semiparametric inference in a model for association in bivanate survival data summary clayton s 1978 model for association in bivariate survival data is both of intrinsic importance and an interesting example of a semiparametric estimation problem that is a problem where inference about a parameter is required in the presence of nuisance functions we derive the asymptotic variance of clayton s estimator obtaining a simple explicit formula for uncensored data and indicating the modification required when the survival times are subject to arbitrary random censorship some comparisons are made with results derived by oakes 1982 for other estimators within this model in the absence of censoring the exact null variance of the score statistic corresponding to clayton s estimator is derived and compared with that of the locally most powerful rank test given by cuzick 1982

a tensor product finite element method for the diffraction grating problem with transparent boundary conditions abstract we consider the diffraction grating problem in optics which has been modeled by a boundary value problem governed by a helmholtz equation with transparent boundary conditions a tensor product finite element method is proposed to numerically solve the problem an fft based matrix decomposition algorithm is developed to solve the linear system arising in the vertically layered medium case which can be used as a preconditioning technique for the general case numerical examples are presented to illustrate the accuracy and efficiency of the method

directional derivative of a minimax function etant donne une fonction a valeur reelle l definie sur x u v ou x est un espace localement convexe et ou u et v sont deux espaces topologiques de hausdorff on etudie l existence et la caracterisation de la derivee directionnelle dh x 0 d a x 0 x dans la direction d x de la fonction minimax h x sup v v o inf u u o l x u v ou u o et v o sont deux ensembles non vides dans u et dans v respectivement

a fast direct solver for quasi periodic scattering problems abstract we consider the numerical solution of the scattering of time harmonic plane waves from an infinite periodic array of reflection or transmission obstacles in a homogeneous background medium in two dimensions boundary integral formulations are ideal since they reduce the problem to n unknowns on the obstacle boundary however for complex geometries and or higher frequencies the resulting dense linear system becomes large ruling out dense direct methods and often ill conditioned despite being 2nd kind rendering fast multipole based iterative schemes also inefficient we present an integral equation based solver with o n complexity which handles such ill conditioning using recent advances in fast direct linear algebra to invert hierarchically the isolated obstacle matrix this is combined with a recent periodizing scheme that is robust for all incident angles including wood s anomalies based upon the free space green s function kernel the resulting solver is extremely efficient when multiple incident angles are needed as occurs in many applications our numerical tests include a complicated obstacle several wavelengths in size with n 10 5 and solution error of 10 10 where the solver is 66 times faster per incident angle than a fast multipole based iterative solution and 600 times faster when incident angles are chosen to share bloch phases

a global algorithm for nonlinear semidefinite programming in this paper we propose a global algorithm for solving nonlinear semidefinite programming problems this algorithm inspired by the classic sqp sequentially quadratic programming method modifies the s sdp sequentially semidefinite programming local method by using a nondifferentiable merit function combined with a line search strategy

on the numerical solution of two point boundary value problems abstract this paper presents a new numerical method for the solution of linear two point boundary value problems of ordinary differential equations after reducing the differential equation to a second kind integral equation the latter are discretized via a high order nystrom scheme a somewhat involved analytical apparatus is then constructed which allows for the solution of the discrete system using o n dot p2 operations where n is the number of nodes on the interval and p is the desired order of convergence thus the advantages of the integral equation formulation small condition number insensitivity to boundary layers insensitivity to end point singularities etc are retained while achieving a computational efficiency previously available only to finite difference or finite element methods keywords two point boundary value problems integral equations chebyshev polynomials approximation theory

estimating local and global measures of association for bivariate interval censored data with a smooth estimate of the density measures of association for bivariate interval censored data have not yet been studied extensively betensky and finkelstein statist med 1999 18 3101 3109 proposed to calculate kendall s coefficient of concordance using a multiple imputation technique but their method becomes computer intensive for moderate to large data sets we suggest a different approach consisting of two steps firstly a bivariate smooth estimate of the density of log event times is determined the smoothing technique is based on a mixture of gaussian densities fixed on a grid with weights determined by a penalized likelihood approach secondly given the smooth approximation several local and global measures of association can be estimated readily the performance of our method is illustrated by an extensive simulation study and is applied to tooth emergence data of permanent teeth measured on 4468 children from the signal tandmobiel study

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

measures of risk the conditions under which the classical measures of risk like the mean the linear correlation coefficient and var can be used are discussed the definition of risk measure and the main recently proposed risk measures are presented the problems connected with co dependence are outlined

statistical inference procedures for bivariate archimedean copulas abstract a bivariate distribution function h x y with marginals f x and g y is said to be generated by an archimedean copula if it can be expressed in the form h x y 1 f x g y for some convex decreasing function defined on 0 1 in such a way that 1 0 many well known systems of bivariate distributions belong to this class including those of gumbel ali mikhail haq thelot clayton frank and hougaard frailty models also fall under that general prescription this article examines the problem of selecting an archimedean copula providing a suitable representation of the dependence structure between two variates x and y in the light of a random sample x 1 y 1 x n y n the key to the estimation procedure is a one dimensional empirical distribution function that can be constructed whether the uniform representation of x and y is archimedean or not and independently of their marginals this semiparametric estimator based on a decomposition of kendall s tau statistic

three dimensional quasi periodic shifted green function throughout the spectrum including wood anomalies this work part ii in a series presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near what are commonly called wood anomaly frequencies at these frequencies there is a grazing rayleigh wave and the quasi periodic green function ceases to exist we present a modification of the green function by adding two types of terms to its lattice sum the first type are transversely shifted green functions with coefficients that annihilate the growth in the original lattice sum and yield algebraic convergence the second type are quasi periodic plane wave solutions of the helmholtz equation which reinstate certain necessary grazing modes without leading to blow up at wood anomalies using the new quasi periodic green function we establish for the first time that the dirichlet problem of scattering by a smooth doubly periodic scattering surface at a wood frequency is uniquely solvable we also present an efficient high order numerical method based on this new green function for scattering by doubly periodic surfaces at and around wood frequencies we believe this is the first solver able to handle wood frequencies for doubly periodic scattering problems in three dimensions we demonstrate the method by applying it to acoustic scattering

a two part joint model for the analysis of survival and longitudinal binary data with excess zeros many longitudinal studies generate both the time to some event of interest and repeated measures data this article is motivated by a study on patients with a renal allograft in which interest lies in the association between longitudinal proteinuria a dichotomous variable measurements and the time to renal graft failure an interesting feature of the sample at hand is that nearly half of the patients were never tested positive for proteinuria 1g day during follow up which introduces a degenerate part in the random effects density for the longitudinal process in this article we propose a two part shared parameter model framework that effectively takes this feature into account and we investigate sensitivity to the various dependence structures used to describe the association between the longitudinal measurements of proteinuria and the time to renal graft failure

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

efficient calculation of two dimensional periodic and waveguide acoustic green s functions new representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane and for the green s function for sound propagation in the canyon formed by two infinitely high parallel rigid or sound soft walls and an impedance ground surface the infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a laplace type integral a pole subtraction technique is used to remove poles in the integrand which lie near the path of integration obtaining a smooth integrand more suitable for numerical integration and a specific numerical integration method is proposed numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types it is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts and for problems of scattering by periodic surfaces

integral equation methods for elliptic problems with boundary conditions of mixed type laplace s equation with mixed boundary conditions that is dirichlet conditions on parts of the boundary and neumann conditions on the remaining contiguous parts is solved on an interior planar domain using an integral equation method rapid execution and high accuracy is obtained by combining equations which are of fredholm s second kind with compact operators on almost the entire boundary with a recursive compressed inverse preconditioning technique then an elastic problem with mixed boundary conditions is formulated and solved in an analogous manner and with similar results this opens up for the rapid and accurate solution of several elliptic problems of mixed type

various lipschitz like properties for functions and sets i directional derivative and tangential characterizations in this work we introduce for extended real valued functions defined on a banach space x the concept of k directionally lipschitzian behavior where k is a bounded subset of x for different types of sets k e g zero singleton or compact the k directionally lipschitzian behavior recovers well known concepts in variational analysis locally lipschitzian directionally lipschitzian or compactly epi lipschitzian properties respectively characterizations of this notion are provided in terms of the lower dini subderivatives we also adapt the concept for sets and establish characterizations of the mentioned behavior in terms of the bouligand tangent cones the special case of convex functions and sets is also studied

a divide and conquer algorithm for the eigendecomposition of symmetric block diagonal plus semiseparable matrices we present a fast and numerically stable algorithm for computing the eigendecomposition of a symmetric block diagonal plus semiseparable matrix we report numerical experiments that indicate that our algorithm is significantly faster than the standard method which treats the given matrix as a general symmetric dense matrix

inferences on the association parameter in copula models for bivariate survival data we investigate two stage parametric and two stage semi parametric estimation procedures for the association parameter in copula models for bivariate survival data where censoring in either or both components is allowed we derive asymptotic properties of the estimators and compare their performance by simulations both parametric and semi parametric estimators of the association parameter are efficient at independence and the parameter estimates in the margins have high efficiency and are robust to misspecification of dependency structures in addition we propose a consistent variance estimator for the semi parametric estimator of the association parameter we apply the proposed methods to an aids data set for illustration

lattice sums for the helmholtz equation a survey of different representations for lattice sums for the helmholtz equation is made these sums arise naturally when dealing with wave scattering by periodic structures one of the main objectives is to show how the various forms depend on the dimension d of the underlying space and the lattice dimension d lambda lattice sums are related to and can be calculated from the quasi periodic green s function and this object serves as the starting point of the analysis

bivariate extreme value theory models and estimation summary bivariate extreme value distributions arise as the limiting distributions of renormalized componentwise maxima no natural parametric family exists for the dependence between the marginal distributions but there are considerable restrictions on the dependence structure we consider modelling the dependence function with parametric models for which two new models are presented tests for independence and discriminating between models are also given the estimation procedure and the flexibility of the new models are illustrated with an application to sea level data extreme value theory has recently been an area of much theoretical and practical work univariate theory is a well documented area whereas bivariate multivariate extreme value theory has until recently received surprisingly little attention in the multivariate case no natural parametric family exists for the dependence structure so this must be modelled in some way in the analysis of environmental extreme value data there is a need for models of dependence between extremes from different sources for example at various sea ports or at various points of a river in this paper we consider bivariate extreme value distributions we assume without loss of generality that we have exponential marginal distributions with unit means the class of bivariate exponential distributions in which we are interested satisfy a strong stability relation exponential variables x y satisfy the stability relation if and only if w min ax by is also exponentially distributed for all a b 0 pickands 1981 therefore the models we will consider have particular application in reliability and survival analysis one approach to modelling the dependence structure is via parametric models this requires a flexible family of models which satisfy certain constraints models are of two kinds either differentiable or nondifferentiable all nondifferentiable models give distri butions which are singular with nonzero probability concentrated on a certain subspace the differentiable models have densities but the existing models are symmetric which leads to the variables being exchangeable here we present two new asymmetric differenti able models which have increased flexibility properties of the differentiable models are examined estimation of the parametric models has previously been by ad hoc methods because there is a nonregular estimation problem when the margins are independent for the

conic version of loewner john ellipsoid theorem we extend john s inscribed ellipsoid theorem as well as loewner s circumscribed ellipsoid theorem from convex bodies to proper cones to be more precise we prove that a proper cone k k in mathbb r n rn contains a unique ellipsoidal cone q mathrm in k qin k of maximal canonical volume and on the other hand it is enclosed by a unique ellipsoidal cone q mathrm circ k qcirc k of minimal canonical volume in addition we explain how to construct the inscribed ellipsoidal cone q mathrm in k qin k the circumscribed ellipsoidal cone q mathrm circ k qcirc k is then obtained by duality arguments the canonical volume of an ellipsoidal cone is defined as the usual n n dimensional volume of a certain truncation of the cone

modelling failure time associations in data with multiple levels of clustering summary in recent years substantial research has been devoted to developing failure time methodology which accounts for possible dependency between observations an example is the univariate frailty model vaupel manton stallard 1979 which incorporates an exchangeable dependence structure by the inclusion of cluster specific random effects in some studies it may be reasonable to expect more than one level of within cluster association for instance association between a parent and child versus that between two siblings in studies of familial disease aggregation or association between two village residents who live in different households versus that between residents of the same household in intervention studies we propose a family of distributional models for failure time data that accounts for multiple levels of clustering and reduces in the case of a single clustering level to a univariate frailty model the resulting survival functions are constructed by a recursive nesting of univariate frailty type distributions through which archimedean copula forms are determined for all bivariate margins properties of the proposed model are developed illustrated and briefly contrasted with multivariate frailty model properties in conclusion we outline the application of our model to marginal risk regression problems

simulated method of moments estimation for copula based multivariate models this article considers the estimation of the parameters of a copula via a simulated method of moments mm type approach this approach is attractive when the likelihood of the copula model is not known in closed form or when the researcher has a set of dependence measures or other functionals of the copula that are of particular interest the proposed approach naturally also nests mm and generalized method of moments estimators drawing on results for simulation based estimation and on recent work in empirical copula process theory we show the consistency and asymptotic normality of the proposed estimator and obtain a simple test of overidentifying restrictions as a specification test the results apply to both iid and time series data we analyze the finite sample behavior of these estimators in an extensive simulation study we apply the model to a group of seven financial stock returns and find evidence of statistically significant tail dependence and mild evidence that the dependence between thes

nonparametric estimation of bivariate failure time associations in the presence of a competing risk most research on the study of associations among paired failure times has either assumed time invariance or been based on complex measures or estimators little has accommodated competing risks this paper targets the conditional cause specific hazard ratio henceforth called the cause specific cross ratio a recent modification of the conditional hazard ratio designed to accommodate competing risks data estimation is accomplished by an intuitive non parametric method that localizes kendall s tau time variance is accommodated through a partitioning of space into bins between which the strength of association may differ inferential procedures are developed small sample performance is evaluated and the methods are applied to the investigation of familial association in dementia onset

on the numerical solution of two point boundary value problems ii abstract in a recent paper greengard and rokhlin introduce a numerical technique for the rapid solution of integral equations resulting from linear two point boundary value problems for second order ordinary differential equations in this paper we extend the method to systems of ordinary differential equations after reducing the system of differential equations to a system of second kind integral equations we discretize the latter via a high order nystrom scheme a somewhat involved analytical apparatus is then constructed which allows for the solution of the discrete system using o n p squared n cubed operations with n the number of nodes on the interval p the desired order of convergence and n the number of equations in the system thus the advantages of the integral equation formulation small condition number insensitivity to boundary layers insensitivity to end point singularities etc are retained while achieving a computational efficiency previously available only to finite difference of finite element methods we in addition present a newton method for solving boundary value problems for nonlinear first order systems in which each newton iterate is the solution of a second kind integral equation the analytical and numerical advantages of integral equations are thus obtained for nonlinear boundary value problems kr

high order corrected trapezoidal quadrature rules for singular functions a class of quadrature formulae is presented applicable to both nonsingular and singular functions generalizing the classical endpoint corrected trapezoidal quadrature rules while the latter rules are usually derived by means of the euler maclaurin formula their generalizations are obtained as solutions of certain systems of linear algebraic equations a procedure is developed for the construction of very high order quadrature rules applicable to functions with a priori specified singularities and relaxing the requirements on the distribution of nodes the scheme applies not only to nonsingular functions but also to a wide class of functions with monotonic singularities numerical experiments are presented demonstrating the practical usefulness of the new class of quadratures tables of quadrature weights are included for singularities of the form s x x lambda for a variety of values of lambda and s x log x

estimating survival under a dependent truncation summary the product limit estimator calculated from data subject to random left truncation relies on the testable assumption of quasi independence between the failure time and the truncation time in this paper we propose a model for a truncated sample of pairs xi y satisfying 1 xi a possible dependency between the truncation time and the variable of interest is modelled with a parametric family of copulas the model also features a distribution function fx and a survival distribution sy associated with the marginal behaviours of x and y in the observable region y x semiparametric estimators for these two functions are proposed they do not make any parametric assumption about either fx or sy we derive an estimator for the copula parameter cx based on the conditional kendall s tau we generalise the copula graphic estimators of zheng klein 1995 to truncated variables the asymptotic distributions of all these estimators are then investigated the methods are illustrated with a real dataset on hiv infection by transfusion and by simulations

efficient numerical solution of acoustic scattering from doubly periodic arrays of axisymmetric objects we present a high order accurate boundary based solver for three dimensional 3d frequency domain scattering from a doubly periodic grating of smooth axisymmetric sound hard or transmission obstacles we build the one obstacle solution operator using separation into p azimuthal modes via the fft the method of fundamental solutions with n proxy points lying on a curve and dense direct least squares solves the effort is o n 3 p with a small constant periodizing then combines fast multipole summation of nearest neighbors with an auxiliary global helmholtz basis expansion to represent the distant contributions and enforcing quasiperiodicity and radiation conditions on the unit cell walls eliminating the auxiliary coefficients and preconditioning with the one obstacle solution operator leaves a well conditioned square linear system that is solved iteratively the solution time per incident wave is then o n p at fixed frequency our scheme avoids singular quadratures periodic green s functions and lattice sums and its convergence rate is unaffected by resonances within obstacles we include numerical examples such as scattering from a grating of period 13 13 comprising highly resonant sound hard cups each needing n p 64800 surface unknowns to 10 digit accuracy in half an hour on a desktop

second order directional derviatives in parametric optimization problems we characterize the second order directional derivative in the sense of ben tal and zowe of a marginal function of the following general form x inf f x y y x this requires us to introduce some geometrical notions as for example the first and second order tangent directions to a multifunction the main results are then applied to some particular types of marginal functions

a fast direct solver for structured linear systems by recursive skeletonization we present a fast direct solver for structured linear systems based on multilevel matrix compression using the recently developed interpolative decomposition of a low rank matrix in a recursive manner we embed an approximation of the original matrix into a larger but highly structured sparse one that allows fast factorization and application of the inverse the algorithm extends the martinsson rokhlin method developed for 2d boundary integral equations and proceeds in two phases a precomputation phase consisting of matrix compression and factorization followed by a solution phase to apply the matrix inverse for boundary integral equations which are not too oscillatory e g based on the green functions for the laplace or low frequency helmholtz equations both phases typically have complexity mathcal o n in two dimensions where n is the number of discretization points in our current implementation the corresponding costs in three dimensions are mathcal o n 3 2 and mathcal o

on assessing the association for bivariate current status data assuming that the two failure times of interest with bivariate current status data follow a bivariate copula model we propose a two stage estimation procedure to estimate the association parameter which is related to kendall s tau asymptotic properties of the proposed semiparametric estimator show that although the first stage marginal estimators have a convergence rate of only n 1 3 the resulting parameter estimator still converges to a normal random variable with the usual n 1 2 rate the variance of the proposed estimator can be consistently estimated simulation results are presented and a community based study of cardiovascular diseases in taiwan provides an illustrative example

efficient algorithms for computing a strong rank revealing qr factorization given anm n matrixm withm n it is shown that there exists a permutation fi and an integer k such that the qr factorization myi q ak ckbk reveals the numerical rank of m the k k upper triangular matrix ak is well conditioned ilckll2 is small and bk is linearly dependent on ak with coefficients bounded by a low degree polynomial in n existing rank revealing qr rrqr algorithms are related to such factorizations and two algorithms are presented for computing them the new algorithms are nearly as efficient as qr with column pivoting for most problems and take o ran2 floating point operations in the worst case

model selection and semiparametric inference for bivariate failure time data abstract we propose model selection procedures for bivariate survival models for censored data generated by the archimedean copula family in route to constructing the selection methodology we develop estimates of some time dependent association measures including estimates of the local and global kendall s tau local odds ratio and other measures defined throughout the literature we propose a goodness of fit based model selection methodology as well as a graphical approach we show that the proposed methods have desirable asymptotic properties and perform well in finite samples

shape sensitivity analysis for a robin problem via minimax differentiability this paper deals with shape sensitivity analysis for a robin problem the structure of eulerian derivative with respect to the shape of the variable domain for a cost functional is established by using differentiability of a minimax combing with function space parametrization and function space embedding finally we apply a gradient type algorithm to our problem numerical examples show that our theory is very useful for practical purpose and the algorithm is feasible

families of multivariate distributions abstract for many years there has been an interest in families of bivariate distributions with marginals as parameters genest and mackay 1986a b showed that several such families that appear in the literature can be derived by a unified method a similar conclusion is obtained in this article through the use of mixture models these models might be regarded as multivariate proportional hazards models with random constants of proportionality the mixture models are useful for two purposes first they make some properties of the derived distributions more transparent the positive dependency property of association is sometimes exposed and a method for simulation of data from the distributions is suggested but the mixture models also allow derivation of several new families of bivariate distributions with marginals as parameters and they indicate obvious multivariate extensions some of the new families of bivariate distributions given in this article extend known distributions by adding a parameter

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

cumulative incidence association models for bivariate competing risks data association models like frailty and copula models are frequently used to analyze clustered survival data and evaluate within cluster associations the assumption of noninformative censoring is commonly applied to these models though it may not be true in many situations in this paper we consider bivariate competing risk data and focus on association models specified for the bivariate cumulative incidence function cif a nonparametrically identifiable quantity copula models are proposed which relate the bivariate cif to its corresponding univariate cifs similarly to independently right censored data and accommodate frailty models for the bivariate cif two estimating equations are developed to estimate the association parameter permitting the univariate cifs to be estimated either parametrically or nonparametrically goodness of fit tests are presented for formally evaluating the parametric models both estimators perform well with moderate sample sizes in simulation studies the practical use of the methodology is illustrated in an analysis of dementia associations

modelling dependence structure with archimedean copulas and applications to the itraxx cds index in this paper we model the dependence structure between credit default swap cds and jump risk using archimedean copulas the paper models and estimates the different relationships that can exist in different ranges of behaviour it studies the bivariate distributions of cds index spreads and the kurtosis of equity return distribution to take into account nonlinear relationships and different structures of dependency we employ three archimedean copula functions gumbel clayton and frank we adopt nonparametric estimation of copula parameters and we find an extreme co movement of cds and stock market conditions in addition tail dependence indicates the extreme co movements and the potential for a simultaneous large loss in stock markets and a significant default risk ignoring the tail dependence would lead to underestimation of the default risk premium

on the compression of low rank matrices a procedure is reported for the compression of rank deficient matrices a matrix a of rank k is represented in the form a u circ b circ v where b is a k times k submatrix of a and u v are well conditioned matrices that each contain a k times k identity submatrix this property enables such compression schemes to be used in certain situations where the singular value decomposition svd cannot be used efficiently numerical examples are presented

semiparametric model for bivariate survival data subject to biased sampling to better understand the relationship between patient characteristics and their residual survival after an intermediate event such as the local cancer recurrence it is of interest to identify patients with the intermediate event and then analyze their residual survival data one challenge in analyzing such data is that the observed residual survival times tend to be longer than those in the target population since patients who die before experiencing the intermediate event are excluded from the identified cohort we propose to jointly model the ordered bivariate survival data using a copula model and appropriately adjusting for the sampling bias we develop an estimating procedure to simultaneously estimate the parameters for the marginal survival functions and the association parameter in the copula model and use a two stage expectation maximization algorithm using empirical process theory we prove that the estimators have strong consistency and asymptotic normality we conduct simulations studies to evaluate the finite sample performance of the proposed method we apply the proposed method to two cohort studies to evaluate the association between patient characteristics and residual survival

a fast algorithm for simulating multiphase flows through periodic geometries of arbitrary shape this paper presents a new boundary integral equation bie method for simulating particulate and multiphase flows through periodic channels of arbitrary smooth shape in two dimensions the authors consider a particular system multiple vesicles suspended in a periodic channel of arbitrary shape to describe the numerical method and test its performance rather than relying on the periodic green s function as classical bie methods do the method combines the free space green s function with a small auxiliary basis and imposes periodicity as an extra linear condition as a result we can exploit existing free space solver libraries quadratures and fast algorithms and handle a large number of vesicles in a geometrically complex channel spectral accuracy in space is achieved using the periodic trapezoid rule and product quadratures while a first order semi implicit scheme evolves particles by treating the vesicle channel interactions explicitly new constraint correction formulas are introduced that pre

frank s family of bivariate distributions summary this paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent the proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the frechet bounds as well as the distribution corresponding to independent variables three nonparametric estimators of the association parameter are suggested and monte carlo experiments are used to compare their small sample behaviour to that of the maximum likelihood estimate

semiparametric gaussian copula models geometry and efficient rank based estimation we propose for multivariate gaussian copula models with unknown margins and structured correlation matrices a rank based semiparametrically efficient estimator for the euclidean copula parameter this estimator is defined as a one step update of a rank based pilot estimator in the direction of the efficient influence function which is calculated explicitly moreover finite dimensional algebraic conditions are given that completely characterize efficiency of the pseudo likelihood estimator and adaptivity of the model with respect to the unknown marginal distributions for correlation matrices structured according to a factor model the pseudo likelihood estimator turns out to be semiparametrically efficient on the other hand for toeplitz correlation matrices the asymptotic relative efficiency of the pseudo likelihood estimator can be as low as 20 these findings are confirmed by monte carlo simulations we indicate how our results can be extended to joint regression models

multivariate hydrological frequency analysis using copulas 1 this article presents the modeling of multivariate extreme values using copulas our approach allows us to model the dependence structure independently of the marginal distributions which is not possible with standard classical methods the methodology has been applied on two different problems in hydrology the first application is concerned with the combined risk in the framework of frequency analysis four copulas have been tested on peak flows from the watershed of peribonka in quebec canada the second application relates to the joint modeling of peak flows and volumes three copulas have been applied to the watershed of the rimouski river in quebec canada this approach using copulas is promising since it allows us to take into account a wide range of correlation which can happen in hydrology

life table methods for heterogeneous populations distributions describing the heterogeneity taking account of heterogeneity between the individuals in population based mortality studies is important a systematic way of describing heterogeneity is by an unobserved quantity called frailty entering the hazard multiplicatively until now most studies have used a gamma distributed frailty which is mathematically convenient for example the distribution among survivors is also gamma this paper shows that several other distributions have equally simple properties the main example being the inverse gaussian distribution consequences of the different distributions are examined the inverse gaussian makes the population homogeneous with time whereas for the gamma the relative heterogeneity is constant

the intrinsic dependence structure of peak volume duration and average intensity of hyetographs and hydrographs 1 the information contained in hyetographs and hydrographs is often synthesized by using key properties such as the peak or maximum value xp volume v duration d and average intensity i these variables play a fundamental role in hydrologic engineering as they are used for instance to define design hyetographs and hydrographs as well as to model and simulate the rainfall and streamflow processes given their inherent variability and the empirical evidence of the presence of a significant degree of association such quantities have been studied as correlated random variables suitable to be modeled by multivariate joint distribution functions the advent of copulas in geosciences simplified the inference procedures allowing for splitting the analysis of the marginal distributions and the study of the so called dependence structure or copula however the attention paid to the modeling task has overlooked a more thorough study of the true nature and origin of the relationships that link and i in this study we apply a set of ad hoc bootstrap algorithms to investigate these aspects by analyzing the hyetographs and hydrographs extracted from 282 daily rainfall series from central eastern europe three 5 min rainfall series from central italy 80 daily streamflow series from the continental united states and two sets of 200 simulated universal multifractal time series our results show that all the pairwise dependence structures between and i exhibit some key properties that can be reproduced by simple bootstrap algorithms that rely on a standard univariate resampling without resort to multivariate techniques therefore the strong similarities between the observed dependence structures and the agreement between the observed and bootstrap samples suggest the existence of a numerical generating mechanism based on the superposition of the effects of sampling data at finite time steps and the process of summing realizations of independent random variables over random durations we also show that the pairwise dependence structures are weakly dependent on the internal patterns of the hyetographs and hydrographs meaning that the temporal evolution of the rainfall and runoff events marginally influences the mutual relationships of and i finally our findings point out that subtle and often overlooked deterministic relationships between the properties of the event hyetographs and hydrographs exist confusing these relationships with genuine stochastic relationships can lead to an incorrect application of multivariate distributions and copulas and to misleading results

approximating a second order directional derivative for nonsmooth convex functions for a lower semicontinuous convex function f the approximate second order directional derivative d delta mapsto f varepsilon x 0 d delta is defined through the varepsilon directional derivative f varepsilon x d the function v d x mapsto v d x f varepsilon x d is for all varepsilon 0 locally lipschitz on inf domf and at those points where it is not differentiable v d admits a directional derivative v d x 0 delta for all delta which we precisely denote by f varepsilon x 0 d delta the objective of the present work is two fold to classify all the possible differentiability properties of v d according to the behavior of the function lambda mapsto f x 0 lambda d on r and to study the existence or nonexistence of the limit of f varepsilon x 0 d delta when varepsilon to 0

shape sensitivity analysis for an interface problem via minimax differentiability this paper deals with the shape sensitivity analysis for the conductivity problem with discontinuous coefficients we consider the geometric inverse problem of locating the interfaces where the jump of the coefficients occurs we propose a reconstruction method based on the minimization of the kohn vogelius functional the reformulation of the functional in a suitable saddle point problem form allows us to obtain the optimality conditions by using the differentiability of the minimax combined with the function space parametrization technique an important advantage of this approach is that it avoids the differentiability of the state variable with respect to the domain the reconstruction is then performed with an iterative algorithm using an appropriate quasi newton method we give some numerical examples showing the efficiency of the method

directional derivative estimates for the optimal value function of a quasidifferentiable programming problem this paper is concerned with the optimal value function arising in the primal decomposition of a quasidifferentiable programming problem in particular estimates for the upper dini directional derivative of this function are derived they involve certain lagrange multipliers occurring in the necessary minimum conditions to the lower level problems this study generalizes some previously published results on this subject

modeling the association of bivariate interval censored data using the copula approach in a survival study it may not be possible to record the exact event time but only that the event has occurred between two time points or still has to occur leading to interval censored survival times recently sun et al scand j stat 2006 33 4 637 649 suggested to fit a clayton copula with nonparametric marginal distributions to estimate the association for bivariate interval censored failure data we propose here to model the marginal distributions with an accelerated failure time model with a flexible error term as suggested by komarek et al j comput graph stat 2005 14 3 726 745 in combination with a one parameter copula in addition we allow the association parameter of the copula to depend on covariates the performance of our method is illustrated by an extensive simulation study and is applied to tooth emergence data of permanent teeth measured on 4468 children from a longitudinal dental study

a family of distributions for modelling non elliptically symmetric multivariate data summary the paucity of distributions that can be used as an aid to modelling the structure of multivariate data is a recognized limitation we present a relatively simple family of distributions for use in describing data which are not elliptically symmetric properties of the family are discussed and it is shown that multivariate pareto burr and logistic distributions are special cases in addition simulation methods for applications in monte carlo robustness studies are outlined and finally the fit to a data set on uranium exploration is compared to that obtained using the usual bivariate normal distribution

a fast direct solver for scattering from periodic structures with multiple material interfaces in two dimensions we present a new integral equation method for the calculation of two dimensional scattering from periodic structures involving triple points multiple materials meeting at a single point the combination of a robust and high order accurate integral representation and a fast direct solver permits the efficient simulation of scattering from fixed structures at multiple angles of incidence we demonstrate the performance of the scheme with several numerical examples

estimating the correlation of bivariate failure times under censoring the analysis of correlations within pairs of survival times is of interest to many research topics in medicine such as the correlation of survival type endpoints of twins the correlation of times till failure in paired organs or the correlation of survival time with a surrogate endpoint the dependence of such times is assumed monotonic and thus quantification by rank correlation coefficients appropriate the typical censoring of such times requires more involved methods of estimation and inference as have been developed in recent years the paper focuses on semiparametric approaches and in particular on the normal copula based estimation of spearman correlation coefficients the copula approach often presented for a mathematically inclined readership is reviewed from the viewpoint of an applied statistician as an alternative to the maximum likelihood methodology for the normal copula approach nce we introduce an iterative multiple imputation imi method which requires only about 0 05 of the computing time of nce without sacrificing statistical performance for imi survival probabilities at death or censoring times are first transformed to normal deviates then those deviates that relate to censored times are iteratively augmented by using conditional multiple imputation until convergence is obtained for the normal scores rank correlation which is similar to spearman s rank correlation statistical properties of nce and imi are compared by means of a monte carlo study and by means of three real data sets which also give an impression of the typical range of applications and of their problems

generalized burr pareto logistic distributions with applications to a uranium exploration data set a distribution developed previously cook and johnson 1981 has been generalizedu sing morgenstern s distribution to include more useful dependence structures the new distribution provides better fits to a uranium survey data set the effectiveness of atkinson s 1982 graphical aid for discriminating separate models is also demonstrated in comparing the usual normal model with the new distribution having normal marginal distributions

acoustic scattering for 3d multi directional periodic structures using the boundary element method an efficient boundary element formulation is proposed to solve three dimensional exterior acoustic scattering problems with multi directional periodicity the multi directional periodic acoustic problem is represented as a multilevel block toeplitz matrix by exploiting the toeplitz structure the computational time and storage requirements to construct and to solve the linear system of equations arising from the boundary element formulation are significantly reduced the generalized minimal residual method is implemented to solve the linear system of equations to efficiently calculate the matrix vector product in the iterative algorithm the original matrix is embedded into a multilevel block circulant matrix a multi dimensional discrete fourier transform is then employed to accelerate the matrix vector product the proposed approach is applicable to a periodic acoustic problem for any arbitrary shape of the structure in both full space and half space two case studies involving sonic crystal barriers