empirical likelihood and quantile regression in longitudinal data analysis we propose a novel quantile regression approach for longitudinal data analysis which naturally incorporates auxiliary information from the conditional mean model to account for within subject correlations the efficiency gain is quantified theoretically and demonstrated empirically via simulation studies and the analysis of a real dataset

analytic torsion and holomorphic determinant bundles i bott chern forms and analytic torsion we attach secondary invariants to any acyclic complex of holomorphic hermitian vector bundles on a complex manifold these were first introduced by bott and chern bot c our new definition uses quillen s superconnections we also give an axiomatic characterization of these classes these results will be used in bgs2 and bgs3 to study the determinant of the cohomology of a holomorphic vector bundle

new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis semiparametric regression models are very useful for longitudinal data analysis the complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis in this article two new approaches are proposed for estimating the regression coefficients in a semiparametric model the asymptotic normality of the resulting estimators is established an innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models the proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters rates of convergence of the resulting estimators are established with a proper choice of regularization parameters and penalty functions the proposed variable selection procedures are shown to perform as well as an oracle estimator a robust standard error formula is derived usi

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

improving generalised estimating equations using quadratic inference functions summary generalised estimating equations enable one to estimate regression parameters consistently in longitudinal data analysis even when the correlation structure is misspecified however under such misspecification the estimator of the regression parameter can be inefficient in this paper we introduce a method of quadratic inference functions that does not involve direct estimation of the correlation parameter and that remains optimal even if the working correlation structure is misspecified the idea is to represent the inverse of the working correlation matrix by the linear combination of basis matrices a representation that is valid for the working correlations most commonly used both asymptotic theory and simulation show that under misspecified working assumptions these estimators are more efficient than estimators from generalised estimating equations this approach also provides a chi squared inference function for testing nested models and a chi squared regression misspecification test furthermore the test statistic follows a chi squared distribution asymptotically whether or not the working correlation structure is correctly specified

median regression models for longitudinal data with dropouts summary recently median regression models have received increasing attention when continuous responses follow a distribution that is quite different from a normal distribution usual mean regression models may fail to produce efficient estimators whereas median regression models may perform satisfactorily in this article we discuss using median regression models to deal with longitudinal data with dropouts weighted estimating equations are proposed to estimate the median regression parameters for incomplete longitudinal data where the weights are determined by modeling the dropout process consistency and the asymptotic distribution of the resultant estimators are established the proposed method is used to analyze a longitudinal data set arising from a controlled trial of hiv disease volberding et al 1990 the new england journal of medicine 322 941 949 simulation studies are conducted to assess the performance of the proposed method under various situations an extension to estimation of the association parameters is outlined

moduli of stability for germs of homogeneous vectorfields on r3 abstract in this paper we will show that there are an uncountable number of homogeneous quadratic vectorfields on r 3 so that no two of these vectorfields are topologically equivalent

median regression for longitudinal data we review and compare three estimators of median regression in linear models with longitudinal data the estimators are constructed based on well known ideas of weighting decorrelating and the working assumption of independence both asymptotic efficiency calculations and finite sample monte carlo studies are used to assess the performance of these estimators we find that their relative performances depend on the nature of covariates the estimator under the working assumption of independence is computationally simple and yet has good relative performance when the covariates are invariant over time or when the within subject correlations are small its relative performance in finite samples is also found to be more favourable than suggested by the asymptotic comparisons

asymptotic expansion of the witten deformation of the analytic torsion given a compact riemannian manifold md g a finite dimensional representation 1 m gl v of the fundamental group 1 m on a vector spacevof dimensionland a hermitian structure on the flat vector bundle formula associated to ray singer rs have introduced the analytic torsiont t m g 0 witten s deformationdq t of the exterior derivativedq dq t e htdqeht withh m ra smooth morse function can be used to define a deformationt h t 0 of the analytic torsiontwitht h 0 t the main results of this paper are to provide assuming that grad ghis morse smale an asymptotic expansion for log t h t fort of the form formula and to present two different formulae fora0 as an application we obtain a shorter derivation of results due to ray singer rs cheeger ch muller mu1 2 which in increasing generality concern the equality for odd dimensional manifolds of the analytic torsion with the average of the reidemeister torsion corresponding to the triangulation t h g and the dual triangulation td d h g

statistical inference in a growth curve quantile regression model for longitudinal data this article describes a polynomial growth curve quantile regression model that provides a comprehensive assessment about the treatment effects on the changes of the distribution of outcomes over time the proposed model has the flexibility as it allows the degree of a polynomial to vary across quantiles a high degree polynomial model fits the data adequately yet it is not desirable due to the complexity of the model we propose the model selection criterion based on an empirical loglikelihood that consistently identifies the optimal degree of a polynomial at each quantile after the parsimonious model is fitted to the data the hypothesis test is further developed to evaluate the treatment effects by comparing the growth curves it is shown that the proposed empirical loglikelihood ratio test statistic follows a chi square distribution asymptotically under the null hypothesis various simulation studies confirm that the proposed test successfully detects the difference between the curves across quantiles when the empirical loglikelihood is employed we incorporate the within subject correlation commonly existing in longitudinal data and gain estimation efficiency of the quantile regression parameters in the growth curve model the proposed process is illustrated through the analysis of randomized controlled longitudinal depression data

a type of moduli for saddle connections of planar diffeomorphisms on considere un diffeomorphisme f sur une variete a 2 dimensions m ayant une paire de points fixes hyperboliques p et q de type selle de sorte que l une des composantes connexes de w u p p est une composante connexe de w s q q q on etudie les conjugaisons hors de la connexion selle on introduit la notion de conjugaison pincee

quasi likelihood for median regression models abstract this article proposes quasi likelihood equations for median regression models the quasi likelihood can be used for dependent observations such as repeated measurements or time series data to construct a quasi likelihood equation we need to specify the relation between the median and the dispersion and also specify the dependency of the observations if a monotone transformation of the original observation has a laplace distribution then the quasi likelihood is the exact likelihood under moderate assumptions the quasi likelihood estimates are consistent and have asymptotically normal distributions the estimates are also shown to have minimal asymptotic variance within a certain class of consistent estimates the proposed method is illustrated using data from a clinical trial

refined analytic torsion given an acyclic representation alpha of the fundamental group of a compact oriented odd dimensional manifold which is close enough to an acyclic unitary representation we define a refinement t alpha of the ray singer torsion associated to alpha which can be viewed as the analytic counterpart of the refined combinatorial torsion introduced by turaev t alpha is equal to the graded determinant of the odd signature operator up to a correction term the metric anomaly needed to make it independent of the choice of the riemannian metric t alpha is a holomorphic function on the space of such representations of the fundamental group when alpha is a unitary representation the absolute value of t alpha is equal to the ray singer torsion and the phase of t alpha is proportional to the eta invariant of the odd signature operator the fact that the ray singer torsion and the eta invariant can be combined into one holomorphic function allows one to use methods of complex analysis to study both invariants in particular using these methods we compute the quotient of the refined analytic torsion and turaev s refinement of the combinatorial torsion generalizing in this way the classical cheeger m uller theorem as an application we extend and improve a result of farber about the relationship between the farber turaev absolute torsion and the eta invariant as part of our construction of t alpha we prove several new results about determinants and eta invariants of non self adjoint elliptic operators

informative estimation and selection of correlation structure for longitudinal data identifying an informative correlation structure is important in improving estimation efficiency for longitudinal data we approximate the empirical estimator of the correlation matrix by groups of known basis matrices that represent different correlation structures and transform the correlation structure selection problem to a covariate selection problem to address both the complexity and the informativeness of the correlation matrix we minimize an objective function that consists of two parts the difference between the empirical information and a model approximation of the correlation matrix and a penalty that penalizes models with too many basis matrices the unique feature of the proposed estimation and selection of correlation structure is that it does not require the specification of the likelihood function and therefore it is applicable for discrete longitudinal data we carry out the proposed method through a groupwise penalty strategy which is able to identify more complex structures the

analytic torsion and r torsion for unimodular representations let m be a closed c manifold of dimension n both r torsion and analytic torsion are smooth invariants of acyclic orthogonal or unitary representations p of the fundamental group 7i m the reidemeister franz torsion or r torsion tm p of p is defined in terms of the combinatorial structure of m given by its smooth triangulations the analytic torsion tm p was introduced by ray and singer rs as an analytic counterpart of r torsion in order to define the analytic torsion one has to choose a riemannian metric on m then tm p is a certain weighted alternating product of regularized determinants of the laplacians on differential qforms of m with values in the flat bundle e defined by p it was conjectured by ray and singer rs that tm p trm p for all acyclic orthogonal or unitary representations p this conjecture was proved independently by cheeger c and the author mu the restriction to orthogonal or unitary representations is certainly a limitation of the applicability of this result if 7i m is infinite because an infinite discrete group will have in general many nonorthogonal finite dimensional representations it is the purpose of the present paper to remove this limitation we call a representation p r m gl e on a finite dimensional real or complex vector space e unimodular if i det p y i 1 for all y e i m then we define r torsion and analytic torsion for unimodular representations and the main result is that for odd dimensional manifolds m the equality of the two torsions extends to all unimodular representations

ray singer type theorem for the refined analytic torsion we show that the refined analytic torsion is a holomorphic section of the determinant line bundle over the space of complex representations of the fundamental group of a closed oriented odd dimensional manifold further we calculate the ratio of the refined analytic torsion and the farber turaev combinatorial torsion as an application we establish a formula relating the eta invariant and the phase of the farber turaev torsion which extends a theorem of farber and earlier results of ours this formula allows to study the spectral flow using methods of combinatorial topology

tuning parameter selectors for the smoothly clipped absolute deviation method summary the penalized least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method it not only automatically and consistently selects the important variables but also produces estimators which are as efficient as the oracle estimator however these attractive features depend on appropriate choice of the tuning parameter we show that the commonly used generalized crossvalidation cannot select the tuning parameter satisfactorily with a nonignorable overfitting effect in the resulting model in addition we propose a bic tuning parameter selector which is shown to be able to identify the true model consistently simulation studies are presented to support theoretical findings and an empirical example is given to illustrate its use in the female labor supply data

anomalies and analytic torsion on hyperbolic manifolds the global additive and multiplicative properties of the laplacian on j forms and related zeta functions are analyzed the explicit form of zeta functions on a product of closed oriented hyperbolic manifolds hd and of the multiplicative anomaly are derived we also calculate in an explicit form the analytic torsion associated with a connected sum of such manifolds

complex valued ray singer torsion abstract in the spirit of ray and singer we define a complex valued analytic torsion using non selfadjoint laplacians we establish an anomaly formula which permits to turn this into a topological invariant conjecturally this analytically defined invariant computes the complex valued reidemeister torsion including its phase we establish this conjecture in some non trivial situations

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

transition functions and moduli of stability for 3 dimensional homogeneous vector fields with a hyperbolic blowing up abstract in the first part of the paper we introduce the normal transition function for saddle connections of planar diffeomorphisms it is a positive multiple of the usual transition function but in its definition we do not need c 1 linearizing coordinates among other nice properties it is found to be analytic when the diffeomorphism is the second part of the paper deals with the existence of a modulus of stability for germs on r 3 of homogeneous vector fields with a hyperbolic blowing up we show that inside a specific class of examples the modulus occurs for a sufficiently high degree