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 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

optimal goodness of fit tests for location scale families of distributions based on the sum of squares of l statistics a class of goodness of fit tests based on sums of squares of l statistics is proposed for testing a composite parametric location and or scale null hypothesis versus a general parametric alternative it is shown that such tests can be constructed optimally to have the same asymptotic power against sequences of local alternatives as the generalized likelihood ratio statistics g l r s and in fact under suitable regularity conditions to be asymptotically equivalent to the g l r s one advantage of the proposed test statistic over the g l r s is that only an estimate of the scale parameter is needed in the computation of the statistic no other parameter estimates are required also an example of the practical implementation of the proposed hypothesis testing procedure is given

estimation and model selection of semiparametric copula based multivariate dynamic models under copula misspecification we introduce a new class of semiparametric copula based multivariate dynamic scomdy models which specify the conditional mean and the conditional variance of a multivariate time series parametrically but specify the multivariate distribution of the standardized innovation semiparametrically as a parametric copula evaluated at nonparametric marginal distributions we first study large sample properties of the estimators of scomdy model parameters under a misspecified parametric copula then propose pseudo likelihood ratio plr tests for model selection between two scomdy models with possibly misspecified copulas and finally develop plr tests for model selection between more than two scomdy models the limiting null distributions of the plr tests do not depend on the estimation of conditional mean and conditional variance parameters hence are very easy to simulate empirical applications to three and higher dimensional daily exchange rate series indicate that a scomdy model with a tail dependent copula is generally preferred

bayesian gaussian copula factor models for mixed data gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data there is rich literature on their extension to mixed categorical and continuous variables using latent gaussian variables or through generalized latent trait models accommodating measurements in the exponential family however when generalizing to non gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions complicating interpretation and introducing artifacts to address this problem we propose a novel class of bayesian gaussian copula factor models that decouple the latent factors from the marginal distributions a semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains we provide new theoretical and empirical justifications for using this likelihood in bayesian inference we propose new default pri

power analyses for longitudinal study designs with missing data existing methods for power analysis for longitudinal study designs are limited in that they do not adequately address random missing data patterns although the pattern of missing data can be assessed during data analysis it is unknown during the design phase of a study the random nature of the missing data pattern adds another layer of complexity in addressing missing data for power analysis in this paper we model the occurrence of missing data with a two state first order markov process and integrate the modelling information into the power function to account for random missing data patterns the markov model is easily specified to accommodate different anticipated missing data processes we develop this approach for the two most popular longitudinal models the generalized estimating equations gee and the linear mixed effects model under the missing completely at random mcar assumption for gee we also limit our consideration to the working independence correlation model the proposed methodology is illustrated with numerous examples that are motivated by real study designs

data driven version of neyman s smooth test of fit abstract neyman s smooth test for testing uniformity is a recognized goodness of fit procedure as stated by lariccia the test can be viewed as a compromise between omnibus test procedures with generally low power in all directions and procedures whose power is focused in the direction of a specific alternative the basic idea behind this test is to embed the null density into say a k dimensional exponential family and then to construct an asymptotically optimal test for the parametric testing problem the resulting procedure is neyman s test with k components the most difficult problem related with using this test is the choice of k recommendations in statistical literature are sometimes confusing some authors advocate a small number of components whereas others show that in some situations a larger number of components is profitable all existing suggestions concerning how to select k exploit in fact some preliminary knowledge about a possible alternative in this article a new data driven met

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

selection of mixed copula model via penalized likelihood a fundamental issue of applying a copula method in applications is how to choose an appropriate copula function for a given problem in this article we address this issue by proposing a new copula selection approach via penalized likelihood plus a shrinkage operator the proposed method selects an appropriate copula function and estimates the related parameters simultaneously we establish the asymptotic properties of the proposed penalized likelihood estimator including the rate of convergence and asymptotic normality and abnormality particularly when the true coefficient parameters may be on the boundary of the parameter space and the dependence parameters are in an unidentified subset of the parameter space we show that the limiting distribution for boundary parameter estimator is half normal and the penalized likelihood estimator for unidentified parameter converges to an arbitrary value finally monte carlo simulation studies are carried out to illustrate the finite sample performance of the pro

a lack of fit test for quantile regression we propose an omnibus lack of fit test for linear or nonlinear quantile regression based on a cusum process of the gradient vector the test does not involve nonparametric smoothing but is consistent for all nonparametric alternatives without any moment conditions on the regression error in addition the test is suitable for detecting the local alternatives of any order arbitrarily close to n 1 2 from the null hypothesis the limiting distribution of the proposed test statistic is non gaussian but can be characterized by a gaussian process we propose a simple sequential resampling scheme to carry out the test whose nominal levels are well approximated in our empirical study for

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

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

data driven smooth tests when the hypothesis is composite in recent years several authors have recommended smooth tests for testing goodness of fit however the number of components in the smooth test statistic should be chosen well otherwise considerable loss of power may occur schwarz s selection rule provides one such good choice earlier results on simple null hypotheses are extended here to composite hypotheses which tend to be of more practical interest for general composite hypotheses consistency of the data driven smooth tests holds at essentially any alternative monte carlo experiments on testing exponentiality and normality show that the data driven version of neyman s test compares well to other even specialized tests over a wide range of alternatives

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

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

statistical inference for conditional quantiles in nonlinear time series models abstract this paper studies the statistical properties of a two step conditional quantile estimator in nonlinear time series models with unspecified error distribution the asymptotic distribution of the quasi maximum likelihood estimators and the filtered empirical percentiles is derived three applications of the asymptotic result are considered first we construct an interval estimator of the conditional quantile without any distributional assumptions second we develop a specification test for the error distribution finally using the specification test we propose methods for estimating the tail index of the error distribution that supports the construction of a new estimator for the conditional quantile at the extreme tail the asymptotic results and their applications are illustrated by simulations and real data analyses in which our methods for analyzing daily and intraday financial return series have been adopted

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

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

composite likelihood bayesian information criteria for model selection in high dimensional data for high dimensional data sets with complicated dependency structures the full likelihood approach often leads to intractable computational complexity this imposes difficulty on model selection given that most traditionally used information criteria require evaluation of the full likelihood we propose a composite likelihood version of the bayes information criterion bic and establish its consistency property for the selection of the true underlying marginal model our proposed bic is shown to be selection consistent under some mild regularity conditions where the number of potential model parameters is allowed to increase to infinity at a certain rate of the sample size simulation studies demonstrate the empirical performance of this new bic especially for the scenario where the number of parameters increases with sample size technical proofs of our theoretical results are provided in the online supplemental materials

generalized covariance adjusted canonical correlation analysis with application to psychiatry the lack of control over covariates in practice motivates the need for their adjustment when measuring the degree of association between two sets of variables for which canonical correlation is traditionally used in most studies however there is also a lack of control over the attributes of responses for the sets of variables of interest in particular a portion of the response variable may be continuous and the other discrete for such settings the traditional partial canonical correlation approach is restrictive since a covariate adjustment for a set of continuous variables is assumed by ignoring the assumption of continuous variates and proceeding with a partial canonical correlation analysis in the presence of continuous and discrete variates results in canonical correlation estimates that are not consistent in this paper we generalize the traditional partial canonical correlation approach to covariate adjustment by allowing the response variables to contain continuous as well as discrete variates the methodology is illustrated with a psychiatric application for examining which sleep variables relate to which depressive symptoms as measured by commonly used constructs that presents with both continuous and discrete outcomes

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

neyman type smooth tests for location scale families summary the smooth tests of neyman 1937 are modified to permit composite alternatives and a choice of orthonormal functions in their construction these orthonormal functions may be chosen to improve detection of particular alternatives the tests are easy to apply and have useful orthogonal components a test for exponentiality is examined and shown to perform well against its competitors

smooth goodness of fit tests a quantile function approach abstract a quantile function based analog to neyman s smooth tests for goodness of fit hypotheses is developed these procedures possess asymptotic and small sample power properties similar to those for smooth tests they are however computationally simple applicable to both complete and type ii censored data and easily focused in the direction of any specific set of alternatives these results are used to develop a new test for exponentiality only location scale null hypotheses will be considered the ideas are easily adapted to other types of nulls however neyman first proposed smooth tests for the goodness of fit hypothesis as stated by kopecky and pierce and by rayner and best the basic idea behind these tests is to embed the null density in a larger exponential family the procedure is then based upon the likelihood ratio test statistic for testing that the additional parameters equal zero smooth type tests may be viewed as a compromise between omnibus test procedures with generally low po

asymptotically chi squared distributed tests of normality for type ii censored samples abstract a method is proposed for testing normality in the case of general type ii censored data that is data for which only a subset of the order statistics are available three test statistics are proposed which are generalizations of the statistics proposed in lariccia 1986 and have many of the same properties specifically they are designed to be asymptotically optimal with respect to specific alternatives and are easily adjusted to be asymptotically optimal with respect to many other types of alternatives under the null hypothesis irrespective of the type or amount of censoring the proposed test statistics are asymptotically distributed as chi squared random variables further results of a simulation study are presented indicating that these statistics converge quite rapidly in distribution to the appropriate chi squared random variables and that the asymptotic critical values provide a useful approximation to the small sample critical values even for n 25 the results of a simulation s