distribution prior to normalization hence the representation concerns expectations not random variables nonetheless a similar method of moments approach can be used to estimate mixture proportions a large part of the paper is devoted to estimate blood cell proportions that correspond to cell age categories each cell class is represented by a random grain and the problem is to estimate the proportions of cells occurring in the various age categories the random behavior of the cells in each category makes the non homothetic theory appropriate because the estimation strategy leads to a system of nonlinear equations whose solution presents computational difficulties the estimation is accomplished via a divide and conquer strategy in which the full mixture problem is partitioned into smaller problems and the solutions of these problems are joined to solve the full problem

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

high performance implementation of chebyshev filter diagonalization for interior eigenvalue computations we study chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices in this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from chebyshev expansions of window functions after the discussion of the conceptual foundations of chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel search space size and filter polynomial degree on the computational accuracy and effort before we describe the necessary steps towards a parallel high performance implementation because chebyshev filter diagonalization avoids the need for matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers to demonstrate the potential of chebyshev filter diagonalization for large scale problems of this kind we include as an example the computation of the 102 innermost eigenpairs of a topological insulator matrix with dimension 109 derived from quantum physics applications

dynamic generalized linear models and bayesian forecasting abstract dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters this leads to the calculation of closed standard form predictive distributions for forecasting and model criticism the structure of the models depends on the time evolution of underlying state variables and the feedback of observational information to these variables is achieved using linear bayesian prediction methods data analytic aspects of the models concerning scale parameters and outliers are discussed and some applications are provided dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and

logistic regression survival analysis and the kaplan meier curve abstract we discuss the use of standard logistic regression techniques to estimate hazard rates and survival curves from censored data these techniques allow the statistician to use parametric regression modeling on censored data in a flexible way that provides both estimates and standard errors an example is given that demonstrates the increased structure that can be seen in a parametric analysis as compared with the nonparametric kaplan meier survival curves in fact the logistic regression estimates are closely related to kaplan meier curves and approach the kaplan meier estimate as the number of parameters grows large

smoothing hazard functions and time varying effects in discrete duration and competing risks models abstract state space or dynamic approaches to discrete or grouped duration data with competing risks or multiple terminating events allow simultaneous modeling and smooth estimation of hazard functions and time varying effects in a flexible way full bayesian or posterior mean estimation using numerical integration techniques or monte carlo methods can become computationally rather demanding or even infeasible for higher dimensions and larger datasets therefore based on previous work on filtering and smoothing for multicategorical time series and longitudinal data our approach uses posterior mode estimation thus we have to maximize posterior densities or equivalently a penalized likelihood which enforces smoothness of hazard functions and time varying effects by a roughness penalty dropping the bayesian smoothness prior and adopting a nonparametric viewpoint one might also start directly from maximizing this penalized likelihood we show how fisher scoring smoothing iterations can be carried ou

structured perturbation analysis of sparse matrix pencils with s specified eigenpairs abstract we study the structured backward error analysis of s specified 1 s n eigenpairs of n by n matrix pencils the structures we consider include t symmetric t skew symmetric hermitian skew hermitian t even t odd h even h odd t palindromic t anti palindromic h palindromic and h anti palindromic matrix pencils minimal structured perturbations are constructed with respect to frobenius norm such that s specified eigenpairs become exact eigenpairs of an appropriately perturbed matrix pencil which preserves sparsity

rational krylov sequence methods for eigenvalue computation abstract algorithms to solve large sparse eigenvalue problems are considered a new class of algorithms which is based on rational functions of the matrix is described the lanczos method the arnoldi method the spectral transformation lanczos method and rayleigh quotient iteration all are special cases but there are also new algorithms which correspond to rational functions with several poles in the simplest case a basis of a rational krylov subspace is found in which the matrix eigenvalue problem is formulated as a linear matrix pencil with a pair of hessenberg matrices

on the non hermitian feast algorithms with oblique projection for eigenvalue problems abstract the feast algorithm due to polizzi is a typical contour integral based eigensolver for computing the eigenvalues along with their eigenvectors inside a given region in the complex plane it was formulated under the circumstance that the considered eigenproblem is hermitian the feast algorithm is stable and accurate and has attracted much attention in recent years however yin et al 2017 observed that the feast algorithm may fail to find the target eigenpairs when applied to non hermitian problems this observation motivated them to formulate a non hermitian version for the feast algorithm the key to the success of their method is that they use the oblique projection rather than the orthogonal projection used in the feast algorithm to extract desired eigenpairs the objective of the present work is two folded firstly we would like to present a new non hermitian scheme for the feast algorithm which also uses the oblique projection technique to extract the desired eigenpairs secondly we would like to study the convergence properties of the non hermitian feast algorithms based on oblique projection to illustrate the effectiveness numerical experiments are reported to demonstrate the numerical performance of the non hermitian feast algorithms based on oblique projection and to validate the convergence properties studied

recursive integral method for transmission eigenvalues the transmission eigenvalue problem arose in the inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse problems for target identification and nondestructive testing the problem is numerically challenging because of the nonself adjointness and complicated spectrum in this talk we introduce a novel recursive contour integral method using the spectrum projection the method can compute both real and complex eigenvalues and does not require any a priori information numerical examples show that the method is effective and robust

a linear regression model for the analysis of life times a linear model is suggested for the influence of covariates on the intensity function this approach is less vulnerable than the cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed a method of non parametric estimation of regression functions is presented this results in plots that may give information on the change over time in the influence of covariates a test method and two goodness of fit plots are also given the approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx

solution of the k th eigenvalue problem in large scale electronic structure calculations abstract we consider computing the k th eigenvalue and its corresponding eigenvector of a generalized hermitian eigenvalue problem of n n large sparse matrices in electronic structure calculations several properties of materials such as those of optoelectronic device materials are governed by the eigenpair with a material specific index k we present a three stage algorithm for computing the k th eigenpair with validation of its index in the first stage of the algorithm we propose an efficient way of finding an interval containing the k th eigenvalue 1 k n with a non standard application of the lanczos method in the second stage spectral bisection for large scale problems is realized using a sparse direct linear solver to narrow down the interval of the k th eigenvalue in the third stage we switch to a modified shift and invert lanczos method to reduce bisection iterations and compute the k th eigenpair with validation numerical results with problem sizes up to 1 5 million are reported and the results demonstrate the accuracy and efficiency of the three stage algorithm

a high order accurate scheme for maxwell s equations with a generalized dispersive material model abstract a high order accurate scheme for solving the time domain maxwell s equations with a generalized dispersive material model is described the equations for the electric field are solved in second order form and a general dispersion model is treated with the addition of one or more polarization vectors which obey a set of auxiliary differential equations ade numerical methods are developed for both second order and fourth order accuracy in space and time the equations are discretized using finite differences and advanced in time with a single stage three level space time scheme which remains stable up to the usual explicit cfl restriction as proven using mode analysis because the equations are treated in their second order form there is no need for grid staggering and instead a collocated grid is used composite overlapping grids are used to treat complex geometries with boundary conforming grids and a high order upwind dissipation is added to ensure robust and stable approximations on overlapping grids numerical results in two and three space dimensions confirm the accuracy and stability of the new schemes

conversions between barycentric rkfun and newton representations of rational interpolants we derive explicit formulas for converting between rational interpolants in barycentric rational krylov rkfun and newton form we show applications of these conversions when working with rational approximants produced by the aaa algorithm y nakatsukasa o sete l n trefethen arxiv preprint 1612 00337 2016 within the rational krylov toolbox and for the solution of nonlinear eigenvalue problems

a filter diagonalization for generalized eigenvalue problems based on the sakurai sugiura projection method the sakurai sugiura projection method which solves generalized eigenvalue problems to find certain eigenvalues in a given domain was reformulated by using the resolvent theory a new interpretation based on filter diagonalization was given and the corresponding filter function was derived explicitly a block version of the method was also proposed which enabled not only resolution of degenerated eigenvalues but also an improvement in numerical accuracy three numerical examples were provided to illustrate the method

stability analysis of time delay systems using a contour integral method in this paper we propose a contour integral method for computing the rightmost characteristic roots of systems of linear time delay differential equations ddes these roots are very important in the context of stability analysis of the time delay systems the effectiveness of the proposed method is illustrated by some numerical experiments

zolotarev quadrature rules and load balancing for the feast eigensolver the feast method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization this relation allows to characterize the convergence of this method in terms of the error of a certain rational approximant to an indicator function we propose improved rational approximants leading to feast variants with faster convergence in particular when using rational approximants based on the work of zolotarev numerical experiments demonstrate the possible computational savings especially for pencils whose eigenvalues are not well separated and when the dimension of the search space is only slightly larger than the number of wanted eigenvalues the new approach improves both convergence robustness and load balancing when feast runs on multiple search intervals in parallel

designing rational filter functions for solving eigenvalue problems by contour integration abstract solving nonlinear eigenvalue problems by contour integration requires an effective discretization for the corresponding contour integrals in this paper it is shown that good rational filter functions can be computed using nonlinear least squares optimization techniques as opposed to designing those functions based on a thorough understanding of complex analysis the conditions that such an effective filter function should satisfy are derived and translated in a nonlinear least squares optimization problem solved by optimization algorithms from tensorlab numerical experiments illustrate the validity of this approach

weighted least squares estimation for aalen s additive risk model abstract cox s proportional hazards model has so far been the most popular model for the regression analysis of censored survival data however the additive risk model of aalen can provide a useful and biologically more plausible alternative aalen s model stipulates that the conditional hazard function for a subject whose covariates are y y 1 yp has the form h t y y t where 1 p is an unknown vector of hazard functions this article discusses inference for based on a weighted least squares wls estimator of the vector of cumulative hazard functions the asymptotic distribution of the wls estimator is derived and used to obtain confidence intervals and bands for the cumulative hazard functions both a grouped data and a continuous data version of the estimator are examined an extensive simulation study is carried out the method is applied to grouped data on the incidence of cancer mortality among japanese atomic bomb survivors

a nonparametric multiplicative hazard model for event history analysis a major issue in exploring and analyzing life history data with multiple states and events is the development and availability of flexible methods that allow simultaneous incorporation and estimation of baseline hazards detection and modelling of nonlinear functional forms of covariates and time varying effects and the possibility to include time dependent covariates in this paper we consider a nonparametric multiplicative hazard model that takes into account these aspects embedded in the counting process approach estimation is based on penalized likelihoods and splines the methods are illustrated by two real data applications one to a more conventional survival data set with two absorbing states and one to more complex sleep electroencephalography data with multiple recurrent states of sleep

dynamic modelling and penalized likelihood estimation for discrete time survival data summmary this paper describes a dynamic or state space approach for analyzing discrete time or grouped survival data simultaneous estimation of baseline hazard functions and of timevarying covariate effects is based on maximization of posterior densities or equivalently a penalized likelihood leading to kalman type smoothing algorithms data driven choice of unknown smoothing parameters is possible via an em type procedure the methods are illustrated by applications to real data