a global sensitivity test for evaluating statistical hypotheses with nonidentifiable models we consider the problem of evaluating a statistical hypothesis when some model characteristics are nonidentifiable from observed data such a scenario is common in meta analysis for assessing publication bias and in longitudinal studies for evaluating a covariate effect when dropouts are likely to be nonignorable one possible approach to this problem is to fix a minimal set of sensitivity parameters conditional upon which hypothesized parameters are identifiable here we extend this idea and show how to evaluate the hypothesis of interest using an infimum statistic over the whole support of the sensitivity parameter we characterize the limiting distribution of the statistic as a process in the sensitivity parameter which involves a careful theoretical analysis of its behavior under model misspecification in practice we suggest a nonparametric bootstrap procedure to implement this infimum test as well as to construct confidence bands for simultaneous pointwise tests across all values of the sensitivity parameter adjusting for multiple testing the methodology s practical utility is illustrated in an analysis of a longitudinal psychiatric study

regression models for longitudinal binary responses with informative drop outs this paper reviews both likelihood based and non likelihood generalized estimating equations regression models for longitudinal binary responses when there are drop outs throughout it is assumed that the regression parameters for the marginal expectations of the binary responses are of primary scientific interest the association or time dependence between the responses is largely regarded as a nuisance characteristic of the data the performance of the methods is compared in terms of asymptotic bias under mis specification of the association between the responses and the missing data mechanism or drop out process

relations d orthogonalite de schur generalisees pour les espaces symetriques reductifs resume nous introduisons une semi norme sur un espace de fonctions c sur un espace symetrique reductif g h nous montrons que les fonctions c k finies propres sous l action de l algebre des operateurs differentiels g invariants et pour lesquelles cette semi norme est finie de meme que pour ses derivees par les elements de l algebre enveloppante de l algebre de lie de g sont temperees reciproquement on explicite cette semi norme pour les fonctions temperees k finies qui sont propres pour un caractere regulier de l algebre des operateurs differentiels g invariants l application de ces resultats aux integrales d eisenstein permet d etablir des relations d orthogonalite de schur generalisees notre travail generalise et precise des resultats de h midorikawa 1988 adv stud pure math 14 257 287 pour les groupes copyright 2001 academic press we introduce a seminorm on a space of c functions on a reductive symmetric space g h we show that the c k finite eigenfunctions of the algebra of all g invariant differential operators on g h for which this semi norm is finite as well as for their derivatives from the left are tempered reciprocally we make explicit this seminorm for the k finite tempered eigenfunctions with a regular character applying those result to eisenstein integrals we obtain general schur orthogonality relations our work generalizes and specifies the results of h midorikawa 1988 adv stud pure math 14 257 287 in the group case

harmonic analysis as spectral theory of laplacians by writing the fourier inversion formula on euclidean space in polar coordinates we obtain f x 0 fgl x dx where fgl x 2fgl x which is the spectral theory of the laplacian how do properties of f relate to properties of the family of eigenfunctions fgl answers are provided for the following spaces l2 s s d in odd dimensions analogous results are obtained for harmonic analysis on hyperbolic space constant curvature semi riemannian spaces the heisenberg group and for differential forms on hyperbolic space for f l2 there is a plancherel formula f 22 limt o 1t bt z f x 2dx d where bt z denotes the ball of radius t about an arbitrary point z which is independent of the dimension and the identical formula holds in hyperbolic space if the parametrization of the eigenvalues is shifted for certain semi riemannian symmetric spaces we obtain a paley wiener theorem that explains the role of discrete series in producing functions of compact support and also involve certain non unitary representations that contain the discrete series representations for the heisenberg group the plancherel formula is of a different nature requiring that the eigenfunctions be almost periodic in one variable

the principal series for a reductive symmetric space ii eisenstein integrals in this paper we develop a theory of eisenstein integrals related to the principal series for a reductive symmetric space g h here g is a real reductive group of harish chandra s class an involution of g and h an open subgroup of the group g of xed points for the group g itself is a symmetric space for the left right action of g g we refer to this setting as the group case up to a normalization our eisenstein integrals generalize those of harish chandra 18 associated with a minimal parabolic subgroup in the group case

non extinction of solutions to a fast diffusive p laplace equation with neumann boundary conditions abstract in this note the authors establish a non extinction result for the changing sign solution with negative initial energy by discussing a suitable differential inequality the result gives an answer to the problem unsolved in qu bai zheng 2014 1 two examples are given in the paper to show the existence of the initial datum with negative initial energy

an application of maximum likelihood and generalized estimating equations to the analysis of ordinal data from a longitudinal study with cases missing at random data are analysed from a longitudinal psychiatric study in which there are no dropouts that do not occur completely at random a marginal proportional odds model is fitted that relates the response severity of side effects to various covariates two methods of estimation are used generalized estimating equations gee and maximum likelihood ml both the complete set of data and the data from only those subjects completing the study are analysed for the completers only data the gee and ml analyses produce very similar results these results differ considerably from those obtained from the analyses of the full data set there are also marked differences between the results obtained from the gee and ml analysis of the full data set the occurrence of such differences is consistent with the presence of a non completely random dropout process and it can be concluded in this example that both the analyses of the completers only and the gee analysis of the full data set produce misleading conclusions about the relationships between the response and covariates

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

two geometric character formulas for reductive lie groups in this paper we prove two formulas for the characters of representations of reductive groups both express the character of a representation in terms of the same geometric data attached to when specialized to the case of a compact lie group one of them reduces to kirillov s character formula in the compact case and the other to an application of the atiyah bott fixed point formula to the borel weil realization of the representation to set the stage let us first recall the borel weil theorem for a connected compact lie group gr for simplicity we assume that gr is simply connected we let gr denote its lie algebra and g c r gr the complexified lie algebra via the adjoint action gr operates on igr the space of all r linear functions gr ir every gr orbit in igr coadjoint orbit for short carries a canonical grinvariant symplectic structure the orbit is said to be integral if some or equivalently any exponentiates to a character e of the isotropy subgroup gr in that case the one dimensional representation spaces of the characters e fit together into a gr equivariant real algebraic hermitian line bundle l the pair l carries a unique positive polarization a gr invariant complex structure on the manifold and the structure of a gr equivariant holomorphic line bundle on l positive in the sense of algebraic geometry the hypothesis of simple connectivity ensures that the square root k of the canonical bundle k exists as a gr equivariant holomorphic line bundle according to the borel weil theorem the natural action of gr on the space of holomorphic l valued half forms h0 o k l is irreducible moreover the association h0 o k l 1 1

complex geometry and the asymptotics of harish chandra modules for real reductive lie groups i let g be a connected semisimple real matrix group it is now apparent that the representation theory of g is intimately connected with the complex geometry of the flag variety 9 by studying appropriate orbit structures on 9 we are naturally led to representation theory in the category of harish chandra modules x or the representation theory of category 9 the jacquet functor j f 9 has proved a useful tool in converting yfw problems into 9 problems which are often more tractable in this paper we advance the philosophy that the complex geometry of 9 associated to yf and 9 interacts in a natural way with the functor j leading to deep new information on the structure of jacquet modules this in turn gives new insight into the structure of certain nilpotent cohomology groups associated to harish chandra modules our techniques are based upon many of the ideas present in the proof of the kazhdan lusztig conjectures and bernstein s proof of the jantzen conjecture

asymptotic expansions and boundary values of eigenfunctions on riemannian symmetric spaces soit x g k un espace de riemann symetrique de type non compacte a bord b k m et soit d x l algebre de tous les operateurs differentiels g invariants sur x on obtient des developpements asymptotiques pour une grande classe de fonctions jointives f sur x

filtration de certains espaces de fonctions sur un espace symetrique reductif we introduce a filtration of a g k module of some space of functions on a reductive symmetric space g h and compute the associated grading as a direct sum of induced representations as an application of this result to the reductive groups viewed as symmetric spaces we are able to realize any harish chandra module as a subquotient of a direct sum of induced representations from parabolic subgroups the inducing representations being trivial on the unipotent radical

global well posedness for a nonlocal semilinear pseudo parabolic equation with conical degeneration abstract this paper deals with a class of nonlocal semilinear pseudo parabolic equation with conical degeneration u t b u t b u u p 1 u 1 b b u p 1 u d x 1 x 1 d x on a manifold with conical singularity where b is fuchsian type laplace operator with totally characteristic degeneracy on the boundary x 1 0 by using the modified method of potential well with galerkin approximation and concavity the global existence uniqueness finite time blow up and asymptotic behavior of the solutions will be discussed at the low initial energy j u 0 d and critical initial energy j u 0 d respectively furthermore we investigate the global existence and finite time blow up of the solutions with the high initial energy j u 0 d by the variational method especially we also derive the threshold results of global existence and nonexistence for the solutions at two different initial energy levels i e low initial level and critical initial level

ground state solution for a fourth order elliptic equation with logarithmic nonlinearity modeling epitaxial growth abstract this paper deals with a fourth order elliptic equation with logarithmic nonlinearity modeling epitaxial growth and the existence of a ground state solution is obtained

global asymptotical behavior and some new blow up conditions of solutions to a thin film equation abstract we consider a thin film equation by exploiting the boundary condition and the variational structure of the equation we consider the global existence and blow up of the solutions for the global solutions we study the asymptotic behavior and for the blow up solutions we study the upper and lower bounds of the blow up time especially we have derived the necessary and sufficient conditions for the solution blowing up in finite time when the initial energy j u 0 d where d is the mountain pass level for j u 0 d we also study the conditions for the solution exists globally and blows up in finite time and we also obtain some necessary and sufficient conditions for the solution blowing up in finite time when the initial energy at arbitrary level furthermore we study the decay behavior of both the global solutions and its corresponding energy functional and the decay ratios are given specially the results generalize the former studies on this equation such as the papers li et al 2016 16 dong and j zhou 2017 4 and sun et al 2018 23

fourier transforms on a semisimple symmetric space let g h be a semisimple symmetric space that is g is a connected semisimple real lie group with an involution and h is an open subgroup of the group of xed points for in g the main purpose of this paper is to study an explicit fourier transform on g h in terms of general representation theory the abstract fourier transform of a compactly supported smooth function f 2 c 1 c g h is given by see 5 1 f f zg h f x x dx for h a unitary irreducible representation of g and 2 h an h invariant distribution vector for here dx is the invariant measure on g h thus f isa smooth vector for h depending linearly on our goal is to obtain an explicit version of the restriction of this fourier transform to representations h in the minimal unitary principal series h for g h under the assumption that the center of g is nite in a sequel 9 to this paper it will be proved that a function f 2 c 1 c g h is uniquely determined by the restriction of f to this series a priori it is known that f is determined by f

induction automorphe pour gl n c for f r or c isomorphism classes of irreducible g k modules for gl n f are parametrized by n dimensional representations of the weil group wf of f we can induce to wr a representation of wc which has index 2 in wr that gives a process of automorphic induction which to an irreducible g k module for gl n c associates an irreducible g k module c r for gl 2n r in the present paper we show that if is unitary and generic then is determined by up to isomorphism via a character identity entirely analogous to the character identity occurring in the automorphic induction process for p adic fields this completes the theory of automorphic induction for local and global representations of gl n over number fields

fonctions d g h finies sur un espace symetrique reductif abstract it is well known that on r n every smooth function annihilated by a finite codimensional ideal in the algebra of constant coefficient differential operators is a linear combination of polynomial exponential functions p x e x hom r n c furthermore the polynomial functions are obtained by applying to the exponential functions e x some constant coefficient differential operator in the parameter we generalize this fact to the reductive symmetric spaces case the role of the exponential functions being taken by the eisenstein integrals

asymptotic behavior of matrix coefficients of admissible representations introduction 869 1 generalities on reductive groups 873 2 the infinitesimal cartan decomposition 876 3 the t radial components 880 4 differential equations satisfied by sphereical functions 885 5 asymptotic behavior of spherical functions on a 888 6 asymptotic behavior of spherical functions along the walls of a 892 7 leading characters and growth estimates on the group 898 8 admissible representations and their matrix coefficients 906 appendix 917

sur le theoreme de paley wiener d arthur the fourier transform of a c function f with compact support on a real reductive lie group g is given by a collection of operators o p e ip e f for a suitable family of representations of g which depends on a family indexed by p in a finite set of parabolic subgroups of g of pairs of parameters e varying in a set of discrete series e lying in a complex finite dimensional vector space the ip e are generalized principal series induced from p it is easy to verify the holomorphy of the fourier transform in the complex parameters also it satisfies some growth properties moreover an intertwining operator between two representations ip e ip e of the family implies an intertwining property for o p e and o p e there is also a way to introduce hsuccessive partial derivatives h of the family of representations ip e along the parameter e and intertwining operators between subquotients of these successive derivatives imply the intertwining property for the successive derivatives of the fourier transform o we show that these properties characterize the collections of operators p e o p e which are fourier transforms of a c function with compact support for g linear the proof which uses harish chandra fs plancherel formula rests on a similar result for left and right k finite functions which is due to j arthur we give also a proof of arthur fs result purely in term of representations involving the work of a knapp and e stein on intertwining integrals and langlands and vogan fs classifications of irreducible representations of g

a survey of models for repeated ordered categorical response data we survey models for analysing repeated observations on an ordered categorical response variable the models presented are univariate models that permit correlation among repeated measurements the models describe simultaneously the dependence of marginal response distributions on values of explanatory variables and on the occasion of response we present models for three transformations of the response distribution cumulative logits adjacent category logits and the mean for scores assigned to response categories we discuss three methods for fitting the models maximum likelihood weighted least squares and semi parametric weighted least squares is easily implemented with sas as illustrated with a study designed to compare a drug with a placebo for the treatment of insomnia

constant term of eisenstein integrals on a reductive p adic symmetric space let h be the fixed point group of a rational involution sigma of a reductive p adic group on a field of characteristic different from 2 let p be a sigma parabolic subgroup of g i e such that sigma p is opposite p we denote the intersection p boolean and sigma p by m kato and takano on one hand and lagier on the other associated canonically to an h form i e an h fixed linear form xi on a smooth admissible g module v a linear form on the jacquet module jp v of v along p which is fixed by m boolean and h we call this operation the constant term of h forms this constant term is linked to the asymptotic behaviour of the generalized coefficients with respect to xi p blanc and the second author defined a family of h forms on certain parabolically induced representations associated to an m boolean and h form eta on the space of the inducing representation the purpose of this article is to describe the constant term of these h forms also it is shown that when eta is discrete i e when the generalized coefficients of eta are square integrable modulo the center the corresponding family of h forms on the induced representations is a family of tempered in a suitable sense h forms a formula for the constant term of eisenstein integrals is given

poisson transforms on vector bundles let g be a connected real semisimple lie group with finite center and k a maximal compact subgroup of g let r v be an irreducible unitary representation of k and g x k tv the associated vector bundle in the algebra of invariant differential operators on g xk v the center of the universal enveloping algebra of lie g induces a certain commutative subalgebra z we are able to determine the characters of z given such a character we define a poisson transform from certain principal series representations to the corresponding space of joint eigensections we prove that for most of the characters this map is a bijection generalizing a famous conjecture by helgason which corresponds to r the trivial representation introduction let g be a connected real semisimple lie group with finite center and k a maximal compact subgroup of g then g k is a riemannian symmetric space of noncompact type we fix an iwasawa decomposition g kan let m be the centralizer of a in k let g and a be the lie algebras of g and a respectiarely and s 0 a the root system for 0 a let s 0 a be the positiare roots in s a for the ordering giaren by n let d g k be the algebra of inarariant differential operators on g k it is well known that the characters of d g k are parametrized by a e a the complex dual space of a let a g k denote the space of joint eigenfunctions corresponding to a we write g k g exp h g n g for each g e g according to g kan for each x e c k m we define pxx e c g k by p x g t k e p h g lk dk k here p is the half sum of s 0 a including multiplicities it turns out that pxq e v g k one can easily extend the definition of px to the space d k m resp a k m of distributions resp analytic functionals on k m in this paragraph we fix a e a such that 2 a ct ct ct is not in n 0 for each ct c s 0 a it is proared by helgason helg2 that pa defines a bijection from c o k m k finite onto e g k k finite he also proares in the rank one case p is a bijection from a k m onto 6 g k he then conjectured this should be true for the higher rank case the conjecture was earentually proared by six japanese mathematicians in kkmoot it should be mentioned that a representation theoretic proof by schmid starting from the kfinite result is indicated in sch lewis then a student of helgason made the following obseraration let 6 g k be the subspace of e g k whereeach element increases at most exporlentially see 02 for definition received by the editors september 28 1994 and in revised form january 30 1995 1991 mathematics subject classification primary 22e46 secondary 43a85 1998 american mathematical society 857 this content downloaded from 157 55 39 198 on fri 17 jun 2016 05 05 10 utc all use subject to http about jstor org terms

impact of missing data due to drop outs on estimators for rates of change in longitudinal studies a simulation study many cohort studies and clinical trials are designed to compare rates of change over time in one or more disease markers in several groups one major problem in such longitudinal studies is missing data due to patient drop out the bias and efficiency of six different methods to estimate rates of changes in longitudinal studies with incomplete observations were compared generalized estimating equation estimates gee proposed by liang and zeger 1986 unweighted average of ordinary least squares olse of individual rates of change uwls weighted average of olse wls conditional linear model estimates cle a covariate type estimates proposed by wu and bailey 1989 random effect re and joint multivariate re jmre estimates the latter method combines a linear re model for the underlying pattern of the marker with a log normal survival model for informative drop out process the performance of these methods in the presence of missing data completely at random mcar at random mar and non ignorable nim were compared in simulation studies data for the disease marker were generated under the linear random effects model with parameter values derived from realistic examples in hiv infection rates of drop out assumed to increase over time were allowed to be independent of marker values or to depend either only on previous marker values or on both previous and current marker values under macr all six methods yielded unbiased estimates of both group mean rates and between group difference however the cross sectional view of the data in the gee method resulted in seriously biased estimates under mar and nim drop out process the bias in the estimates ranged from 30 per cent to 50 per cent the degree of bias in the gee estimates increases with the severity of non randomness and with the proportion of mar data under mcar and mar all the other five methods performed relatively well re and jmre estimates were more efficient that is had smaller variance than uwls wls and cl estimates under nim wls and particularly re estimates tended to underestimate the average rate of marker change bias approximately 10 per cent under nim uwls cl and jmre performed better in terms of bias 3 5 per cent with the jmre giving the most efficient estimates given that markers are key variables related to disease progression missing marker data are likely to be at least mar thus the gee method may not be appropriate for analysing such longitudinal marker data the potential biases due to incomplete data require greater recognition in reports of longitudinal studies sensitivity analyses to assess the effect of drop outs on inferences about the target parameters are important

fourier inversion on a reductive symmetric space let x be a semisimple symmetric space in previous papers 8 and 9 we have dened an explicit fourier transform for x and shown that this transform is injective on the space c 1 c x ofcompactly supported smooth functions on x in the present paper which is a continuation of these papers we establish an inversion formula for this transform

primitive ideals and representations certain theorems of joseph and king relating primitive ideals to characters in category o are extended to the case of arbitrary g modules with finite dimensional n cohomology a derived functor construction analogous to a construction of zuckerman in the case of a nilpotent lie algebra is used to extend the results applications to harish chandra modules are also given

asymptotic expansions and hua harmonic functions on bounded homogeneous domains let d be a homogeneous siegel domain of type ii we prove that every bounded hua harmonic function f on d is pluriharmonic the proof is based on asymptotic expansion of f

blow up in a system of partial differential equations with conserved first integral part ii problems with convection a reaction diffusion convection equation with a nonlocal term is studied the nonlocal operator acts to conserve the spatial integral of the unknown function as time evolves the equations are parameterised by and for 1 the equation arises as a similarity solution of the navier stokes equations and the nonlocal term plays the role of pressure for 0 the equation is a nonlocal reaction diffusion problem the aim of the paper is to determine for which values of the parameter blow up occurs and to study its form in particular interest is focused on the three cases 1 2 and 1 it is observed that for any 0 1 2 nonuniform global blow up occurs if 1 2 1 then the blow up is global and uniform while for 1 the navier stokes equations there are exact solutions with initial data of arbitrarily large l l 2 and h 1 norms that decay to zero furthermore one of these exact solutions is proved to be nonlinearly stable in l 2 for arbitrarily large supremum norm an understanding of this transition from blow up behaviour to decay behaviour is achieved by a combination of analysis asymptotics and numerical techniques

critical fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux we establish the critical fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux and then determine the blow up rates and the blow up sets for the nonglobal solutions

blow up for a thin film equation with positive initial energy abstract in this paper we consider a thin film equation with nonlocal source which was studied by qu and zhou 2016 11 where the authors derived the conditions for global existence blow up and extinction we consider the case that the initial energy is positive and establish a blow up result for this case furthermore the upper bound of the blow up time is derived

patterson sullivan distributions in higher rank for a compact locally symmetric space x of non positive curvature we consider sequences of normalized joint eigenfunctions which belong to the principal spectrum of the algebra of invariant differential operators using an h pseudo differential calculus on x we define and study lifted quantum limits as weak limit points of wigner distributions the helgason boundary values of the eigenfunctions allow us to construct patterson sullivan distributions on the space of weyl chambers these distributions are asymptotic to lifted quantum limits and satisfy additional invariance properties which makes them useful in the context of quantum ergodicity our results generalize results for compact hyperbolic surfaces obtained by anantharaman and zelditch

espace de schwartz pour la transformation de fourier hypergeometrique resume let r be a reduced root system in an euclidean vector space e w the weyl group of r one determines the hypergeometric fourier transform cf e opdam cuspidal hypergeometric functions preprint of the related schwartz space of w invariant functions on e introduced by tinfou the answer is very natural and quite similar to results of harish chandra the proof requires a theory of the constant term for w invariant functions satisfying the hypergeometric system this is analogous to harish chandra s theory once one has realized that simple difference operators play here the role of some elements of the unipotent radical of a parabolic subalgebra also the fact that the parameter of cuspidal hypergeometric functions might be singular introduces new difficulties this theory being established one can take advantage of the techniques we used for real reductive symmetric spaces cf the introduction to the article by the author formule de plancherel pour les espaces symetriques reductifs ann math 147 1998 417 452 especially the truncation and its consequences

proportional odds models for repeated composite and long ordinal outcome scales in many medical studies researchers widely use composite or long ordinal scores that is scores that have a large number of categories and a natural ordering often resulting from the sum of a number of short ordinal scores to assess function or quality of life typically we analyse these using unjustified assumptions of normality for the outcome measure which are unlikely to be even approximately true scores of this type are better analysed using methods reserved for more conventional short ordinal scores such as the proportional odds model we can avoid the need for a large number of cut point parameters that define the divisions between the score categories for long ordinal scores in the proportional odds model by the inclusion of orthogonal polynomial contrasts we introduce the repeated measures proportional odds logistic regression model and describe for long ordinal outcomes modifications to the generalized estimating equation methodology used for parameter estimation we introduce data from a trial assessing two surgical interventions briefly describe and re analyse these using the new model and compare inferences from the new analysis with previously published results for the primary outcome measure hip function at 12 months postoperatively we use a simulation study to illustrate how this model also has more general application for conventional short ordinal scores to select amongst competing models of varying complexity for the cut point parameters

an appraisal of methods for the analysis of longitudinal categorical data with mar drop outs a number of methods for analysing longitudinal ordinal categorical data with missing at random drop outs are considered two are maximum likelihood methods maxlik which employ marginal global odds ratios to model associations the remainder use weighted or unweighted generalized estimating equations gee two of the gee use cholesky decomposed standardized residuals to model the association structure while another three extend methods developed for longitudinal binary data in which the association structures are modelled using either gaussian estimation multivariate normal estimating equations or conditional residuals simulated data sets were used to discover differences among the methods in terms of biases variances and convergence rates when the association structure is misspecified the methods were also applied to a real medical data set two of the gee methods referred to as cond and ml norm in this paper and by their originators were found to have relatively good convergence rates and mean squared errors for all sample sizes 80 120 300 considered and one more referred to as mgee in this paper and by its originators worked fairly well for all but the smallest sample size 80

van den ban schlichtkrull wallach asymptotic expansions on nonsymmetric domains if it is annihilated by every element of dg x the algebra of all g invariant differential operators without constant term one of the most beautiful results in the harmonic analysis of symmetric spaces is the helgason conjecture which states that on a riemannian symmetric space of noncompact type a function is harmonic if and only if it is the poisson integral of a hyperfunction over the furstenberg boundary g po where po is a minimal parabolic subgroup see 14 17 one of the more remarkable aspects of this theorem is its generality one obtains a complete description of all solutions to the system of invariant differential operators on x without imposing any boundary or growth conditions if x is a hermitian symmetric space then one is typically interested in complex function theory in which case one is interested in functions whose boundary values are supported on the shilov boundary rather than the furstenberg boundary the shilov boundary is g p where p is a certain maximal parabolic containing po in this case it turns out that the algebra of g invariant differential operators is not necessarily the most appropriate one for

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

simple fitting algorithms for incomplete categorical data a popular approach to estimation based on incomplete data is the em algorithm for categorical data this paper presents a simple expression of the observed data log likelihood and its derivatives in terms of the complete data for a broad class of models and missing data patterns we show that using the observed data likelihood directly is easy and has some advantages one can gain considerable computational speed over the em algorithm and a straightforward variance estimator is obtained for the parameter estimates the general formulation treats a wide range of missing data problems in a uniform way two examples are worked out in full

global cross ratio models for bivariate discrete ordered responses summary a family of statistical models is presented for bivariate discrete response to a regressor when both components of the response have ordered categories association between components is expressed in terms of global cross ratios cross product ratios of quadrant probabilities for each double dichotomy of the response table of probabilities into quadrants pearson and heron 1913 biometrika 9 159 315 these models are extensions to the work of plackett 1965 journal of the american statistical association 60 516 522 and mantel and brown 1973 biometrics 29 649 665 the marginal cumulative probabilities may satisfy linear logistic or other generalized linear models mccullagh 1980 journal of the royal statistical society series b 42 109 142 an analysis of patients postoperative pain level and medication frequency illustrates these methods

geometric realization of discrete series for semisimple symmetric spaces let g be a connected semisimple lie group a an involution of g and h the connected component of the fixed point set of a containing the identity then g h is a semisimple symmetric space we assume g is a real form of a complex lie group and rank g h rank k k c h where k is a a stable maximal compact subgroup of g flensted jensen using his duality principle and poisson transform constructed countably many discrete series in u g h f j i then using deep results of hyperfunction theory and microlocal analysis oshima and matsuki gave a detailed characterization of these discrete series including a proof of flensted jensen s conjecture c 0 om based on these results we give the discrete series a geometric interpretation in locally symmetric spaces f c where g k and f cg is a cocompact discrete group such that f c h c h is cocompact our geometric interpretation is the following first of all to a flensted jensen function which is the generating function of a discrete series v we associate a harmonic form cb z on g with values in a finite dimensional g module v right g translates of coefficients of 5z realizes the contragredient t of r and tba is left invariant under h and under right k action it transforms according to the minimal k type with highest weight of 3 is the pull back of a v valued from coz on and v determines a locally constant bundle e on f so that if convergence holds

blow up versus extinction in a nonlocal p laplace equation with neumann boundary conditions abstract this paper studies a fast diffusive p laplace equation with the nonlocal source u q u q d x in a bounded domain subject to homogeneous neumann boundary value condition a critical criterion is determined that the changing sign solutions blow up in finite time with q 1 and non positive initial energy associated and must be global for any initial energy if q 1 in particular the conditions are obtained under which the changing sign solutions vanish in finite time

the plancherel decomposition for a reductive symmetric space i spherical functions we prove the plancherel formula for spherical schwartz functions on a reductive symmetric space our starting point is an inversion formula for spherical smooth compactly supported functions the latter formula was earlier obtained from the most continuous part of the plancherel formula by means of a residue calculus in the course of the present paper we also obtain new proofs of the uniform tempered estimates for normalized eisenstein integrals and of the maass selberg relations satisfied by the associated c functions

local boundary data of eigenfunctions on a riemannian symmetric space let x g k be a riemannian symmetric space of non compact type and let d x be the algebra of invariant differential operators on x in a previous paper 1 we developed a theory of asymptotic expansions for joint eigenfunctions of d x of at most exponential growth in the present paper we show that local asymptotic data determine the eigenfunctions completely we also develop a theory of asymptotic expansions along walls both results are of importance for the theory of the discrete series of a semisimple symmetric space let a be a maximal abelian split subspace of the lie algebra 9 of g and denote by a its complexified dual let e be the restricted root system of a in g and w the associated weyl group then harish chandra s isomorphism d x s a w determines a bijection 2 z from a w to the set d x of algebra homomorphisms d x c given 2ca let ga x denote the joint eigenspace of functions f e c o x satisfying

marginal modelling of multivariate categorical data this paper describes likelihood methods of analysis for multivariate categorical data the joint distribution is specified in terms of marginal mean functions and pairwise and higher order association measures for the association the emphasis is on global odds ratios the method allows flexible formulation of a broad class of designs such as repeated measurements longitudinal studies interrater agreement and cross over trials the proposed model can be used for parameter estimation and hypothesis testing simple fitting algorithms are proposed the method is illustrated using a data example

generalized convexity and the existence of finite time blow up solutions for an evolutionary problem abstract in this paper we study a class of nonlinearities for which a nonlocal parabolic equation with neumann robin boundary conditions for p laplacian has finite time blow up solutions

global existence and finite time blow up of the solution for a thin film equation with high initial energy abstract this paper is devoted to the study of a thin film equation which was considered extensively in recent years we obtain the conditions for global existence and finite time blow up of solution for the high initial energy case i e j u 0 d while the previous works only considered the case j u 0 d here d is the mountain pass level moreover for the blow up solution with j u 0 d we obtain the lower bound estimate of the blow up time and blow up rate

normalizations of eisenstein integrals for reductive symmetric spaces abstract we construct minimal eisenstein integrals for a reductive symmetric space g h as matrix coefficients of the minimal principal series of g the eisenstein integrals thus obtained include those from the minimal principal series in addition we obtain related eisenstein integrals but with different normalizations specialized to the case of the group this wider class includes harish chandra s minimal eisenstein integrals

blow up and extinction for a thin film equation with initial boundary value conditions abstract in this paper we consider an initial boundary value problem for a thin film equation with the nonlocal source u q u q d x in a bounded domain due to the comparison principle being invalid we use the potential well method to give a threshold result of global existence and non existence for the sign changing weak solutions further we obtain the conditions under which the global solutions extinct in finite time and study the asymptotic behavior of the non extinct solutions

the plancherel decomposition for a reductive symmetric space ii representation theory we obtain the plancherel decomposition for a reductive symmetric space in the sense of representation theory our starting point is the plancherel formula for spherical schwartz functions obtained in part i the formula for schwartz functions involves eisenstein integrals obtained by a residual calculus in the present paper we identify these integrals as matrix coefficients of the generalized principal series

holomorphic l p type for sub laplacians on connected lie groups we study the problem of determining all connected lie groups g which have the following property hlp every sub laplacian l on g is of holomorphic lp type for 1 p p 2 first we show that semi simple non compact lie groups with finite center have this property by using holomorphic families of representations in the class one principal series of g and the kunze stein phenomenon we then apply an lp transference principle essentially due to anker to show that every connected lie group g whose semi simple quotient by its radical is non compact has property hlp for the convenience of the reader we give a self contained proof of this transference principle which generalizes the well known coifman weiss principle one is thus reduced to studying those groups for which the semi simple quotient is compact i e to compact extensions of solvable lie groups in this article we consider semi direct extensions of exponential solvable lie groups by connected compact lie groups it had been proved in joint work by w hebisch and the two first named authors that every exponential solvable lie group s which has a non regular co adjoint orbit whose restriction to the nilradical is closed has property hlp and we show here that hlp remains valid for compact extensions of these groups

classical and quantum resonances for hyperbolic surfaces for compact and for convex co compact oriented hyperbolic surfaces we prove an explicit correspondence between classical ruelle resonant states and quantum resonant states except at negative integers where the correspondence involves holomorphic sections of line bundles

sensitivity analysis of longitudinal binary quality of life data with drop out an example using the eortc qlq c30 analysing quality of life data qol may be complicated for several reasons quality of life data not only involves repeated measures but is also usually collected on ordered categorical responses in addition it is evident that not all patients provide the same number of assessments due to attrition caused by death or other medical reasons in the recent statistical literature increasing attention is given to methods which can handle non continuous outcomes in the presence of missing data the aim of this paper is to investigate the effect on statistical conclusions of applying different modelling techniques to qol data generated from an eortc phase iii trial treatment effects and treatment differences are of major concern first a random effects model is fitted relating a binary longitudinal response derived from the physical functioning scale of the qlq c30 to several covariates in a second approach marginal models are fitted retaining the response variable and the mean structure used before the fitted marginal models only differ with respect to the considered estimation procedure generalized estimating equations gee weighted generalized estimating equations wgee and maximum likelihood ml copyright c 2001 john wiley sons ltd

global existence and finite time blow up for a class of semilinear pseudo parabolic equations abstract in this paper we study a class of semilinear pseudo parabolic equations by introducing a family of potential wells we prove the invariance of some sets global existence nonexistence and asymptotic behavior of solutions with initial energy j u 0 d moreover we obtain finite time blow up with high initial energy j u 0 d by comparison principle

blow up phenomena for a nonlocal semilinear parabolic equation with positive initial energy abstract this paper is concerned with the blow up of solutions to the following semilinear parabolic equation u t u u p 1 u 1 u p 1 u d x x t 0 under homogeneous neumann boundary condition in a bounded domain r n n 1 with smooth boundary for all p 1 we prove that the classical solutions to the above equation blow up in finite time when the initial energy is positive and initial data is suitably large this result improves a recent result by gao and han 2011 which asserts the blow up of classical solutions for n 3 provided that 1 p n 2 n 2

the oshima sekiguchi and liouville theorems on heintze groups abstract let l be an elliptic operator on a riemannian manifold m a function f annihilated by l is said to be l harmonic f is said to have moderate growth if and only if f grows at most exponentially in the riemannian distance if m is a rank one symmetric space and l is the laplace beltrami operator for m the oshima sekiguchi theorem t oshima j sekiguchi eigenspaces of invariant differential operators on an affine symmetric space invent math 57 1980 1 81 states that a l harmonic function f has moderate growth if and only if f is the poisson integral of a distribution on the furstenberg boundary in this work we prove that this result generalizes to a very large class of homogeneous riemannian manifolds of negative curvature we also i prove a liouville type theorem that characterizes the polynomial like harmonic functions which vanish on the boundary in terms of their growth properties ii describe all polynomial like harmonic functions and iii give asymptotic expansions for the poisson kernel one consequence of this work is that every schwartz distribution on the boundary is the boundary value for a l harmonic function f which is uniquely determined modulo polynomial like harmonic functions

plongements de series discretes pour un espace symetrique reductif resume using the realization of a discrete series a of a semi simple symmetric space g h as a space of boundary values in the dual space gd kd we construct an explicit embedding of a in a principal series ind 1 associated to an open subgroup q1 of a minimal stable parabolic subgoup q of g the construction of q1 and uses the properties of what we call a fundamental system of roots

a mixed effects regression model for three level ordinal response data three level data occur frequently in behaviour and medical sciences for example in a multi centre trial subjects within a given site are randomly assigned to treatments and then studied over time in this example the repeated observations level 1 are nested within subjects level 2 who are nested within sites level 3 similarly in twin studies repeated measurements level 1 are taken on each twin level 2 within each twin pair level 3 a three level mixed effects regression model is described here random effects at the second and third level are included in the model additionally both proportional odds and non proportional odds models are developed the latter allows the effects of explanatory variables to vary across the cumulative logits of the model a maximum marginal likelihood mml solution is described and gauss hermite numerical quadrature is used to integrate over the distribution of random effects the random effects are normally distributed in this instance features of this model are illustrated using data from a school based smoking prevention trial and an alzheimer s disease clinical trial

paquets d ondes dans l espace de schwartz d un espace symetrique reductif resume we study holomorphic families of k finite eigenfunctions on symmetric spaces g h called functions ii hol by analogy with hc eisenstein integrals cf b3 d suitably normalized by a polynomial factor provide examples of such families a function ii hol is said ii hol if roughly speaking its constant term along any stable parabolic subgroup is a finite sum of functions ii hol s where s varies in a determined finite set we prove that for a function ii hol one can form wave packets in the schwartz space we prove also a criterion for a function ii hol to be ii hol an important fact is that for minimal stable parabolic subgroups our criterion implies with the help of the maas selberg relations cf b2 b3 a normalization of eisenstein integrals all the article relies on the theory of the constant term cf c

scattering theory for the laplacian on symmetric spaces of noncompact type and its application to a conjecture of strichartz abstract in this paper we develop the scattering theory for the laplacian on symmetric spaces of noncompact type we study the asymptotic properties of the resolvent in the framework of the agmon hormander space our approach is based on a detailed analysis of the helgason fourier transform and generalized spherical functions on symmetric spaces of noncompact type as an application of our scattering theory we prove a conjecture by strichartz concerning a characterization of a family of generalized eigenfunctions of the laplacian

integrales d eisenstein pour les espaces symetriques reductifs temperance majorations petite matriceb resume sharp majorations for the meromorphic continuation of eisenstein integrals for reductive symmetric spaces are proved using a technique due to e p van den ban the problem reduces to prove temperedness when the parameter is pure imaginary starting with a result for good parameters established by using a result of flensted jensen oshima and schlichtkrull 1985 one gets temperedness by a repeated use of translations functors for discrete series cf vogan 1988 for generalized principal series and for the poisson transform a key role is played by oshima s 1988 criterion for temperedness the existence of a small b matrix is also proved

marginal modeling of correlated ordinal data using a multivariate plackett distribution abstract an extension of the bivariate model suggested by dale is proposed for the analysis of dependent ordinal categorical data the so called multivariate dale model is constructed by first generalizing the bivariate plackett distribution to any dimensions because the approach is likelihood based it satisfies properties that are not fulfilled by other popular methods such as the generalized estimating equations approach the proposed method models both the marginal and the association structure in a flexible way the attractiveness of the multivariate dale model is illustrated in three key examples covering areas such as crossover trials longitudinal studies with patients dropping out from the study and discriminant analysis applications the differences and similarities with the generalized estimating approach are highlighted

support d asymptotiques et croissance des fonctions propres sur un espace symetrique semi simple abstract we associate several distribution boundary values to an eigenfunction with moderate growth on a riemannian symmetric space g k the associated character of the algebra d g k of invariant differential operators is allowed to be non regular we prove results on the support of these boundary values these allow us to recover the theorems of matsuki oshima and oshima on the equivalence between growth of an eigenfunction and limitations on the supports of its boundary values our approach is based on an asymptotic analysis that makes no use of hyperfunction theory

the analysis of longitudinal ordinal data with nonrandom drop out a model is proposed for longitudinal ordinal data with nonrandom drop out which combines the multivariate dale model for longitudinal ordinal data with a logistic regression model for drop out since response and drop out are modelled as conditionally independent given complete data the resulting likelihood can be maximised relatively simply using the em algorithm which with acceleration is acceptably fast and with appropriate additions can produce estimates of precision the approach is illustrated with an example such modelling of nonrandom drop out requires caution because the interpretation of the fitted models depends on assumptions that are unexaminable in a fundamental sense and the conclusions cannot be regarded as necessarily robust the main role of such modelling may be as a component of a sensitivity analysis

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

jacquet modules and dirac cohomology abstract we show that dirac cohomology of the jacquet module of a harish chandra module is a harish chandra module for the corresponding levi subgroup we obtain an explicit formula of dirac cohomology of the jacquet module for most of the principal series based on our determination of dirac cohomology of irreducible generalized verma modules with regular infinitesimal characters

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

a characterization of the l2 range of the poisson transform related to strichartz conjecture on symmetric spaces of noncompact type abstract the main purpose of this paper is to solve strichartz conjecture concerning an image characterization of the poisson transform in the l 2 theory on symmetric spaces of noncompact type we prove that the poisson transform provides an isomorphism between the l 2 space on the boundary and a certain weighted l 2 space consisting of joint eigenfunctions on symmetric spaces of noncompact type our approach is based on the scattering theory for the schrodinger operator moreover we give a fourier restriction estimate and an asymptotic formula for the poisson transform

global existence and blow up of solutions to a nonlocal parabolic equation with singular potential abstract in this paper we study a nonlocal parabolic equation with singular potential on a bounded smooth domain with homogeneous neumann boundary condition firstly we find a threshold of global existence and blow up to the solutions of the problem when the initial data is at the low energy level i e j u 0 d where j u 0 is the initial energy and d is the mountain pass level moreover when j u 0 d the vacuum isolating behavior of the solutions is also discussed secondly we prove that there exist solutions of the problem with arbitrary initial energy that blow up in finite time we also obtain the upper bounds of the blow up time for blow up solutions

marginal analysis of ordinal clustered longitudinal data with informative cluster size the issue of informative cluster size ics often arises in the analysis of dental data ics describes a situation where the outcome of interest is related to cluster size much of the work on modeling marginal inference in longitudinal studies with potential ics has focused on continuous outcomes however periodontal disease outcomes including clinical attachment loss are often assessed using ordinal scoring systems in addition participants may lose teeth over the course of the study due to advancing disease status here we develop longitudinal cluster weighted generalized estimating equations cwgee to model the association of ordinal clustered longitudinal outcomes with participant level health related covariates including metabolic syndrome and smoking status and potentially decreasing cluster size due to tooth loss by fitting a proportional odds logistic regression model the within teeth correlation coefficient over time is estimated using the two stage quasi least squares method the motivation for our work stems from the department of veterans affairs dental longitudinal study in which participants regularly received general and oral health examinations in an extensive simulation study we compare results obtained from cwgee with various working correlation structures to those obtained from conventional gee which does not account for ics our proposed method yields results with very low bias and excellent coverage probability in contrast to a conventional generalized estimating equations approach