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 nonparametric estimation procedure for bivariate extreme value copulas summary a bivariate extreme value distribution with fixed marginals is generated by a onedimensional map called a dependence function this paper proposes a new nonparametric estimator of this function its asymptotic properties are examined and its small sample behaviour is compared to that of other rank based and likelihood based procedures the new estimator is shown to be uniformly strongly convergent and asymptotically unbiased through simulations it is also seen to perform reasonably well against the maximum likelihood estimator based on the correct model and to have smaller l1 l2 and l errors than any existing nonparametric alternative the n consistency of the proposed estimator leads to nonparametric estimation of tawn s 1988 dependence measure that may be used to test independence in small samples

on the structure and estimation of hierarchical archimedean copulas in this paper we provide a method for estimating multivariate distributions defined through hierarchical archimedean copulas in general the true structure of the hierarchy is unknown but we develop a computationally efficient technique to determine it from the data for this purpose we introduce a hierarchical estimation procedure for the parameters and provide an asymptotic analysis we consider both parametric and nonparametric estimation of the marginal distributions a simulation study and an empirical application show the effectiveness of the grouping procedure in the sense of structure selection

homogeneous mean values weights and asymptotics 1 the weights w1 wn associated with a mean value m x1 xn are defined as partial derivatives of m and identified for various homogeneous means 2 we prove theorem 1 if a1 an are real and x then m a1 x an x x wiai o 1x provided only that m satisfies very general hypotheses in particular this asymptotic formula originally discovered by l hoehn and i niven math mag 58 1985 151 156 in special cases is valid for power means dresher means mixed means and hypergeometric means 3 we prove theorem 2 if x1 x2 is an infinite sequence of positive numbers lying in a finite interval 0 xi and if the arithmetic mean of the first n values approaches a limit as n then the hypergeometric mean approaches the same limit this theorem was first established for the special case of the logarithmic mean of any order by a o pittenger j math anal appl 123 1987 281 291

global stabilization of the generalized korteweg de vries equation posed on a finite domain this paper is concerned with the internal stabilization of the generalized korteweg de vries equation on a bounded domain the global well posedness and the exponential stability are investigated when the exponent in the nonlinear term ranges over the interval 1 4 the global exponential stability is obtained whatever the location where the damping is active confirming positively a conjecture of perla menzala vasconcellos and zuazua quart appl math 60 2002 pp 111 129

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

improved kernel estimation of copulas weak convergence and goodness of fit testing we reconsider the existing kernel estimators for a copula function as proposed in gijbels and mielniczuk comm statist theory methods 19 1990 445 464 fermanian radulovic and wegkamp bernoulli 10 2004 847 860 and chen and huang canad j statist 35 2007 265 282 all of these estimators have as a drawback that they can suffer from a comer bias problem a way to deal with this is to impose rather stringent conditions on the copula outruling as such many classical families of copulas in this paper we propose improved estimators that take care of the typical corner bias problem for gijbels and mielniczuk comm statist theory methods 19 1990 445 464 and chen and huang canad j statist 35 2007 265 282 the improvement involves shrinking the bandwidth with an appropriate functional factor for fermanian radulovic and wegkamp bernoulli 10 2004 847 860 this is done by using a transformation the theoretical contribution of the paper is a weak convergence result for the three improved estimators under conditions that are met for most copula families we also discuss the choice of bandwidth parameters theoretically and practically and illustrate the finite sample behaviour of the estimators in a simulation study the improved estimators are applied to goodness of fit testing for copulas

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

on the estimation of pareto fronts from the point of view of copula theory a probabilistic framework is applied to pareto front estimation a link between pareto front and level lines of a multivariate distribution is given parametric approximations of pareto front are provided for archimedean copulas consequences and limits of the archimedean hypothesis are discussed the full estimation methodology is analyzed on several examples given a first set of observations from a design of experiments sampled randomly in the design space the corresponding set of non dominated points usually does not give a good approximation of the pareto front we propose here to study this problem from the point of view of multivariate analysis introducing a probabilistic framework with the use of copulas this approach enables the expression of level lines in the objective space giving an estimation of the position of the pareto front when the level tends to zero in particular when it is possible to use archimedean copulas analytical expressions for pareto front estimators are available several case studies illustrate the interest of the approach which can be used at the beginning of the optimization when sampling randomly in the design space

on the asymptotic behaviour of the pseudolikelihood ratio test statistic this paper concerns the asymptotic distribution of the likehood ratio statistic t for testing h 0 0 based on the pseudolikelihood l where is a simple estimator of we show that the asymptotic distribution of t under h 0 is a weighted sum of indepepdent x 1 2 variables where the weights involve the asymptotic joint covariance matrix of and the score function for some sufficient conditions are provided for the limiting distribution to be x 2 the result is extended to allow 0 to be a boundary value of the parameter space and to be misspecified in l we also examine the issue of power loss when is misspecified in l several examples including variance component models multivariate survival models genetic linkage analysis and the behrens fisher problem are presented to demonstrate the scope of the problems considered and to illustrate the results

estimation of dependence between paired correlated failure times in the presence of covariate measurement error summary in many biomedical studies covariates are subject to measurement error although it is well known that the regression coefficients estimators can be substantially biased if the measurement error is not accommodated there has been little study of the effect of covariate measurement error on the estimation of the dependence between bivariate failure times we show that the dependence parameter estimator in the clayton oakes model can be considerably biased if the measurement error in the covariate is not accommodated in contrast with the typical bias towards the null for marginal regression coefficients the dependence parameter can be biased in either direction we introduce a bias reduction technique for the bivariate survival function in copula models while assuming an additive measurement error model and replicated measurement for the covariates and we study the large and small sample properties of the dependence parameter estimator proposed

exact boundary controllability for the linear korteweg de vries equation on the half line this paper is concerned with the controllability of the linear korteweg de vries equation on the domain o 0 infty the control being applied at the left endpoint x 0 it is shown that the em exact boundary controllability holds true in l 2 0 infty provided that the solutions are not required to be in l infty 0 t l 2 0 infty the proof rests on a carleman s estimate and an approximation theorem a similar result is obtained for the heat equation and for the schrodinger equation

boundary control of the korteweg de vries burgers equation further results on stabilization and well posedness with numerical demonstration we consider the korteweg de vries burgers equation on the interval 0 1 motivated by simulations resulting in modest decay rates with recently proposed control laws by liu and krstic which keeps some of the boundary conditions as homogeneous we propose a strengthened set of feedback boundary conditions we establish stability properties of the closed loop system prove well posedness and illustrate the performance improvement by a simulation example

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

decay of solutions of some nonlinear wave equations abstract we study the large time behaviour of solutions to the initial value problem for the korteweg de vries equation and for the regularized long wave equation with a dissipative term appended using energy estimates a maximum principle and a transformation of cole hopf type sharp rates of temporal decay of certain norms of the solution are obtained

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

exact boundary controllability of the korteweg de vries equation we consider boundary control of the distributed parameter system described by the korteweg de vries kdv equation posed on a finite interval alpha leq x leq beta left begin array l u t u x uu x u xxx 0 u alpha t h 1 t qquad u beta t h 2 t qquad u x beta t h 3 t u end array right qquad for t geq 0 it is shown that by choosing appropriate control inputs h j t j 1 2 3 one can always guide the system from a given initial state phi in h s alpha beta to a given terminal state psi in h s alpha beta in the time period 0 t so long as phi and psi satisfy phi cdot w cdot 0 h s alpha beta leq delta quad mbox and quad psi cdot w cdot t h s alpha beta leq delta for some delta 0 independent of phi and psi where s geq 0 and w equiv w x t is a given smooth solution of the kdv equation this exact boundary controllability is established by considering a related initial value control problem of the kdv equation posed on the whole line r various recently discovered smoothing properties of the kdv equation have played important roles in our approach

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

semiparametric estimation of marginal mark distribution in many applications the outcome of interest is a mark such that its observation is contingent upon occurrence of an event with incomplete follow up data the marginal mark distribution is however nonparametrically nowhere identifiable in many practical situations to address this problem we suggest a semiparametric model that postulates a normal copula for the association between the mark and survival time but leaves the marginals unspecified we show identifiability of the marginal mark distribution under this model and propose an inference procedure the estimated marginal distribution function is consistent and asymptotically normal and it provides a basis for estimating summaries of the mark furthermore we propose graphical model checking methods and kolmogorov smirnov type goodness of fit tests simulation studies demonstrate that the inference procedure performs well in practical settings the method is applied to the estimation of lifetime medical cost in a lung cancer trial

semiparametric dynamic max copula model for multivariate time series summary the paper presents a novel non linear framework for the construction of flexible multivariate dependence structure i e copulas from existing copulas based on a straightforward pairwise max rule the newly constructed max copula has a closed form and has strong interpretability compared with the classical linear symmetric mixture copula the max copula can be viewed as a non linear asymmetric framework it is capable of modelling asymmetric dependence and joint tail behaviour while also offering good performance in non extremal behaviour modelling max copulas that are based on single factor and block factor models are developed to offer parsimonious modelling for structured dependence especially in high dimensional applications combined with semiparametric time series models the max copula can be used to develop flexible and accurate models for multivariate time series a new semiparametric composite maximum likelihood method is proposed for parameter estimation where the consistency and asymptotic normality of estimators are established the flexibility of the max copula and the accuracy of the proposed estimation procedure are illustrated through extensive numerical experiments real data applications in value at risk estimation and portfolio optimization for financial risk management demonstrate the max copula s promising ability to capture accurately joint movements of high dimensional multivariate stock returns under both normal and crisis regimes of the financial market

exact controllability of a nonlinear korteweg de vries equation on a critical spatial domain we consider the boundary controllability problem for a nonlinear korteweg de vries equation with the dirichlet boundary condition we study this problem for a spatial domain with a critical length for which the linearized control system is not controllable in order to deal with the nonlinearity we use a power series expansion of second order we prove that the nonlinear term gives the local exact controllability around the origin provided that the time of control is large enough

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

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

estimation and model selection of semiparametric multivariate survival functions under general censorship we study estimation and model selection of semiparametric models of multivariate survival functions for censored data which are characterized by possibly misspecified parametric copulas and nonparametric marginal survivals we obtain the consistency and root n asymptotic normality of a two step copula estimator to the pseudo true copula parameter value according to klic and provide a simple consistent estimator of its asymptotic variance allowing for a first step nonparametric estimation of the marginal survivals we establish the asymptotic distribution of the penalized pseudo likelihood ratio statistic for comparing multiple semiparametric multivariate survival functions subject to copula misspecification and general censorship an empirical application is provided

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

local likelihood estimation of complex tail dependence structures applied to u s precipitation extremes to disentangle the complex nonstationary dependence structure of precipitation extremes over the entire contiguous united states u s we propose a flexible local approach based on factor copula

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

rapid stabilization for a korteweg de vries equation from the left dirichlet boundary condition this paper deals with the stabilization problem for the korteweg de vries equation posed on a bounded interval the control acts on the left dirichlet boundary condition at the right end point dirichlet and neumann homogeneous boundary conditions are considered the proposed feedback law forces the exponential decay of the system under a smallness condition on the initial data moreover the decay rate can be tuned to be as large as desired the feedback control law is designed by using the backstepping method

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

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

extensions of subcopulas abstract in view of sklar s theorem the probability distribution function of every not necessarily continuous random vector can be uniquely decomposed in terms of the marginal distributions of its components and a suitable subcopula the study of such latter functions is therefore of interest for understanding the dependence information of non continuous variables here we investigate some analytical properties of the class of subcopulas including compactness with respect to a novel metric approximations and baire category results moreover under a suitable assumption we describe all possible extensions from a subcopula to a copula in any dimension

nonparametric estimation and inference for conditional density based granger causality measures we propose a nonparametric estimation and inference for conditional density based granger causality measures that quantify linear and nonlinear granger causalities we first show how to write the causality measures in terms of copula densities thereafter we suggest consistent estimators for these measures based on a consistent nonparametric estimator of copula densities furthermore we establish the asymptotic normality of these nonparametric estimators and discuss the validity of a local smoothed bootstrap that we use in finite sample settings to compute a bootstrap bias corrected estimator and to perform statistical tests a monte carlo simulation study reveals that the bootstrap bias corrected estimator behaves well and the corresponding test has quite good finite sample size and power properties for a variety of typical data generating processes and different sample sizes finally two empirical applications are considered to illustrate the practical relevance of nonparametric causality measures

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

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

boosting the decay of solutions of the linearised korteweg de vries burgers equation to a predetermined rate from the boundary abstractthe aim of this article is to extend recent results on the boundary feedback controllability of the korteweg de vries equation to the korteweg de vries burgers equation which is posed on a bounded domain in the first part of the paper it is proven that all the sufficiently small solutions can be steered to zero at any desired exponential rate by means of a suitably constructed boundary feedback controller in the second part an observer is proposed when a type of boundary measurement is available while there is no full access to the medium

convergence results for patchwork copulas abstract we present a general construction that allows to extend a given subcopula to a copula in such a way that the extension is affine on some specific segments of the copula domain this construction is hence applied to provide convergence theorems for approximating a copula in strong convergence and in d 1 metric related to the markov kernel representation of a copula

nonparametric inference for copulas and measures of dependence under length biased sampling and informative censoring length biased data are often encountered in cross sectional surveys and prevalent cohort studies on disease durations under length biased sampling subjects with longer disease durations have great

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

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

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

a copula approach for detecting prognostic genes associated with survival outcome in microarray studies a challenging and crucial issue in clinical studies in cancer involving gene microarray experiments is the discovery among a large number of genes of a relatively small panel of genes whose elements are associated with a relevant clinical outcome variable such as time to death or time to recurrence of disease a semiparametric approach using dependence functions known as copulas is considered to quantify and estimate the pairwise association between the outcome and each gene expression these time to event type endpoints are typically subject to censoring as not all events are realized at the time of the analysis furthermore given that the total number of genes is typically large it is imperative to control a relevant error rate in any gene discovery procedure the proposed method addresses the two aforementioned issues by direct incorporation of the censoring mechanism and by appropriate statistical adjustment for multiplicity the performance of the proposed method is studied through simulation and illustrated with an application using a case study in lung cancer

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

goodness of fit test for specification of semiparametric copula dependence models this paper concerns goodness of fit tests for semiparametric copula models our contribution is two fold we first propose a new test constructed via the comparison between in sample and out of sample pseudo likelihoods under the null hypothesis that the copula model is correctly specified we show that the proposed test statistic converges in probability to a constant equal to the dimension of the parameter space we establish the asymptotic normality and investigate the local power of the test we also extend the proposed test to the specification test of a class of multivariate time series models and propose a new bootstrap procedure to establish the finite sample null distribution which is shown to have better control of type i error than the commonly used bootstrap secondly we introduce a bonferroni based hybrid mechanism to combine several test statistics which yields a useful test this hybrid method is particularly appealing when there exists no single dominant optimal test we conduct comprehensive simulation experiments to compare the proposed new test and hybrid approach with two of the best blanket tests in the literature for illustration we apply the proposed tests to analyze two real datasets

semi nonparametric var forecasts for hedge funds during the recent crisis abstract the need to provide accurate value at risk var forecasting measures has triggered an important literature in econophysics although these accurate var models and methodologies are particularly demanded for hedge fund managers there exist few articles specifically devoted to implement new techniques in hedge fund returns var forecasting this article advances in these issues by comparing the performance of risk measures based on parametric distributions the normal student s t and skewed t semi nonparametric snp methodologies based on gram charlier gc series and the extreme value theory evt approach our results show that normal student s t and skewed t based methodologies fail to forecast hedge fund var whilst snp and evt approaches accurately success on it we extend these results to the multivariate framework by providing an explicit formula for the gc copula and its density that encompasses the gaussian copula and accounts for non linear dependences we show that the var obtained by the meta gc accurately captures portfolio risk and outperforms regulatory var estimates obtained through the meta gaussian and student s t distributions

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

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

exact controllability and stabilizability of the korteweg de vries equation in this paper we consider distributed control of the system described by the korteweg de vries equation i atu uaxu e3 u f on the interval 0 0 with periodic boundary conditions ii au 27r t ku o t k 0 1 2 where the distributed control f f x t is restricted so that the volume f u x t dx of the solution is conserved both exact controllability and stabilizibility questions are studied for the system in the case of open loop control if the control f is allowed to act on the whole spatial domain 0 27r it is shown that the system is globally exactly controllable i e for given t 0 and functions q x x with the same volume one can alway find a control f so that the system i ii has a solution u x t satisfying u x 0 0 x u x t x if the control f is allowed to act on only a small subset of the domain 0 27r then the same result still holds if the initial and terminal states b and 0 have small amplitude in a certain sense in the case of closed loop control the distributed control f is assumed to be generated by a linear feedback law conserving the volume while monotonically reducing f u x t 2dx the solutions of the resulting closed loop system are shown to have uniform exponential decay to a constant state as in the open loop control case a small amplitude assumption is needed if the control is allowed to act on only a small subdomain the smoothing property of the periodic linear kdv equation discovered recently by bourgain has played an important role in establishing the exact controllability and stabilizability results presented in this paper

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

fitting bivariate copulas to the dependence structure between storm characteristics a detailed analysis based on 105 year 10 min rainfall 1 the use of copulas as flexible tools for constructing marginal free distribution functions for multivariate phenomena such as rainfall recently enjoys substantial attention by researchers in hydrology in this study commonly used bivariate copulas and techniques for fitting such bivariate copulas are applied to different couples of storm variables based on an extensive data set of 105 years of 10 min rainfall observed at uccle belgium in the analysis various problems that can occur are highlighted and opportunities for further research are outlined after selecting storms and introducing a meaningful solution to circumvent the presence of abundant ties in the data a detailed seasonal dependence analysis is provided together with a study on tail dependence further different existing parameter estimation techniques and goodness of fit methods for selecting the most appropriate bivariate copulas are applied and compared finally attention is given to the presence of asymmetric dependence and nonexchangeability

boundary feedback stabilization of the korteweg de vries burgers equation posed on a finite interval abstract this paper studies the boundary feedback stabilization problem of the korteweg de vries burgers equation posed on a finite interval a linear boundary feedback control law is proposed then the resulting closed loop nonlinear system is shown not only to be globally well posed but also to be exponentially stable in the space h s 0 l with s 0 3 the sharp kato smoothing property of the associated linear problem is revealed through the boundary integral operator which plays a key role in our analysis

on metric spaces of subcopulas abstract in this work we show that two distance functions independently defined on the space of subcopulas are topological equivalent in this process we also defined another distance function equivalent to the first two distances moreover all metric spaces of subcopulas with fixed domain under the supremum distance are metric subspaces under this new distance function we also prove that the sklar correspondence can be viewed as a lipschitz map under these metrics thus the rate of convergence of empirical subcopulas can be computed directly from the rate of convergence of empirical distributions the same holds for other statistics results

modelling multivariate failure time associations in the presence of a competing risk there has been much research on analysing multivariate failure times but little that has accommodated failures that arise in the presence of a competing failure process this paper studies the problem of describing associations among times to such failures it proposes a modified conditional hazard ratio measure of association that is tailored to competing risks data develops frailty models and a nonparametric method for describing the proposed measure and contrasts estimation by proposed methods with the standard of treating competing risks as independently censoring failure times due to targeted causes the methods are investigated on simulated and real data

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

copula based regression estimation and inference we investigate a new approach to estimating a regression function based on copulas the main idea behind this approach is to write the regression function in terms of a copula and marginal distributions once the copula and the marginal distributions are estimated we use the plug in method to construct our new estimator because various methods are available in the literature for estimating both a copula and a distribution this idea provides a rich and flexible family of regression estimators we provide some asymptotic results related to this copula based regression modeling when the copula is estimated via profile likelihood and the marginals are estimated nonparametrically we also study the finite sample performance of the estimator and illustrate its usefulness by analyzing data from air pollution studies

copula model generated by dabrowska s association measure summary we propose a new archimedean copula model for bivariate survival data that is motivated by dabrowska s 1988 measure of association the model can represent negatively correlated or moderately positively correlated data but not highly positively correlated data local and global measures of association are calculated a generalisation is presented

efficient estimation of semiparametric multivariate copula models we propose a sieve maximum likelihood estimation procedure for a broad class of semiparametric multivariate distributions a joint distribution in this class is characterized by a parametric copula function evaluated at nonparametric marginal distributions this class of distributions has gained popularity in diverse fields due to its flexibility in separately modeling the dependence structure and the marginal behaviors of a multivariate random variable and its circumvention of the curse of dimensionality associated with purely nonparametric multivariate distributions we show that the plug in sieve maximum likelihood estimators mles of all smooth functionals including the finite dimensional copula parameters and the unknown marginal distributions are semiparametrically efficient and that their asymptotic variances can be estimated consistently moreover prior restrictions on the marginal distributions can be easily incorporated into the sieve maximum likelihood estimation procedure to achieve fu

consensus algorithms with state dependent weights we provide an analysis of a distributed consensus type algorithm with weights dependent only on the received data our approach does not require any global knowledge of the network which distinguishes our approach from most other contributions in general the weights may be further modified by any function this in turn may model various network behaviors e g link failures and time varying networks we provide general convergence conditions prove several important properties derive steady states for such locally derived weights as well as analyze the convergence rate of the algorithm applications of such weight model include distributed algorithms which do not require exact average and have no global information about the network topology

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

parameter estimation of bivariate distributions in presence of outliers an application to fgm copula abstract existing outliers always make it difficult to estimate the dependence parameter of bivariate variables parameter estimation plays a major role in statistical inference and applied statistics bivariate copula is one of the effective tool to study the outliers because of its simplicity in this article we use bivariate copula and obtain a formula for it in presence of outliers as a prevalent way we consider n sample pairs of x i y i in which we have k pairs of outliers and n k pairs of real data and introduce their likelihood function in presence of k outliers and then estimate the corresponding dependence parameter and the noise parameter using some different methods via copula function also some measures of dependence are obtained and compared in presence of outliers empirically finally fgm copula and its application to real case study are considered for illustrating the results

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

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