approximation of cvar minimization for hedging under exponential levy models in this paper we study the hedging problem based on the cvar in incomplete markets as the superhedging is quite expensive in terms of initial capital we construct a self financing strategy that minimizes the cvar of hedging risk under a budget constraint on the initial capital in incomplete markets no explicit solution can be provided to approximate the problem we apply the neyman pearson lemma approach with a specific equivalent martingale measure afterwards we explicit the solution for call options hedging under the exponential levy class of price models this approach leads to an efficient and easy to implement method using the fast fourier transform we illustrate numerical results for the merton model

on the spaces lp x ω and wm p x ω in this paper we present some basic results on the generalized lebesgue spaces l p x omega and generalized lebesgue sobolev spaces w m w p x omega these results provide the necessary framework for the study of variational problems and elliptic equations with non standard p x growth conditions c 2001 academic press

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

existence of solutions for a p x kirchhoff type equation this paper is concerned with the existence and multiplicity of solutions to a class of p x kirchhoff type problem with dirichlet boundary data by means of a direct variational approach and the theory of the variable exponent sobolev spaces we establish conditions ensuring the existence and multiplicity of solutions for the problem

maximally orthogonalized higher order bases over generalized wires quadrilaterals and hexahedra this paper presents a general theory of maximally orthogonalized div and curl conforming higher order basis functions hobfs over generalized wires quadrilaterals and hexahedra in particular all elements of such bases necessary for fast and easy implementation are listed up to order n 8 numerical results given for div conforming bases applied in an iterative method of moments solution of integral equations show that the condition number and the number of iterations are a much lower than in the case of other hobfs of polynomial type and b practically not dependent on the applied expansion order

comparison and sub supersolution principles for the fractional p x laplacian abstract in this paper we study the new fractional sobolev space w s q x p x y where q and p are variable exponents and s 0 1 and the related nonlocal operator which is a fractional version of the nonhomogeneous p x laplace operator we first give some further qualitative properties of w s q x p x y we also show the strong comparison principle for the fractional p x laplace operator a sub super solution for the nonlocal equations involving the fractional p x laplacian is established

hierarchical divergence conforming nedelec elements for volumetric cells a new family of hierarchical divergence conforming vector bases is proposed for tetrahedral prism and brick cells these functions span the divergence conforming reduced curl spaces of nedelec the bases are constructed from orthogonal scalar polynomials to enhance their linear independence which is a simpler process than an orthogonalization applied to the final vector functions specific functions are tabulated to order 6 5 these basis are intended for use with numerical solutions of volume integral equations or differential equations containing divergence operators

a semiparametric estimation procedure of dependence parameters in multivariate families of distributions summary this paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions the proposed estimator obtained as a solution of a pseudo likelihood equation is shown to be consistent asymptotically normal and fully efficient at independence a natural estimator of its asymptotic variance is proved to be consistent comparisons are made with alternative semiparametric estimators in the special case of clayton s model for association in bivariate data

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

numerical characterization of divergence conforming constrained basis functions for surface integral equations this paper presents an algebraic method of generating arbitrary order basis functions suitable for use in moment methods the basis functions are constructed by enforcing a set of suitable constraints on a more general set of functions leading to a matrix representation of the constraint condition the desired bases are then found through use of the singular value decomposition divergence conforming constrained bases are presented for quadrilateral meshes for use in electric and magnetic field integral equations appropriate constraints for enforcing normal continuity at cell boundaries are discussed a variety of problems are analyzed using the constrained bases and results show that the constrained bases exhibit exponential convergence for smooth structures and produce systems whose condition numbers grow relatively slowly with increasing basis order

estimation of copula based semiparametric time series models this paper studies the estimation of a class of copula based semiparametric stationary markov models these models are characterized by nonparametric marginal distributions and parametric copula functions while the copulas capture all the scale free temporal dependence of the processes simple estimators of the marginal distribution and the copula parameter are provided and their asymptotic properties are established under easily verifiable conditions these results are used to obtain root n consistent and asymptotically normal estimators of important features of the transition distribution such as the nonlinear conditional moments and conditional quantiles the semiparametric conditional quantile estimators are automatically monotonic across quantiles which is attractive for portfolio conditional value at risk calculations

divergence conforming constrained basis functions for hexahedral volume elements this communication presents an algebraic method for constructing arbitrary order divergence conforming basis functions on hexahedral volume elements the appropriate constraints within and on the boundaries of elements are provided in particular the handling of faces where quantities are discontinuous is discussed the resulting bases are numerically characterized in terms of error convergence and system conditioning for a moment method discretization of the electric field volume integral equation for dielectric scatterers results show the accuracy of the proposed method as well as the low system matrix condition number that can be maintained as the basis order and mesh discretization are increased

constrained locally corrected nystrom method a generalization of the locally corrected nystrom lcn discretization method is outlined wherein sparse transformations of the lcn system matrix are obtained via singular value decompositions of local constraint matrices the local constraint matrices are used to impose normal continuity of the currents across boundaries shared by mesh elements due to the method s simplicity and flexibility it is straightforward to develop high order constrained lcn clcn systems for different formulations and mesh element types numerical examples demonstrate the memory savings provided by the clcn method and its improved accuracy when applied to geometries with sharp edges it is also shown that the clcn method maintains the high order convergence of the lcn method and it eliminates the need to include line charges in nystrom based discretizations of formulations that involve the continuity equation

nonparametric tests for constant tail dependence with an application to energy and finance the present paper proposes new tests for detecting structural breaks in the tail dependence of multivariate time series using the concept of tail copulas to obtain asymptotic properties we derive a new limit result for the sequential empirical tail copula process moreover consistency of both the tests and a change point estimator are proven we analyze the finite sample behavior of the tests by monte carlo simulations finally and crucial from a risk management perspective we apply the new findings to datasets from energy and financial markets

elliptic equations with indefinite concave nonlinearities near the origin in this note existence of infinitely many solutions is proved for an elliptic equation with indefinite concave nonlinearities

pseudo maximum likelihood estimation in two classes of semiparametric diffusion models abstract two classes of semiparametric diffusion models are considered where either the drift or the diffusion term is parameterized while the other term is left unspecified we propose a pseudo maximum likelihood estimator pmle of the parametric component that maximizes the likelihood with a preliminary estimator of the unspecified term plugged in it is demonstrated how models and estimators can be used in a two step specification testing strategy of semiparametric and fully parametric models and shown that approximate simulated versions of the pmle inherit the properties of the actual but infeasible estimator a simulation study investigates the finite sample performance of the pmle

on semi competing risks data summary we consider a variation of the competing risks problem in which a terminal event censors a non terminal event but not vice versa the joint distribution of the events is formulated via a gamma frailty model in the upper wedge where data are observable day et al 1997 with the marginal distributions unspecified an estimator for the association parameter is obtained from a concordance estimating function a novel plug in estimator for the marginal distribution of the non terminal event is shown to be uniformly consistent and to converge weakly to a gaussian process the assumptions on the joint distribution outside the upper wedge are weaker than those usually made in competing risks analyses simulations demonstrate that the methods work well with practical sample sizes the proposals are illustrated with data on morbidity and mortality in leukaemia patients

nonparametric inference on levy measures and copulas in this paper nonparametric methods to assess the multivariate levy measure are introduced starting from high frequency observations of a levy process x we construct estimators for its tail integrals and the pareto levy copula and prove weak convergence of these estimators in certain function spaces given n observations of increments over intervals of length n the rate of convergence is k 1 2 n for kn n n which is natural concerning inference on the levy measure analytic properties of the pareto levy copula which to the best of our knowledge have not been mentioned before in the literature are provided as well we conclude with a short simulation study on the performance of our estimators

a priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractional p laplacian abstract we obtain fundamental imbeddings for fractional sobolev spaces with variable exponents which are a generalization of the well known fractional sobolev spaces as an application we obtain a priori bounds and multiplicity of solutions to some nonlinear elliptic problems involving the fractional p laplacian

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

high order divergence conforming constrained bases for triangular cells this paper presents an algebraic technique for generating arbitrary order divergence conforming bases for curvilinear triangular cells the bases are constructed by enforcing appropriate constraints on a linear combination of general functions and then extracting the desired bases using singular value decompositions koornwinder dubiner polynomials are chosen as the general function set basic constraints are presented to obtain divergence conforming bases and additional constraints are presented to further enforce the bases to be nedelec results from a variety of problems are given to show that the bases exhibit high order convergence and also produce systems that are relatively well conditioned compared to other basis sets

higher order interpolatory vector bases for computational electromagnetics low order vector basis functions compatible with the nedelec 1980 representations are widely used for electromagnetic field problems higher order functions are receiving wider application but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases in this paper fully interpolatory higher order vector basis functions of the nedelec type are defined in a unified and consistent manner for the most common element shapes it is shown that these functions can be obtained as the product of zeroth order nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties of the vector functions are discussed and expressions for the vector functions of arbitrary polynomial order are presented sample numerical results confirm the faster convergence of the higher order functions

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

multiplicity of weak solutions to non local elliptic equations involving the fractional p x laplacian this paper is devoted to study the several existence results of a sequence of infinitely many solutions to the nonlocal elliptic problem involving the fractional p x laplacian without assuming the ambrosetti and rabinowitz type condition the strategy of the proof for these results is to approach the problem variationally by using the fountain theorem and the dual fountain theorem in addition we prove that the sequence of weak solutions becomes bounded solutions

efficient estimation of multivariate semi nonparametric garch filtered copula models abstract this paper considers estimation of semi nonparametric garch filtered copula models in which the individual time series are modeled by semi nonparametric garch and the joint distributions of the multivariate standardized innovations are characterized by parametric copulas with nonparametric marginal distributions the models extend those of chen and fan 2006 to allow for semi nonparametric conditional means and volatilities which are estimated via the method of sieves the fitted residuals are then used to estimate the copula parameters and the marginal densities of the standardized innovations jointly via the sieve maximum likelihood sml we show that even using nonparametric filtered data the copula parameters estimated via our sml and the two step procedure of chen and fan 2006 are still root n consistent and asymptotically normal and the asymptotic variances of both estimators do not depend on the nonparametric filtering errors even more surprisingly our sml copula estimator using the filtered data achieves the full semiparametric efficiency bound as if the standardized innovations were directly observed these nice properties lead to simple and more accurate estimation of value at risk var for multivariate financial data with flexible dynamics contemporaneous tail dependence and asymmetric distributions of innovations monte carlo studies demonstrate that our sml estimators of the copula parameters and the marginal distributions of the standardized innovations have smaller variances and smaller mean squared errors compared to those of the two step estimators in finite samples a real data application is presented

superlinear problems without ambrosetti and rabinowitz growth condition superlinear elliptic boundary value problems without ambrosetti and rabinowitz growth condition are considered existence of nontrivial solution result is established by combining some arguments used by struwe and tarantello and schechter and zou also by wang and wei firstly by using the mountain pass theorem due to ambrosetti and rabinowitz is constructed a solution for almost every parameter by varying the parameter then it is considered the continuation of the solutions

differential equations connecting var and cvar abstract the value at risk var is a very important risk measure for practitioners supervisors and researchers many practitioners draw on var as a critical instrument in risk management and other actuarial financial problems while supervisors and regulators must deal with var due to the basel accords and solvency ii among other reasons from a theoretical point of view var presents some drawbacks overcome by other risk measures such as the conditional value at risk cvar var is neither differentiable nor sub additive because it is neither continuous nor convex on the contrary cvar satisfies all of these properties and this simplifies many analytical studies if var is replaced by cvar in this paper several differential equations connecting both var and cvar will be given they will allow us to address several important issues involving var with the help of the cvar properties this new methodology seems to be very efficient in particular a new var representation theorem may be found and optimization problems involving var or probabilistic constraints always have an equivalent differentiable optimization problem applications in var marginal var cvar and marginal cvar estimates will be addressed as well illustrative actuarial and financial examples will be likewise presented

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

exact relationship between the locally corrected nystrom scheme and rwg moment method for the mixed potential integral equation the exact relationship between the rao wilton glisson rwg method of moments mom and the locally corrected nystrom lcn method for the mixed potential mp electric field integral equation efie is presented as an extension to our work where we established analogous exact relationship for solving the efie in its vector potential vp form it is shown that in order to achieve one such relationship for the mp efie the first and zeroth order lcn methods must be respectively used for the discretization of the vp and scalar potential terms of the mp efie the resulting numerical scheme is a point based rwg mom discretization of the mp efie via the nystrom method due to the mp formulation of the efie the proposed method establishes notably higher accuracy compared to either rwg mom or lcn discretizations of the efie in the vp form the increased accuracy is attributed to the analytical cancellation of the line charge contributions in the mp formulation as opposed to numerical cancellation inherent in the vp formulation of the efie the detailed study and explanations of the above cancellations is presented along with their impact on the accuracy of the respective schemes for both canonical and realistic scattering targets at different frequencies

fractional schrodinger equation some properties of the fractional schrodinger equation are studied we prove the hermiticity of the fractional hamilton operator and establish the parity conservation law for fractional quantum mechanics as physical applications of the fractional schrodinger equation we find the energy spectra of a hydrogenlike atom fractional bohr atom and of a fractional oscillator in the semiclassical approximation an equation for the fractional probability current density is developed and discussed we also discuss the relationships between the fractional and standard schrodinger equations

analysing bivariate survival data with interval sampling and application to cancer epidemiology in biomedical studies ordered bivariate survival data are frequently encountered when bivariate failure events are used as outcomes to identify the progression of a disease in cancer studies interest could be focused on bivariate failure times for example time from birth to cancer onset and time from cancer onset to death this paper considers a sampling scheme termed interval sampling in which the first failure event is identified within a calendar time interval the time of the initiating event can be retrospectively confirmed and the occurrence of the second failure event is observed subject to right censoring in a cancer data application the initiating first and second events could correspond to birth cancer onset and death the fact that the data are collected conditional on the first failure event occurring within a time interval induces bias interval sampling is widely used for collection of disease registry data by governments and medical institutions though the interval sampling bias is frequently overlooked by researchers this paper develops statistical methods for analysing such data semiparametric methods are proposed under semi stationarity and stationarity numerical studies demonstrate that the proposed estimation approaches perform well with moderate sample sizes we apply the proposed methods to ovarian cancer registry data

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

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

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

the existence of a nontrivial solution to a nonlinear elliptic boundary value problem of p laplacian type without the ambrosetti rabinowitz condition abstract in this paper we study the existence of a nontrivial solution to the following nonlinear elliptic boundary value problem of p laplacian type p p u f x u x u 0 x where p 1 r 1 r n is a bounded domain and p u d i v u p 2 u is the p laplacian of u f c 0 r 1 r 1 is p superlinear at t 0 and subcritical at t we prove that under suitable conditions for all 0 the problem p has at least one nontrivial solution without assuming the ambrosetti rabinowitz condition our main result extends a result for p for when p 2 given by miyagaki and souto 2008 in 8 to the general problem p where p 1 meanwhile our result is stronger than a similar result of li and zhou 2003 given in 15

a semiparametric random effects model for multivariate competing risks data we propose a semiparametric random effects model for multivariate competing risks data when the failures of a particular type are of interest under this model the marginal cumulative incidence functions follow a generalized semiparametric additive model the associations between the cause specific failure times can be studied through dependence parameters of copula functions that are allowed to depend on cluster level covariates a cross odds ratio type measure is proposed to describe the associations between cause specific failure times and its relationship to the dependence parameters is explored we develop a two stage estimation procedure where the marginal models are estimated in the first stage and the dependence parameters are estimated in the second stage the large sample properties of the proposed estimators are derived the proposed procedures are applied to danish twin data to model the cumulative incidence for the age of natural menopause and to investigate the association in the onset of natural menopause between monozygotic and dizygotic twins

well conditioned muller formulation for electromagnetic scattering by dielectric objects numerical solution of electromagnetic scattering by homogeneous dielectric objects with the method of moments mom and rao wilton glisson rwg basis functions is discussed it is shown that the low frequency breakdown associated to the mom solution of scattering by dielectric objects can be avoided by the classical muller formulation without the loop tree or loop star basis functions two variations of the muller formulation t mu spl uml ller and n muller are considered it is demonstrated that only the n muller formulation with the galerkin method and rwg functions gives stable solution discretization of the n muller formulation leads to a well conditioned matrix equation and rapidly converging iterative solutions on a wide frequency range from very low frequencies to microwave frequencies at zero frequency the n muller formulation decouples into the electrostatic and magnetostatic integral equations

estimation of copula models with discrete margins via bayesian data augmentation estimation of copula models with discrete margins can be difficult beyond the bivariate case we show how this can be achieved by augmenting the likelihood with continuous latent variables and computing inference using the resulting augmented posterior to evaluate this we propose two efficient markov chain monte carlo sampling schemes one generates the latent variables as a block using a metropolis hastings step with a proposal that is close to its target distribution the other generates them one at a time our method applies to all parametric copulas where the conditional copula functions can be evaluated not just elliptical copulas as in much previous work moreover the copula parameters can be estimated joint with any marginal parameters and bayesian selection ideas can be employed we establish the effectiveness of the estimation method by modeling consumer behavior in online retail using archimedean and gaussian copulas the example shows that elliptical copulas can be poor at modeling depend

trade and currency options hedging model abstract this paper examines the trade and options hedging strategies for an exporting firm we present a trade and currency options hedging model at the first place aiming to minimize the conditional value at risk cvar in the proposed model a copula function is used to deduce the distribution function of the hedged portfolio then according to the equivalent formulas of cvar definition we transform the proposed model into a simple structure by the equivalence transformation method finally an empirical study of a gold exporting firm in china is conducted to illustrate the application of the proposed model the results show that for an importing firm to export the gold to a foreign country with currency options hedging is superior to that of selling the gold in the domestic market with or without currency options hedging in particular if the firm sells the gold only in the domestic market it is suggested to be equipped with currency options hedging simultaneously we analyze the sensitivities of the budget and the risk aversion degree and find out that the optimal option contract is affected by the budget in addition the risk aversion degree of the decision maker has no effects on the optimal strike price since currency options hedging is conducive to decrease cvar the firm is thus suggested to increase the budget on options

when uniform weak convergence fails empirical processes for dependence functions via epi and hypographs for copulas whose partial derivatives are not continuous everywhere on the interior of the unit cube the empirical copula process does not converge weakly with respect to the supremum distance this makes it hard to verify asymptotic properties of inference procedures for such copulas to resolve the issue a new metric for locally bounded functions is introduced and the corresponding weak convergence theory is developed convergence with respect to the new metric is related to epi and hypoconvergence and is weaker than uniform convergence still for continuous limits it is equivalent to locally uniform convergence whereas under mild side conditions it implies lp convergence even in cases where uniform convergence fails weak convergence with respect to the new metric is established for empirical copula and tail dependence processes no additional assumptions are needed for tail dependence functions and for copulas the assumptions reduce to existence and continuity of the partial derivatives almost everywhere on the unit cube the results are applied to obtain asymptotic properties of minimum distance estimators goodness of fit tests and resampling procedures

higher order hierarchical legendre basis functions for electromagnetic modeling this paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments mom the basis is derived from orthogonal legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements while maintaining most of their desirable features expressions are presented for wire surface and volume elements but emphasis is given to the surface elements in this case the new hierarchical basis leads to a near orthogonal expansion of the unknown surface current and implicitly an orthogonal expansion of the surface charge in addition all higher order terms in the expansion have two vanishing moments in contrast to existing formulations these properties allow the use of very high order basis functions without introducing ill conditioning of the resulting mom matrix numerical results confirm that the condition number of the mom matrix obtained with this new basis is much lower than existing higher order interpolatory and hierarchical basis functions as a consequence of the excellent condition numbers we demonstrate that even very high order mom systems e g tenth order can be solved efficiently with an iterative solver in relatively few iterations

multivariate countermonotonicity and the minimal copulas frchethoeffding upper and lower bounds play an important role in various bivariate optimization problems because they are the maximum and minimum of bivariate copulas in concordance order respectively however while the frchethoeffding upper bound is the maximum of any multivariate copulas there is no minimum copula available for dimensions d3 therefore multivariate minimization problems with respect to a copula are not straightforward as the corresponding maximization problems when the minimum copula is absent minimal copulas are useful for multivariate minimization problems we illustrate the motivation of generalizing the joint mixability to d countermonotonicity defined in lee and ahn 2014 through variance minimization problems and show that d countermonotonic copulas are minimal copulas

checking the adequacy of the gamma frailty model for multivariate failure times summary multivariate failure time data arise when the sample consists of clusters and each cluster contains several dependent failure times the semiparametric gamma frailty model vaupel manton stallard 1979 clayton 1978 oakes 1982 for multivariate failure times characterises the intracluster dependence by the gamma frailty distribution while allowing the marginal distributions to be unspecified this paper develops both graphical and numerical techniques for checking the adequacy of this model the proposed techniques are based on the posterior expectation of the frailty given the observable data two examples from genetics are provided

on superlinear p x laplacian problems without ambrosetti and rabinowitz condition abstract in this paper we consider the p x laplacian equations on the bounded domain the nonlinearity is superlinear but does not satisfy the usual ambrosetti rabinowitz condition near infinity or its dual version near zero existence and multiplicity results are obtained via morse theory and modified functional methods in a sense we expand a recent result of gasinski and papageorgiou l gasinski n s papageorgiou anisotropic nonlinear neumann problems calc var partial differential equations 42 2011 323 354

some comments on copula based regression in a recent article noh el ghouch and bouezmarni proposed a new semiparametric estimate of a regression function with a multivariate predictor which is based on a specification of the dependence structure between the predictor and the response by means of a parametric copula this comment investigates the effect which occurs under misspecification of the parametric model we demonstrate by means of several examples that even for a one or two dimensional predictor the error caused by a wrong specification of the parametric family is rather severe if the regression is not monotone in one of the components of the predictor moreover we also show that these problems occur for all of the commonly used copula families and we illustrate in several examples that the copula based regression may lead to invalid results even when flexible copula models such as vine copulas with the common parametric families are used in the estimation procedure