a regression model for multivariate random length data multivariate random length data occur when we observe multiple measurements of a quantitative variable and the variable number of these measurements is also an observed outcome for each experimental unit for example for a patient with coronary artery disease we may observe a number of lesions in that patient s coronary arteries along with percentage of blockage of each lesion barnhart and sampson first proposed the multiple population model to analyse multivariate random length data without covariates this paper extends their approach to deal with multiple covariates we propose a new multiple population regression model with covariates and discuss the estimation issues we analyse data from the type ii coronary intervention study to illustrate the methodology

a joint modeling approach for multivariate survival data with random length summary in many biomedical studies that involve correlated data an outcome is often repeatedly measured for each individual subject along with the number of these measurements which is also treated as an observed outcome this type of data has been referred as multivariate random length data by barnhart and sampson 1995 a common approach to handling such type of data is to jointly model the multiple measurements and the random length in previous literature a key assumption is the multivariate normality for the multiple measurements motivated by a reproductive study we propose a new copula based joint model which relaxes the normality assumption specifically we adopt the clayton oakes model for multiple measurements with flexible marginal distributions specified as semi parametric transformation models the random length is modeled via a generalized linear model we develop an approximate em algorithm to derive parameter estimators and standard errors of the estimators are obtained through bootstrapping procedures and the finite sample performance of the proposed method is investigated using simulation studies we apply our method to the mount sinai study of women office workers msswow where women were prospectively followed for 1 year for studying fertility

systems of multidimensional discrete inequalities on considere des systemes lineaires de m inegalites discretes comprenant des fonctions a n variables independantes

perron s method for hamilton jacobi equations on considere l existence des solutions d equations aux derivees partielles non lineaires scalaires d ordre 1 f x u du 0 dans ou est un sous ensemble ouvert de r n f r r n r est continue u r est l inconnue

maximum likelihood estimation of intraclass correlation in the analysis of familial data estimating equation approach summary we introduce a generalized model for estimating intraclass correlation in the analysis of familial data this model incorporates the models of donner koval 1980 donner bull 1983 rosner 1984 and miunoz rosner carey 1986 as special cases we then obtain the maximum likelihood estimates of the parameters of the model in particular we obtain a single estimating equation to be solved iteratively for the estimation of the intraclass correlation p and discuss all the special cases asymptotic variance for the estimate of the intraclass correlation is obtained for all the models and some examples are given

holder gradient estimates for fully nonlinear elliptic equations in this paper we prove interior and global holder estimates for lipschitz viscosity solutions of second order nonlinear uniformly elliptic equations the smoothness hypotheses on the operators are more general than previously considered for classical solutions so that our estimates are also new in this case and readily extend to embrace obstacle problems in particular isaac s equations of stochastic differential game theory constitute a special case of our results and moreover our techniques in combination with recent existence theorems of ishii lead to existence theorems for continuously differentiable viscosity solutions of the uniformly elliptic isaac s equation

hamilton jacobi equations in infinite dimensions i uniqueness of viscosity solutions soient un espace de banach v son dual v et des solutions d une equation h x u du 0 dans etablies dans un sous ensemble de v h v r v r est continue on demontre que des solutions classiques sont determinees de facon unique par leurs valeurs limites on montre que l extension de la notion de solutions viscosite aux espaces de banach reussit dans des espaces munis de la propriete de radon nikodym

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions part i the case of bounded stochastic evolutions on etudie des equations elliptiques degenerees d ordre 2 non lineaires de la forme f d 2 u du u x 0 dans h ou h est un espace de hilbert separable x un point generique dans h u une fonction de h r

viscosity solutions of hamilton jacobi equations in infinite dimensions iv hamiltonians with unbounded linear terms in this work we show how to interpret s and e in the viscosity sense when the solutions may be expected to be weakly sequentially continuous in particular we introduce notions which allow us to handle the terms and for which we can obtain existence and uniqueness results in a variety of circumstances

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions iii uniqueness of viscosity solutions for general second order equations we prove here the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second order equations in an infinite dimensional hilbert space the uniqueness is proved using the so called inf and sup convolutions which allow some reduction to finite dimensional problems

the maximum principle for viscosity solutions of fully nonlinear second order partial differential equations we prove that viscosity solutions in w1 of the second order fully nonlinear equation f d2u du u 0 are unique when i f is degenerate elliptic and decreasing in u or ii f is uniformly elliptic and nonincreasing in u we do not assume that f is convex the method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions respectively this method is completely different from that used in lions 8 9 for second order problems with f convex in d 2 u and from that used by crandall lions 3 and crandall evans lions 2 for fully nonlinear first order problems

representation of solutions of hamilton jacobi equations on etudie le probleme de cauchy pour l equation de hamilton jacobi u t h t x du 0 dans o t r n avec la condition initiale u o x u o x pour x r n on a t 0 hi o t r n r n r et u o r n r sont donnes on represente la solution viscosite comme la fonction valeur d un jeu differentiel approprie

hamilton jacobi equations in infinite dimensions iii on etudie des equations de la forme f x u du 0 dans ou est un sous ensemble ouvert d un espace de banach v la fonction inconnue u r est continue du x est la derivee de frechet de u en x et f est une fonction non lineaire qui est une application continue de r v dans r on introduit la notion de solution viscosite stricte afin d eliminer l hypothese que v a la propriete de radon nikodym

estimation of the interclass correlation coefficient summary a noniterative method for estimating the interclass correlation coefficient is derived from the technique of weighted sums of squares the asymptotic variance of this estimator is derived under the assumption of normality through extensive monte carlo simulations the sample variance of this estimator is found not to differ greatly from that of the maximum likelihood estimator an important problem in genetics is the estimation of the degree of resemblance between a mother and her children as measured by the interclass correlation coefficient because parents produce differing numbers of offspring during their reproductive period the maximum likelihood estimation of the interclass correlation presents computational difficulties requiring an iterative solution therefore a number of noniterative estimators have been proposed in the literature these estimators will be shown to be associated with special cases of the generalized estimator derived from the weighted sums of squares of measurements on parents and offspring because our purpose is to provide a comprehensive approach to the noniterative point and interval estimation problems for the interclass correlation coefficient the asymptotic variance of the proposed estimator is derived under the assumption of normality moreover the sample variances of two special cases of the proposed estimator are compared to that of the maximum likelihood estimator through monte carlo simulations by a theoretical argument it is shown that the estimator proposed by srivastava 1984 has a uniformly smaller asymptotic variance than the ensemble estimator proposed by rosner donner hennekens 1977 smith 1957 used the weighted sums of squares approach for the estimation problem concerning the intraclass correlation coefficient which measures the degree to which siblings resemble one another our results together with those of smith 1957 provide a unified approach to estimation problems concerning familial correlations among a parent and offspring

multiple population models for multivariate random length data with applications in clinical trials this paper focuses on the development and study of multiple population models for multivariate random length data of the type often encountered in clinical trials if experimental outcomes per subject consist of multiple measurements of a quantitative variable and the number of these measurements then a multivariate random length vector is observed for this type of data the experimental treatment is likely to affect both the quantitative measurements and the number of these measurements one example of such data is from the national heart lung and blood institute type ii coronary intervention study brensike et al 1982 controlled clinical trials 3 91 111 1984 circulation 69 313 324 the outcome data consist of vectors of lesion sizes with lengths determined by the number of underlying lesions assessed from the patients angiograms where both the numbers and the lesion sizes depend on patients overall disease status we propose models which can realistically describe the relationships between the quantitative variables and the number of responses the asymptotic covariance of the maximum likelihood estimators is obtained data from the type ii study are analyzed using this multiple population model

viscosity solutions of hamilton jacobi equations in infinite dimensions v unbounded linear terms and b continuous solutions we continue the systematic study of first order hamilton jacobi equations in infinite dimensions begun in parts i iv of this series 121 our approach relies on as before an appropriate interpretation of the notion of viscosity solutions as introduced in 11 lo in the interim the strong development of viscosity solution theory in many directions has continued unabated in addition to the many references given in earlier papers in this series which we will not repeat here see 12 we would like to point out that a complete theory of second order fully nonlinear and possibly degenerate elliptic equations in finite dimensions has been made possible by the use of viscosity solutions s 9 18 20 22 19 32 331 for example and there is now a substantial body of work concerning second order equations in infinite dimensions 25 271 however in this work we come back to the particular situation studied in 12 part iv namely we come back to hamilton jacobi equations in

interior a priori estimates for solutions of fully non linear equations on etend une theorie de perturbations aux solutions d equations uniformement elliptiques d ordre 2 totalement non lineaires

the necessary conditions for optimal control in hilbert spaces obtention du principe maximum de pontryagin pour une classe generale de problemes de commande de type lagragien afin qu associe avec un ensemble de conditions necessaires une commande soit satisfaite le principe est demontre en utilisant la programmation dynamique et l equation resultante d hamilton jacobi bellman de dimension finie

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author