generalized functional extended redundancy analysis functional extended redundancy analysis fera was recently developed to integrate data reduction into functional linear models this technique extracts a component from each of multiple sets of predictor data in such a way that the component accounts for the maximum variance of response data moreover it permits predictor and or response data to be functional fera can be of use in describing overall characteristics of each set of predictor data and in summarizing the relationships between predictor and response data in this paper we extend fera into the framework of generalized linear models glm so that it can deal with response data generated from a variety of distributions specifically the proposed method reduces each set of predictor functions to a component and uses the component for explaining exponential family responses as in glm we specify the random systematic and link function parts of the proposed method we develop an iterative algorithm to maximize a penalized log likelihood criterion that is derived in combination with a basis function expansion approach we conduct two simulation studies to investigate the performance of the proposed method based on synthetic data in addition we apply the proposed method to two examples to demonstrate its empirical usefulness

limiting angle of brownian motion on certain manifolds suppose that m is a complete simply connected riemannian manifold of non positive sectional curvature with dimension m 3 if outside a fixed compact set the sectional curvatures are bounded above by a negative constant multiple of the inverse of the square of the geodesic distance from a fixed point and below by another negative constant multiple of the square of the geodesic distance then the angular part of brownian motion on m tends to a limit as time tends to infinity and the closure of the support of the distribution of this limit is the entire s m 1 this improves a result of hsu and march

the bivariate probit model maximum likelihood estimation pseudo true parameters and partial identification abstract this paper examines the notion of identification by functional form for two equation triangular systems for binary endogenous variables by providing a bridge between the literature on the recursive bivariate probit model and that on partial identification we evaluate the impact of functional form on the performance of quasi maximum likelihood estimators and investigate the practical importance of available instruments in both cases of correct and incorrect distributional specification finally we calculate average treatment effect bounds and demonstrate how properties of the estimators are explicable via a link between the notion of pseudo true parameters and the concepts of partial identification

a comparison of several vector quantization codebook generation approaches a review and a performance comparison of several often used vector quantization vq codebook generation algorithms are presented the codebook generation algorithms discussed include the linde buzo gray lbg binary splitting algorithm the pairwise nearest neighbor algorithm the simulated annealing algorithm and the fuzzy c means clustering analysis algorithm a new directed search binary splitting method which reduces the complexity of the lbg algorithm is presented also a new initial codebook selection method which can obtain a good initial codebook is presented by using this initial codebook selection algorithm the overall lbg codebook generation time can be reduced by a factor of 1 5 2

asymptotic dirichlet problems for harmonic functions on riemannian manifolds we define the asymptotic dirichlet problem and give a sufficient condition for solving it this proves an existence of nontrivial bounded harmonic functions on certain classes of noncompact complete riemannian manifolds 0 introduction in this paper we will prove the existence of nonconstant bounded harmonic functions on certain classes of noncompact riemannian manifolds by defining and solving an asymptotically defined dirichlet problem for harmonic functions the motivation comes from the classical uniformization theorem of riemann surfaces which says that a simply connected riemann surface is biholo morphic to the riemann sphere s2 the complex plane c or the unit disk d this is a geometric theorem but its original proof due to koebe relies heavily on function theory the function theoretic interpretation of this theorem is the following among the noncompact simply connected surfaces c is characterized by the fact that it admits no nonconstant bounded harmonic functions and d by that it admits nonconstant bounded harmonic functions the geometric aspect of the uniformization theorem could be roughly stated as follows let m be a simply connected riemann surface equipped with a complete riemannian metric with gaussian curvature km if km c 0 then m is biholo morphic to s2 if km c 0 then m is biholomorphic to d if km is close to zero then m is biholomorphic to c the following precise version is due to greene and wu gw1 p 120

approximations for expected generation number a deterministic formula is commonly used to approximate the expected generation number of a population of growing cells however this can give misleading results because it does not allow for natural variation in the times that individual cells take to reproduce here we present more accurate approximations for both symmetric and asymmetric cell division based on the first two moments of the generation time distribution these approximations are also robust we illustrate the improved approximations using data that arise from monitoring individual yeast cells under a microscope and also demonstrate how the approximations can be used when such detailed data are not available

an alternative quasi likelihood approach bayesian analysis and data based inference for model specification abstract this paper studies an alternative quasi likelihood approach under possible model misspecification we derive a filtered likelihood from a given quasi likelihood ql called a limited information quasi likelihood li ql that contains relevant but limited information on the data generation process our li ql approach in one hand extends robustness of the ql approach to inference problems for which the existing approach does not apply our study in this paper on the other hand builds a bridge between the classical and bayesian approaches for statistical inference under possible model misspecification we can establish a large sample correspondence between the classical ql approach and our li ql based bayesian approach an interesting finding is that the asymptotic distribution of an li ql based posterior and that of the corresponding quasi maximum likelihood estimator share the same sandwich type second moment based on the li ql we can develop inference methods that are useful for practical applications under possible model misspecification in particular we can develop the bayesian counterparts of classical ql methods that carry all the nice features of the latter studied in white 1982 in addition we can develop a bayesian method for analyzing model specification based on an li ql

positive harmonic functions on complete manifolds of negative curvature this paper studies the interaction between the geometry of complete riemannian manifolds of negative curvature and some aspects of function theory on these spaces the study of harmonic functions on the unit disc provides a classical and beautiful example of this interaction we recall some aspects of this below there is a well known representation of positive harmonic functions on the unit disc u due to herglotz 13 in terms of positive borel measures tt on the circle s1

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

improvement of the k means clustering filtering algorithm in this paper we present a modified filtering algorithm mfa by making use of center variations to speed up clustering process our method first divides clusters into static and active groups we use the information of cluster displacements to reject unlikely cluster centers for all nodes in the kd tree we reduce the computational complexity of filtering algorithm fa through finding candidates for each node mainly from the set of active cluster centers two conditions for determining the set of candidate cluster centers for each node from active clusters are developed our approach is different from the major available algorithm which passes no information from one stage of iteration to the next theoretical analysis shows that our method can reduce the computational complexity in terms of the number of distance calculations of fa at each stage of iteration by a factor of fc ac where fc and ac are the numbers of total clusters and active clusters respectively compared with the fa our algorithm can effectively reduce the computing time and number of distance calculations it is noted that our proposed algorithm can generate the same clusters as that produced by hard k means clustering the superiority of our method is more remarkable when a larger data set with higher dimension is used

saddlepoint approximations for short and long memory time series a frequency domain approach abstract saddlepoint techniques provide numerically accurate small sample approximations to the distribution of estimators and test statistics except for a few simple models these approximations are not available in the framework of stationary time series we contribute to fill this gap under short or long range serial dependence for gaussian and non gaussian processes we show how to derive and implement saddlepoint approximations for two relevant classes of frequency domain statistics ratio statistics and whittle s estimator we compare our new approximations to the ones obtained by the standard asymptotic theory and by two widely applied bootstrap methods the numerical exercises for whittle s estimator show that our approximations yield accuracy s improvements while preserving analytical tractability a real data example concludes the paper

heat semigroup on a complete riemannian manifold let m be a complete riemannian manifold and p t x y the minimal heat kernel on m let p t be the associated semigroup we say that m is stochastically complete if int m p t x y dy 1 for all t 0 x in m we say that m has the c 0 diffusion property or the feller property if p tf vanishes at infinity for all t 0 whenever f is so let x 0 in m and let kappa r 2 geq inf ric x rho x x 0 leq r rho is the riemannian distance we prove that m is stochastically complete and has the c 0 diffusion property if int infty c kappa r 1 dr infty by studying the radial part of the riemannian brownian motion on m

a fast vq codebook generation algorithm using codeword displacement in this paper we present a fast codebook generation algorithm called cgaucd codebook generation algorithm using codeword displacement by making use of the codeword displacement between successive partition processes by implementing a fast search algorithm named mfaupi modified fast algorithm using projection and inequality for vq encoding in the partition step of cgaucd the codebook generation time can be further reduced significantly using mfaupi the computing time of cgaucd can be reduced by a factor of 4 7 7 6 compared to generalized lloyd algorithm gla our proposed method can reduce the codebook generation time by a factor of 35 9 121 2 compared to the best codebook generation algorithm to our knowledge our approach can further reduce the corresponding computing time by 26 0 32 8 it is noted that our proposed algorithm can generate the same codebook as that produced by the gla the superiority of our method is more remarkable when a larger codebook is generated

quasi likelihood and its application a general approach to optimal parameter estimation the general framework an alternative approach e sufficiency asymptotic confidence zones of minimum size asymptotic quasi likelihood combining estimating functions projected quasi likelihood bypassing the likelihood hypothesis testing infinite dimensional problems miscellaneous applications consistency and asymptotic normality for estimating functions complements and strategies for application

saddlepoint approximations to the moments of multitype age dependent branching processes with applications this article proposes saddlepoint approximations to the expectation and variance covariance function of multitype age dependent branching processes the proposed approximations are found accurate easy to implement and much faster to compute than by simulating the process multiple applications are presented including the analyses of clonal data on the generation of oligodendrocytes from their immediate progenitor cells and on the proliferation of hela cells new estimators are also constructed to analyze clonal data the proposed methods are finally used to approximate the distribution of the generation which has recently found several applications in cell biology

martin compactification of a complete surface with negative curvature in this paper we consider the martin compactification associated with the operator mathcal l delta 1 of a complete non compact surface sigma 2 with negative curvature in particular we investigate positive eigenfunctions with eigenvalue one of the laplace operator delta of sigma 2 and prove a uniqueness result such eigenfunctions are unique up to a positive multiplicative constant if they vanish on the part of the geometric boundary s infty sigma 2 of sigma 2 where the curvature is bounded above by a negative constant and satisfy some growth estimate on the other part of s infty sigma 2 where the curvature approaches zero this uniqueness result plays an essential role in our recent paper cao and he infinitesimal rigidity of steady gradient ricci soliton in dimension three arxiv 1412 2714 2014 preprint in which we prove an infinitesimal rigidity theorem for deformations of certain three dimensional collapsed gradient steady ricci soliton with a non trivial killing vector field

exit probability estimates for martingales in geodesic balls using curvature kallenberg and sztencel have recently discovered exponential upper bounds independent of dimension on the probability that a vector martingale will exit from a ball in euclidean space by timet this article extends their results to martingales on riemannian manifolds including brownian motion and shows how exit probabilities depend on curvature using comparison with rotationally symmetric manifolds these estimates are easily computable and are sharp up to a constant factor in certain cases

the dirichlet problem at infinity for a negatively curved manifold on considere une n variete de riemann complete m qui est connexe et simplement connexe et a des courbures sectionnelles k bornees par 2 constantes finies negatives on etudie l existence de fonctions harmoniques bornees non constantes pour ces varietes

approximating likelihoods for large spatial data sets summary likelihood methods are often difficult to use with large irregularly sited spatial data sets owing to the computational burden even for gaussian models exact calculations of the likelihood for n observations require o n3 operations since any joint density can be written as a product of conditional densities based on some ordering of the observations one way to lessen the computations is to condition on only some of the past observations when computing the conditional densities we show how this approach can be adapted to approximate the restricted likelihood and we demonstrate how an estimating equations approach allows us to judge the efficacy of the resulting approximation previous work has suggested conditioning on those past observations that are closest to the observation whose conditional density we are approximating through theoretical numerical and practical examples we show that there can often be considerable benefit in conditioning on some distant observations as well

new approximations to the malthusian parameter approximations to the malthusian parameter of an age dependent branching process are obtained in terms of the moments of the lifetime distribution by exploiting a link with renewal theory in several examples the new approximations are more accurate than those currently in use even when based on only the first two moments the new approximations are extended to include a form of asymmetric cell division that occurs in some species of yeast when used for inference the new approximations are shown to have high efficiency

a fast k means clustering algorithm using cluster center displacement in this paper we present a fast k means clustering algorithm fkmcucd using the displacements of cluster centers to reject unlikely candidates for a data point the computing time of our proposed algorithm increases linearly with the data dimension d whereas the computational complexity of major available kd tree based algorithms increases exponentially with the value of d theoretical analysis shows that our method can reduce the computational complexity of full search by a factor of sf and sf is independent of vector dimension the experimental results show that compared to full search our proposed method can reduce computational complexity by a factor of 1 37 4 39 using the data set from six real images compared with the filtering algorithm which is among the available best algorithms of k means clustering our algorithm can effectively reduce the computing time it is noted that our proposed algorithm can generate the same clusters as that produced by hard k means clustering the superiority of our method is more remarkable when a larger data set with higher dimension is used

estimating space and space time covariance functions for large data sets a weighted composite likelihood approach in this article we propose two methods for estimating space and space time covariance functions from a gaussian random field based on the composite likelihood idea the first method relies on the maximization of a weighted version of the composite likelihood function while the second one is based on the solution of a weighted composite score equation this last scheme is quite general and could be applied to any kind of composite likelihood an information criterion for model selection based on the first estimation method is also introduced the methods are useful for practitioners looking for a good balance between computational complexity and statistical efficiency the effectiveness of the methods is illustrated through examples simulation experiments and by analyzing a dataset on ozone measurements

convergence of gaussian quasi likelihood random fields for ergodic levy driven sde observed at high frequency this paper investigates the gaussian quasi likelihood estimation of an exponentially ergodic multidimensional markov process which is expressed as a solution to a levy driven stochastic differential equations whose coefficients are supposed to be known except for the finite dimensional parameters to be estimated we suppose that the process is observed under the condition for the rapidly increasing experimental design by means of the polynomial type large deviation inequality the mighty convergence of the corresponding statistical random fields is derived which especially leads to the asymptotic normality at rate p nhn for all the target parameters and also to the convergence of their moments in our results the diffusion coefficient may be degenerate or even null although the resulting estimator is not asymptotically efficient in the presence of jumps we do not require any specific form of the driving levy measure rendering that the proposed estimation procedure is practical and somewhat robust to underlying model specification

dirichlet problem at infinity on gromov hyperbolic metric measure spaces we study the asymptotic dirichlet problem for p harmonic functions in a very general setting of gromov hyperbolic metric measure spaces

existence of non trivial harmonic functions on cartan hadamard manifolds of unbounded curvature the liouville property of a complete riemannian manifold m i e the question whether there exist non trivial bounded harmonic functions on m attracted a lot of attention for cartan hadamard manifolds the role of lower curvature bounds is still an open problem we discuss examples of cartan hadamard manifolds of unbounded curvature where the limiting angle of brownian motion degenerates to a single point on the sphere at infinity but where nevertheless the space of bounded harmonic functions is as rich as in the non degenerate case to see the full boundary the point at infinity has to be blown up in a non trivial way such examples indicate that the situation concerning the famous conjecture of greene and wu about existence of non trivial bounded harmonic functions on cartan hadamard manifolds is much more complicated than one might have expected

on the structure of vector quantizers vector quantization is intrinsically superior to predictive coding transform coding and other suboptimal and em ad hoc procedures since it achieves optimal rate distortion performance subject only to a constraint on memory or block length of the observable signal segment being encoded the key limitation of existing techniques is the very large randomly generated code books which must be stored and the computational complexity of the associated encoding procedures the quantization operation is decomposed into its rudimentary structural components this leads to a simple and elegant approach to derive analytical properties of optimal quantizers some useful properties of quantizers and algorithmic approaches are given which are relevant to the complexity of both storage and processing in the encoding operation highly disordered quantizers which have been designed using a clustering algorithm are considered finally lattice quantizers are examined which circumvent the need for a code book by using a highly structured code based on lattices the code vectors are algorithmically generated in a simple manner rather than stored in a code book and fast algorithms perform the encoding algorithm with negligible complexity

efficient restricted estimators for conditional mean models with missing data summary consider a conditional mean model with missing data on the response or explanatory variables due to two phase sampling or nonresponse robins et al 1994 introduced a class of augmented inverse probability weighted estimators depending on a vector of functions of explanatory variables and a vector of functions of coarsened data tsiatis 2006 studied two classes of restricted estimators class 1 with both vectors restricted to finite dimensional linear subspaces and class 2 with the first vector of functions restricted to a finite dimensional linear subspace we introduce a third class of restricted estimators class 3 with the second vector of functions restricted to a finite dimensional subspace we derive a new estimator which is asymptotically optimal in class 1 by the methods of nonparametric and empirical likelihood we propose a hybrid strategy to obtain estimators that are asymptotically optimal in class 1 and locally optimal in class 2 or class 3 the advantages of the hybrid likelihood estimator based on classes 1 and 3 are shown in a simulation study and a real data example

a mixture model with dependent observations for the analysis of csfe labeling experiments recent advances in flow cytometry have resulted in the development of powerful bioassays to analyze the proliferation of cell populations the carboxy fluorescein diacetate succinimidyl ester cfse labeling experiment is one such assay that is widely used to study cell kinetics and as a standard tool for investigating lymphocyte proliferation several mathematical models have been proposed to describe cell proliferation during cfse experiments the statistical analysis of cfse labeling data has received little attention but it poses a number of methodological issues in this article we approach their analysis using a mixture model the mixing proportions are specified through an age dependent branching process that models the temporal organization of the cell population because the cfse molecules are partitioned between daughter cells when their mother divides the observations generated by this assay are dependent the data structure can be compared with that of a partially observed random effects mod

identification of multitype branching processes we solve the problem of constructing an asymptotic global confidence region for the means and the covariance matrices of the reproduction distributions involved in a supercritical multitype branching process our approach is based on a central limit theorem associated with a quadratic law of large numbers performed by the maximum likelihood or the multidimensional lotka nagaev estimator of the reproduction law means the extension of this approach to the least squares estimator of the mean matrix is also briefly discussed on resout le probleme de construction d une region de confiance asymptotique et globale pour les moyennes et les matrices de covariance des lois de reproduction d un processus de branchement multitype et supercritique notre approche est basee sur un theoreme de limite centrale associe a une loi forte quadratique verifiee par l estimateur du maximum de vraisemblance ou l estimateur multidimensionnel de lotka nagaev des moyennes des lois de reproduction l extension de cette approche a l estimateur des moindres carres de la matrice des moyennes est aussi brievement commentee

estimating division and death rates from cfse data the division tracking dye carboxyfluorescin diacetate succinimidyl ester cfse is currently the most informative labeling technique for characterizing the division history of cells in the immune system gett and hodgkin nat immunol 1 2000 239 244 have proposed to normalize cfse data by the 2 fold expansion that is associated with each division and have argued that the mean of the normalized data increases linearly with time t with a slope reflecting the division rate p we develop a number of mathematical models for the clonal expansion of quiescent cells after stimulation and show within the context of these models under which conditions this approach is valid we compare three means of the distribution of cells over the cfse profile at time t the mean t the mean of the normalized distribution 2 t and the mean of the normalized distribution excluding nondivided cells 2 t in the simplest models which deal with homogeneous populations of cells with constant division and death rates the normalized frequency distribution of the cells over the respective division numbers is a poisson distribution with mean 2 t pt where p is the division rate the fact that in the data these distributions seem gaussian is therefore insufficient to establish that the times at which cells are recruited into the first division have a gaussian variation because the poisson distribution approaches the gaussian distribution for large pt excluding nondivided cells complicates the data analysis because 2 t pt and only approaches a slope p after an initial transient in models where the first division of the quiescent cells takes longer than later divisions all three means have an initial transient before they approach an asymptotic regime which is the expected t 2pt and 2 t 2 t pt such a transient markedly complicates the data analysis after the same initial transients the normalized cell numbers tend to decrease at a rate e dt where d is the death rate nonlinear parameter fitting of cfse data obtained from gett and hodgkin to ordinary differential equation ode models with first order terms for cell proliferation and death gave poor fits to the data the smith martin model with an explicit time delay for the deterministic phase of the cell cycle performed much better nevertheless the insights gained from analysis of the odes proved useful as we showed by generating virtual cfse data with a simulation model where cell cylce times were drawn from various distributions and then computing the various mean division numbers

image coding using vector quantization a review a review of vector quantization techniques used for encoding digital images is presented first the concept of vector quantization is introduced then its application to digital images is explained spatial predictive transform hybrid binary and subband vector quantizers are reviewed the emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques or when it is used in different domains

brownian motion and dirichlet problems at infinity we discuss angular convergence of riemannian brownian motion on a cartan hadamard manifold and show that the dirichlet problem at infinity for such a manifold is uniquely solvable under the curvature conditions ce 2 ar x km x a2 vspace 0 5pt 0 and cr x 2 km x 1 r x 2 2 2 respectively

the limiting angle of certain riemannian brownian motions let m be a cartan hadamard manifold of dimension d 3 let p m and x exp r x x be geodesic polar coordinates with pole p and let x be the brownian motion on m let sectm x denote the sectional curvature of any plane section in mx we prove that for each c 2 there is a 0 1 such that if l2r x 2 sectm x cr x 2 for all x in the complement of a compact set then limt xt exists a s and defines a nontrivial invariant random variable the dirichlet problem at infinity and a conjecture of greene and wu are also discussed

parametric estimation from approximate data non gaussian diffusions we study the problem of parameters estimation in indirect observability contexts where x t in r r is an unobservable stationary process parametrized by a vector of unknown parameters and all observable data are generated by an approximating process y varepsilon t which is close to x t in l 4 norm we construct consistent parameter estimators which are smooth functions of the sub sampled empirical mean and empirical lagged covariance matrices computed from the observable data we derive explicit optimal sub sampling schemes specifying the best paired choices of sub sampling time step and number of observations we show that these choices ensure that our parameter estimators reach optimized asymptotic l 2 convergence rates which are constant multiples of the l 4 norm y varepsilon t x t

detection and characterization of cluster substructure i linear structure fuzzy c lines in part i a generalization of the fuzzy c means or fuzzy isodata clustering algorithms is developed necessary conditions for minimization of a generalized total weighted squared orthogonal error objective function lead to a picard iteration scheme which generates simultaneously i c fuzzy clusters in the data ii a set of c prototypical straight lines in feature space which best fit the data in a well defined sense iii a set of c prototpyical centers of mass on the c lines which characterize the core of each linear fuzzy cluster theoretical optimization is achieved using principal components of generalized within cluster fuzzy scatter matrices a convergence theorem for each algorithm in the infinite family is given the algorithms are exemplified by five numerical examples using both real and artificial data sets having essentially linear substructure in part ii the fuzzy c means and fuzzy c lines algorithms are shown to be special cases of a more general class of fuzzy algorithms the

a new vector quantization clustering algorithm the pairwise nearest neighbor pnn algorithm is presented as an alternative to the linde buzo gray 1980 lbg generalized lloyd 1982 algorithm for vector quantization clustering the pnn algorithm derives a vector quantization codebook in a diminishingly small fraction of the time previously required without sacrificing performance in addition the time needed to generate a codebook grows only o n log n in training set size and is independent of the number of code words desired using this method one can either minimize the number of code words needed subject to a maximum rate the pnn algorithm can be used with squared error and weighted squared error distortion measure simulations on a variety of images encoded at 1 2 b pixel indicate that pnn codebooks can be developed in roughly 5 of the time required by the lbg algorithm

a directional mixed effects model for compositional expenditure data abstractcompositional data are vectors of proportions defined on the unit simplex and this type of constrained data occur frequently in government surveys it is also possible for the compositional data to be correlated due to the clustering or grouping of the observations within small domains or areas we propose a new class of the mixed model for compositional data based on the kent distribution for directional data where the random effects also have kent distributions one useful property of the new directional mixed model is that the marginal mean direction has a closed form and is interpretable the random effects enter the model in a multiplicative way via the product of a set of rotation matrices and the conditional mean direction is a random rotation of the marginal mean direction in small area estimation settings the mean proportions are usually of primary interest and these are shown to be simple functions of the marginal mean direction for estimation we apply a quasi likelihood method whic

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

the dirichlet problem at infinity for manifolds of negative curvature on considere l existence de fonctions harmoniques bornees sur des varietes simplement connexes n n de courbure negative