one fixed point actions on spheres ii the object of this paper is to treat the following old question of montgomery and samelson m s and some of its consequences which groups act smoothly on a closed homotopy sphere with exactly one fixed point and what are the isotropy representations of g which occur on the tangent space at the fixed point the first and only previously existing example of such an action was given by e stein for the group sl 2 z st a related question was solved by oliver o which groups act smoothly on a disk without fixed points a group which acts on a sphere with one fixed point acts on a disk without fixed points in p the author announced

waldhausen s classification theorem for finitely uniformizable 3 orbifolds we define a map between two orbifolds with respect to this map we generalize 3 manifold theory to 3 orbifolds as the main goal we generalize the waldhausen s classification theorem of haken 3 manifolds to finitely uniformizable 3 orbifolds for applications of the developed theory we introduce an invariant for links and tangles by using the orbifold fundamental group with the invariant we classify a class of links and show the untangling theorem

ends of maps ii versions of the finiteness obstruction and simple homotopy theory within e overx are developed this provides a setting for obstructions to the map analogs of the end ands cobordism theorems for manifolds these are applied to study equivariant mapping cylinder neighborhoods in topological group actions triangulations of locally triangulable spaces and block bundle structures on approximate fibrations

conditional cumulant of exposure method in logistic missing covariate regression summary we consider estimation in logistic regression where some covariate variables may be missing at random satten and kupper 1993 journal of the american statistical association88 200 208 proposed estimating odds ratio parameters using methods based on the probability of exposure by approximating a partial likelihood we extend their idea and propose a method that estimates the cumulant generating function of the missing covariate given observed covariates and surrogates in the controls our proposed method first estimates some lower order cumulants of the conditional distribution of the unobserved data and then solves a resulting estimating equation for the logistic regression parameter a simple version of the proposed method is to replace a missing covariate by the summation of its conditional mean and conditional variance given observed data in the controls we note that one important property of the proposed method is that when the validation is only on controls a class of inverse selection probability weighted semiparametric estimators cannot be applied because selection probabilities on cases are zeros the proposed estimator performs well unless the relative risk parameters are large even though it is technically inconsistent small sample simulations are conducted we illustrate the method by an example of real data analysis

the homotopy type of four dimensional knot complements one of the more useful ways of studying knots is by studying various algebraic invariants of their complements this paper studies the general problem of characterizing smooth four dimensional knot complements and gives examples which show how certain algebraic invariants can fail to determine the k n o t complement for example two well known theorems in three manifold theory show that i the homotopy type of a knot exterior in s 3 is determined by its fundamental group and ii the homeomorphism type of a knot exterior in s 3 is determined by its fundamental group together with the conjugacy class of the z x7z subgroup of 1 coming from the boundary so that a boundary preserving homotopy equivalence between knot exteriors can be deformed to a homeomorphism we show how both of these properties can fail in dimension four for a knot in s 4 we have the following hierarchy of properties of their exteriors that is successively stronger statements which one might make about two knot exteriors x and x the exterior of a knot k in s 4 is s 4 k x 2 the complement of an open tubular neighborhood of k

frechet integration and adaptive metric selection for interpretable covariances of multivariate functional data summary for multivariate functional data recorded for a sample of subjects on a common domain one 10 is often interested in the covariance between pairs of the component functions extending the notion of a covariance matrix for multivariate data to the functional case a straightforward approach is to integrate the pointwise covariance matrices over the functional time domain we generalize this approach by defining the frintegral which depends on the metric chosen for the space of covariance matrices and demonstrate that the ordinary integration is a special 15 case when the frobenius metric is used as the space of covariance matrices is nonlinear we propose a class of power metrics as alternatives to the frobenius metric for any such power metric the calculation of frintegrals is equivalent to transforming the covariance matrices with the chosen power applying the classical riemann integral to the transformed matrices and finally applying the inverse transformation to return to the original scale we also propose data 20 adaptive metric selection with respect to a user specified target criterion for example fastest decline of the eigenvalues establish consistency of the proposed procedures and demonstrate their effectiveness in a simulation the proposed functional covariance approach through fr echet integration is illustrated in a comparison of connectivity between brain voxels for normal subjects and alzheimer s patients based on fmri data 25

a pairwise interaction model for multivariate functional and longitudinal data functional data vectors consisting of samples of multivariate data where each component is a random function are encountered increasingly often but have not yet been comprehensively investigated we introduce a simple pairwise interaction model that leads to an interpretable and straightforward decomposition of multivariate functional data and of their variation into component specific processes and pairwise interaction processes the latter quantify the degree of pairwise interactions between the components of the functional data vectors while the component specific processes reflect the functional variation of a particular functional vector component that cannot be explained by the other components thus the proposed model provides an extension of the usual notion of a covariance or correlation matrix for multivariate vector data to functional data vectors and generates an interpretable functional interaction map the decomposition provided by the model can also serve as a basis for subsequent analysis such as study of the network structure of functional data vectors the decomposition of the total variance into componentwise and interaction contributions can be quantified by an formula see text like decomposition we provide consistency results for the proposed methods and illustrate the model by applying it to sparsely sampled longitudinal data from the baltimore longitudinal study of aging examining the relationships between body mass index and blood fats

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

semiparametric pseudo likelihoods in generalized linear models with nonignorable missing data we consider identifiability and estimation in a generalized linear model in which the response variable and some covariates have missing values and the missing data mechanism is nonignorable and unspecified we adopt a pseudo likelihood approach that makes use of an instrumental variable to help identifying unknown parameters in the presence of nonignorable missing data explicit conditions for the identifiability of parameters are given some asymptotic properties of the parameter estimators based on maximizing the pseudo likelihood are established explicit asymptotic covariance matrix and its estimator are also derived in some cases for the numerical maximization of the pseudo likelihood we develop a two step iteration algorithm that decomposes a nonconcave maximization problem into two problems of maximizing concave functions some simulation results and an application to a dataset from cotton factory workers are also presented

logistic regression with incompletely observed categorical covariates a comparison of three approaches summary a logistic regression analysis based on the complete cases neglects the information due to subjects with missing values in at least one but not in all covariates three different approaches allowing the use of this information are compared maximum likelihood estimation pseudo maximum likelihood estimation and probability imputation the first two yield consistent estimates of the regression coefficients and asymptotic normality allows the construction of asymptotically valid confidence intervals the only necessary assumption is that the probability for the occurrence of missing values does not depend on the true value of the hidden covariates whereas there may be a dependence on completely observed covariates and on the outcome variable their relative efficiency and the gain relative to a complete case analysis is investigated comparison with imputation methods shows that imputation of conditional probabilities can be regarded as a close approximation to the pseudo maximum likelihood estimation whereas imputation of unconditional probabilities is associated with serious bias

free involutions on s 1 s n topological free involutions on s 1 s n are classified up to conjugation weprovethatthisisthesameasclassifyingquotientmanifoldsuptohomeomorphism there are exactly four possible homotopy types of such quotients and surgery theory is used to classify all manifolds within each homotopy type

functional data analysis for sparse longitudinal data we propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data the method aims at irregularly spaced longitudinal data where the number of repeated measurements available per subject is small in contrast classical functional data analysis requires a large number of regularly spaced measurements per subject we assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random subject specific trajectory plus measurement errors basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories and the estimation of the variance of the measurement errors the eigenfunction basis is estimated from the data and functional principal components score estimates are obtained by a conditioning step this conditional estimation method is conceptually simple and straightforward to implement

multivariate logistic models for incomplete binary responses abstract in this article we describe a likelihood based regression model appropriate for analyzing incomplete multivariate binary responses we focus on marginal models that is models where the marginal mean or expectation of the binary response is related to a set of covariates the association between the binary responses is modeled in terms of conditional log odds ratios when the nonresponse mechanism is ignorable it is not necessary to specify a nonresponse model and valid inferences can be obtained provided that the likelihood for the responses has been correctly specified but when the nonresponse mechanism is nonignorable valid inferences can only be obtained by incorporating a model for nonresponse an unresolved issue with nonignorable models concerns the identifiability of the parameters so far no general and practically useful necessary and sufficient conditions for identifiability are available here we suggest some simple procedures for examining the identifiability status of nonign

the algebraic characterization of the exteriors of certain 2 knots we study 2 knots with virtually solvable group by applying recent work of freedman to the 4 manifolds obtained by surgery on such knots in particular we show that gluck reconstruction is the only ambiguity in recovering the cappell shaneson knots as top locally flat knots from their groups alone

structure sets vanish for certain bundles over seifert manifolds let m i be a compact orientable manifold which is the total space of a fiber bundle over a compact orientable manifold k3 with an effective circle action of hyperbolic type assume that the fiber n in this bundle is a closed orientable manifold with noetherian integral group ring with vanishing projective class and whitehead groups and such that the structure set sjop n x dk 3 of topological surgery vanishes for sufficiently large k then the projective class and whitehead groups of m vanish and st0p m 3 x dk 3 0 if n k 3 or if at3 is closed and n 2 the unil groups of cappell are the main obstacle here and these results give new examples of generalized free products of groups such that unily vanishes in spite of the failure of cappell s sufficient condition a conjecture of long standing holds that a closed aspherical manifold is de termined up to homeomorphism by its fundamental group this claim is now known to be valid for aspherical manifolds of dimensions greater than four whose funda mental groups contain nilpotent subgroups of finite index 8 10 earlier work verified the conjecture for poly z fundamental groups subject to the same dimen sion restrictions 30 pp 228 231 this paper will show that the conjecture and related statements are valid for compact manifolds m which are total spaces of certain bundles over surfaces or 3 manifolds the fibers of these bundles are closed orientable manifolds n satisfy ing these two hypotheses

invariants of conformal laplacians the conformal laplacian d d d n 2 s 4 n 1 acting on functions on a riemannian manifold mn with scalar curvature s is a conformally invariant operator in this paper we will use d to construct new conformal invariants one of these is a pointwise invariant one is the integral of a local expression and one is a nonlocal spectral invariant derived from functional determinants we begin in 1 by describing the laplacian d and its green function in the context of conformal geometry we then derive a basic formula giving the variation in the heat kernel of d this formula is strikingly simpler than the corresponding formula for the ordinary laplacian given by ray and singer 15 the heat kernel of d has an asymptotic expansion k t x x 4 t n 2 ak x tk in 2 we prove that a n 2 2 is a pointwise conformal invariant of weight 2 i e it satisfies a n 2 2 x 2g 2a n 2 2 x g where g is the metric and is any smooth positive function in particular this shows the existence of a nontrivial locally computable conformally invariant density naturally associated to the conformal structure of an even dimensional manifold the key to the proof is to consider the parametrix of the green s function which is obtained from the heat kernel by an integral transform one finds that a n 2 2 occurs as the coefficient of the first log term in this parametrix and its conformal invariance then follows directly from the conformal invariance of the green s function in 3 we show that an 2 is a global conformal invariant the calculations in 4 show that it is not a pointwise invariant the proof is a direct calculation of the invariant of an 2 using equation 1 10

on the orders of periodic diffeomorphisms of 4 manifolds this paper initiated an investigation on the following question sup pose a smooth 4 manifold does not admit any smooth circle actions does there exist a constant c 0 such that the manifold support no smooth zp actions of prime order for p c we gave affirmative results to this question for the case of holomorphic and symplectic actions with an interesting finding that the constant c in the holomorphic case is topological in nature while in the symplectic case it involves also the smooth structure of the manifold

estimating the number of classes estimating the unknown number of classes in a population has numerous important applications in a poisson mixture model the problem is reduced to estimating the odds that a class is undetected in a sample the discontinuity of the odds prevents the existence of locally unbiased and informative estimators and restricts confidence intervals to be one sided confidence intervals for the number of classes are also necessarily one sided a sequence of lower bounds to the odds is developed and used to define pseudo maximum likelihood estimators for the number of classes

functional linear regression analysis for longitudinal data we propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data where both the predictor and response are functions of a covariate such as time predictor and response processes have smooth random trajectories and the data consist of a small number of noisy repeated measurements made at irregular times for a sample of subjects in longitudinal studies the number of repeated measurements per subject is often small and may be modeled as a discrete random number and accordingly only a finite and asymptotically nonincreasing number of measurements are available for each subject or experimental unit we propose a functional regression approach for this situation using functional principal component analysis where we estimate the functional principal component scores through conditional expectations this allows the prediction of an unobserved response trajectory from sparse measurements of a predictor trajectory the resulting technique is flexible and allows for different patterns regarding the timing of the measurements obtained for predictor and response trajectories asymptotic properties for a sample of n subjects are investigated under mild conditions as n oo and we obtain consistent estimation for the regression function besides convergence results for the components of functional linear regression such as the regression parameter function we construct asymptotic pointwise confidence bands for the predicted trajectories a functional coefficient of determination as a measure of the variance explained by the functional regression model is introduced extending the standard r 2 to the functional case the proposed methods are illustrated with a simulation study longitudinal primary biliary liver cirrhosis data and an analysis of the longitudinal relationship between blood pressure and body mass index

finite group actions on 3 manifolds if g is a finite group acting smoothly on a closed surface f it is well known that g leaves invariant some riemannian metric of constant curvature on f thus any action of g on the 2 sphere s 2 is conjugate in diff s 2 to an orthogonal action if g acts on the torus sx s 1 there is a g invariant flat metric on s a s 1 and if g acts on a surface f with negative euler number then f admits a g invariant hyperbolic metric recently thurston th 1 th 2 th 3 has described the eight 3 dimensional geometries which provide geometric structures for closed 3 manifolds in the same way that the 2 sphere s 2 the euclidean plane e 2 and the hyperbolic plane h 2 provide geometric structures for surfaces see also the survey article by scott sc4 thurston also conjectured that if m is a closed 3 manifold with a geometric structure modelled on one of these eight geometries say x then any smooth action of a finite group g on m should leave invariant some metric on m inducing the geometry x we will say that g preserves the geometric structure on m in this case it should be noted that the restriction to smooth actions of g on m is essential for bing bi showed that there are involutions of s 3 whose fixed set is a wild 2 sphere however in dimension two it was proved by eilenberg ei that any action of a finite group on a surface is conjugate to a smooth action in this paper our main result asserts that thurston s conjecture holds for five of the eight geometries the result is the following

dynamical correlation for multivariate longitudinal data nonparametric methodology for longitudinal data analysis is becoming increasingly popular the analysis of multivariate longitudinal data where data on several time courses are recorded for each subject has received considerably less attention despite its importance for practical data analysis in particular there is a need for measures and estimates to capture dependency between the components of vector valued longitudinal data we propose and analyze a simple and effective nonparametric method to quantify the covariation of components of multivariate longitudinal observations which are viewed as realizations of a random process this includes the notion of a correlation between derivatives and time shifted versions the concept of dynamical correlation is based on a scalar product obtained from pairs of standardized smoothed curves the proposed method can be used when observation times are irregular and not matching between subjects or between responses within a subject for higher dimensional dat

sw gr from the seiberg witten equations to pseudo holomorphic curves the purpose of this article is to explain how pseudo holomorphic curves in a symplectic 4 manifold can be constructed from solutions to the seiberg witten equations as such the main theorem proved here theorem 1 3 is an existence theorem for pseudo holomorphic curves this article thus provides a proof of roughly half of the main theorem in the announcement t1 that theorem theorem 4 1 asserts an equivalence between the seiberg witten invariants for a symplectic manifold and a certain gromov invariant which counts with signs the number of pseudoholomorphic curves in a given homology class the seiberg witten invariants were introduced to mathematicians by witten w based on his joint work with nat seiberg sw1 sw2 a description of these invariants is given in section 1 see also km1 t1 suffice it to say here that when x is a compact oriented 4 dimensional manifold with

comparing the shapes of regression functions summary does a regression function follow a specified shape do two regression functions have the same shape how can regression functions be grouped based on shape these questions can occur when investigating monotonicity when counting local maxima or when studying variation in families of curves one can address these questions by considering the rank correlation coefficient between two functions this correlation is a generalisation of the rank correlation between two finite sets of numbers and is equal to one if and only if the two functions have the same shape a sample rank correlation based on smoothed estimates of the regression functions consistently estimates the true correlation this sample rank correlation can be used as a measure of similarity between functions in cluster analysis and as a measure of monotonicity or modality

an instanton invariant for 3 manifolds to an oriented closed 3 dimensional manifoldm withh1 m 0 we assign a 8 graded homology groupi m whose euler characteristic is twice casson s invariant the definition uses a construction on the space of instantons onm

groups generated by reflections and aspherical manifolds not covered by euclidean space a coxeter system r v is a group r a coxeter group together with a set of generators v such that each element of v has order two and such that all relations in r are consequences of relations of the form vw m v w 1 where v w e v and m v w denotes the order of vw the m v w s which are positive integers or oo obviously determine the coxeter system up to isomorphism the list of finite coxeter groups is short and well known however general coxeter groups are much more flexible in fact the set v and the m v w s can be specified arbitrarily at least if v is finite subject only to the conditions m v v 1 and m v w m w v 2 if v w suppose that r v is a coxeter system that x is a hausdorff space and that xv v v is a locally finite family of closed subspaces indexed by v the xv are called the panels of x 2 there is a classical method for constructing a transformation group from these data for each x e x let v x denote the set of v in v such that x e xv for each subset s of v let rs be the subgroup generated by s and let xs be the face of x defined by

fully parametric and semi parametric regression models for common events with covariate measurement error in main study validation study designs the derivation of the likelihood function for binary data from two types of main study validation study designs where model covariates are measured with error is elaborated rather than limiting consideration to a restricted family of models with convenient mathematical properties we suggest that empirical considerations customized to the data at hand should drive model choices the joint likelihood function for the main study in which the covariates are measured with error and the validation study in which they are not is maximized and estimation and inference proceeds using standard theory although the choice of the measurement error model is driven by empirical considerations the relatively small validation study sizes typically seen may lead to misspecification resulting in bias in estimation and inference about exposure disease relationships by using a nonparametric form for the measurement error model the resulting semi parametric methods suggested by robins rotnitzky and zhao 1994 journal of the american statistical association 89 864 866 and robins hsieh and newey 1995 journal of the royal statistical society series b 57 409 424 are free from bias due to misspecification of the measurement error model trading efficiency for robustness as usual these fully and semi parametric methods are illustrated with a detailed example from a main study validation study of the health effects of occupational exposure to chemotherapeutics among pharmacists valanis et al 1993 american journal of hospital pharmacy 50 455 462 a constant prevalence ratio model for common binary events with gamma covariate measurement error is derived and empirically verified by the available data a careful reanalysis of the data taking measurement error fully into account leads to a threefold increase in the log relative risk and no loss of statistical power the semi parametric estimates are consistent with the parametric results providing reassurance that important bias due to misspecification of the measurement error model is unlikely

smooth s cobordisms of elliptic 3 manifolds the main result of this paper states that a symplectic s cobordism of elliptic 3 manifolds is diffeomorphic to a product assuming a canonical contact structure on the boundary based on this theorem we conjecture that a smooth s cobordism of elliptic 3 manifolds is smoothly a product if its universal cover is smoothly a product we explain how the conjecture fits naturally into the program of taubes of constructing symplectic structures on an oriented smooth 4 manifold with b 1 from generic self dual harmonic forms the paper also contains an auxiliary result of independent interest which generalizes taubes theorem sw gr to the case of symplectic 4 orbifolds

finite group actions on the moduli space of self dual connections i let m be a smooth simply connected closed 4 manifold with positive definite intersection form suppose a finite group g acts smoothly on m let 7r e m be the instanton number one quaternion line bundle over m with a smooth g action such that 7r is an equivariant map we first show that there exists a baire set in the g invariant metrics on m such that the moduli space g of g invariant irreducible self dual connections is a manifold by utilizing the g transversality theory of t petrie we then identify cohomology obstructions to globally perturbing the full space of irreducible self dual connections to a g manifold when g z2 and the fixed point set of the z2 action on m is a nonempty collection of isolated points and riemann surfaces

gauge theory on asymptotically periodic 4 manifolds il existe une famille non denombrable de classes de diffeomorphismes des 4 varietes orientees homeomorphes a r 4

the orientation of yang mills moduli spaces and 4 manifold topology si x est une 4 variete lisse orientee fermee dont la forme intersection q h 2 x z torsion z est definie negative alors la forme est equivalente sur les entiers a la forme standard 1 1 1 soit x une 4 variete lisse orientee fermee avec les trois proprietes suivantes 1 h 1 x z n a pas de 2 torsion 2 la forme intersection q sur h 2 x torsion a une partie positive de rang 1 ou 2 3 la forme intersection est paire alors q est equivalente sur les entiers a une des formes 01 10 01 10 01 10

maximum likelihood estimation and model selection in contingency tables with missing data abstract in many studies the values of one or more variables are missing for subsets of the original sample this article focuses on the problem of obtaining maximum likelihood estimates mle for the parameters of log linear models under this type of incomplete data the appropriate systems of equations are presented and the expectation maximization em algorithm dempster laird and rubin 1977 is suggested as one of the possible methods for solving them the algorithm has certain advantages but other alternatives may be computationally more effective tests of fit for log linear models in the presence of incomplete data are considered the data from the protective services project for older persons blenkner bloom and nielsen 1971 blenkner bloom and weber 1974 are used to illustrate the procedures discussed in the article

dehn surgery on knots in d dehn considered the following method for constructing 3 manifolds remove a solid torus neighborhood n k of some knot x in the 3 sphere s and sew it back differently in particular he showed that taking x to be the trefoil one could obtain infinitely many non simply connected homology spheres o in this way let mx s n k then the different resewings are parametrized by the isotopy class r of the simple closed curve on the torus omk that bounds a meridional disk in the re attached solid torus we denote the resulting closed oriented 3 manifold by mk and say that it is obtained by r dehn surgery on x more generally one can consider the manifolds ml obtained by r dehn surgery on a fc component link l xi u u kk in s where r r it turns out that every closed oriented 3 manifold can be constructed in this way wal lie thus a good understanding of dehn surgery might lead to progress on general questions about the structure of 3 manifolds starting with the case of knots it is natural to extend the context a little and consider the manifolds m r obtained by attaching a solid torus v to an arbitrary compact oriented irreducible every 2 sphere bounds a 3 ball 3 manifold m with dm an incompressible torus where r is the isotopy class slope on dm of the boundary of a meridional disk of v we say that m r is the result of r dehn filling on m an observed feature of this construction is that

maximum likelihood estimation for mixed continuous and categorical data with missing values summary maximum likelihood procedures for analysing mixed continuous and categorical data with missing values are presented the general location model of olkin tate 1961 and extensions introduced by krzanowski 1980 1982 form the basis for our methods maximum likelihood estimation with incomplete data is achieved by an application of the em algorithm dempster laird rubin 1977 special cases of the algorithm include orchard woodbury s 1972 algorithm for incomplete normal samples fuchs s 1982 algorithms for log linear modelling of partially classified contingency tables and day s 1969 algorithm for multivariate normal mixtures applications include a imputation of missing values b logistic regression and discriminant analysis with missing predictors and unclassified observations c linear regression with missing continuous and categorical predictors and d parametric cluster analysis with incomplete data methods are illustrated using data from the st louis risk research project some key word8 cluster analysis discriminant analysis em algorithm incomplete data linear regression logistic regression log linear model mixture model

covariate measurement error in generalized linear models summary the em algorithm is used to obtain estimators of regression coefficients for generalized linear models with canonical link when normally distributed covariates are masked by normally distributed measurement errors by casting the true covariates as missing data the em procedure suggests an iterative scheme in which each cycle consists of an e step requiring the computation of approximate first and second conditional moments of the true covariates given the observed data followed by an m step in which regression parameters are updated by iteratively reweighted least squares based on these approximations the proposed procedure is compared numerically with the exact maximum likelihood solution obtained by using gaussian quadrature instead of the approximations in the e step of the em algorithm and with alternative estimators for simple logistic regression with measurement error the results for the proposed procedure are encouraging a procedure is proposed in this paper for estimating regression coefficients in generalized linear models when one or more of the covariates is measured with error this work is related to the paper by carroll et al 1984 in which maximum likelihood estimates are considered for the structural logistic regression model these authors provide estimates for the computationally simpler probit regression model and suggest that the structural logistic regression can be done in principle this paper follows up on that suggestion but differs in detail from similar work by armstrong 1985 other procedures with related aims have been suggested by stefanski carroll 1985 wolter fuller 1982 and prentice 1982 for a quick introduction to the proposed method it is convenient to display the naive estimator which ignores measurement error in its standard computational form if yi is an observed response variable and xi is the observed covariate then for the model which equates the canonical parameter of the distribution of yi to xtf3 the maximum likelihood estimator of f3 can be obtained by iteratively reweighted least squares the estimate of f3 after s 1 cycles is given by

canonical correlation analysis when the data are curves summary it is not immediately straightforward to extend canonical correlation analysis to the context of functional data analysis where the data are themselves curves or functions the obvious approach breaks down and it is necessary to use a method involving smoothing in some way such a method is introduced and discussed with reference to a data set on human gait the breakdown of the unsmoothed method is illustrated in a practical context and is demonstrated theoretically a consistency theorem for the smoothed method is proved in an increasing number of problems in a wide range of fields the data observed are not the univariate or multivariate observations of classical statistics but are func tions observed continuously ramsay and dalzell 1991 give the name functional data analysis to the analysis of data of this kind in most cases the observations will be functions of time or a closely related variable but there are clearly applications where the functions are surfaces observed over two or three dimensional space the motivating example for the present paper is a set of data on children s gait collected by the motion analysis laboratory at children s hospital san diego california see olshen et al 1989 for full details for each of a number of children several angles made by the child s joints knee hip etc are observed during the child s gait cycle one aim of the study is to gain understanding of the gait cycle of a normal child to make comparisons with children suffering from walking diffi culties these data motivated rice and silverman 1991 to discuss the extension of principal component analysis to the functional setting and to explain how smoothing can be incorporated into the analysis in a natural way in a substantial complemen tary paper ramsay and dalzell 1991 discuss different approaches to regression and principal component analysis in functional data analysis illustrating their work by a meteorological example the insights of functional data analysis may be helpful in chemometrics for instance a standard chemometric problem is the analysis of spectra observed in chromatography and these are to all intents and purposes functional observations another obvious area of potential relevance is the analysis of growth curve data the focus in the present paper will be on canonical correlation analysis cca in the gait example one might ask how variability in the knee angle cycle is related to

functional singular component analysis summary aiming at quantifying the dependence of pairs of functional data x y we develop the concept of functional singular value decomposition for covariance and functional singular component analysis building on the concept of canonical expansion of compact operators in functional analysis we demonstrate the estimation of the resulting singular values functions and components for the practically relevant case of sparse and noise contaminated longitudinal data and provide asymptotic consistency results expanding bivariate functional data into singular functions emerges as a natural extension of the popular functional principal component analysis for single processes to the case of paired processes a natural application of the functional singular value decomposition is a measure of functional correlation owing to the involvement of an inverse operation most previously considered functional correlation measures are plagued by numerical instabilities and strong sensitivity to the choice of smoothing parameters these problems are exacerbated for the case of sparse longitudinal data on which we focus the functional correlation measure that is derived from the functional singular value decomposition behaves well with respect to numerical stability and statistical error as we demonstrate in a simulation study practical feasibility for applications to longitudinal data is illustrated with examples from a study on aging and on line auctions

incomplete data in generalized linear models abstract this article examines incomplete data for the class of generalized linear models in which incompleteness is due to partially missing covariates on some observations under the assumption that the missing data are missing at random it is shown that the e step of the em algorithm for any generalized linear model can be expressed as a weighted complete data log likelihood when the unobserved covariates are assumed to come from a discrete distribution with finite range expressing the e step in this manner allows for a straightforward maximization in the m step thus leading to maximum likelihood estimates mle s for the parameters asymptotic variances of the mle s are also derived and results are illustrated with two examples

one fixed point actions and homology 3 spheres one of the best known three dimensional manifolds is the poincare homology three sphere 1 2 3 5 this closed 3 manifold has the same homology groups as the standard sphere s3 but is not simply connected see pnc p 106 or br2 section 1 8 numerous investigations during the past century have shown that this manifold has many remarkable properties several equivalent descriptions of 1 2 3 5 are summarized in kis from the viewpoint of transformation groups one noteworthy property is that 1 2 3 5 is the only nonsimply connected homology sphere admitting a transitive action of a compact lie group brl the manifold 1 2 3 5 also figures importantly in regularity questions for group actions on spherelike manifolds linear or orthogonal actions of finite groups on spheres are generally viewed as the simplest and most regular examples of such actions and one of the themes of transformation groups is to determine the extent to which arbitrary actions on spherelike manifolds resemble linear actions one distinguishing feature of linear actions is that their fixed point sets if nonempty are also spheres the well known results of p a smith cf br2 show that continuous p group actions on homology spheres all resemble linear actions in this respect i e the fixed point sets are always zp homology cohomology spheres on the other hand outside the family of p groups there are many exotic group actions perhaps the most elementary example of this type involves 1 2 3 5 if a is the subgroup of the rotation group so3 given by the symmetries of a regular icosahedron so that a is isomorphic to the alternating group a5 then the quotient space s03 a is the poincare homology 3 sphere and the induced action of a5 a has exactly one fixed point this example suggests that general actions of finite groups on homology spheres can be quite different from linear actions and much of the work on exotic finite group actions during the past three decades was at least partially motivated by the existence of this group action

pseudo maximum likelihood estimation the asymptotic distribution gong and samaniego 1981 define pseudo maximum likelihood estimation and derive the asymptotic distribution of the resulting estimates this note gives a simpler and more elegant expression for the asymptotic variance of a pseudo maximum likelihood estimate

smoothed functional principal components analysis by choice of norm the principal components analysis of functional data is often enhanced by the use of smoothing it is shown that an attractive method of incorporating smoothing is to replace the usual l 2 orthonormality constraint on the principal components by orthonormality with respect to an inner product that takes account of the roughness of the functions the method is easily implemented in practice by making use of appropriate function transforms fourier transforms for periodic data and standard principal components analysis programs several alternative possible interpretations of the smoothed principal components as obtained by the method are presented some theoretical properties of the method are discussed the estimates are shown to be consistent under appropriate conditions and asymptotic expansion techniques are used to investigate their bias and variance properties these indicate that the form of smoothing proposed is advantageous under mild conditions indeed milder than those for existing methods of smoothed functional principal components analysis the choice of smoothing parameter by cross validation is discussed the methodology of the paper is illustrated by an application to a biomechanical data set obtained in the study of the behaviour of the human thumb forefinger system

modeling and forecasting daily electricity load curves a hybrid approach we propose a hybrid approach for the modeling and the short term forecasting of electricity loads two building blocks of our approach are 1 modeling the overall trend and seasonality by fitting a generalized additive model to the weekly averages of the load and 2 modeling the dependence structure across consecutive daily loads via curve linear regression for the latter a new methodology is proposed for linear regression with both curve response and curve regressors the key idea behind the proposed methodology is dimension reduction based on a singular value decomposition in a hilbert space which reduces the curve regression problem to several ordinary i e scalar linear regression problems we illustrate the hybrid method using french electricity loads between 1996 and 2009 on which we also compare our method with other available models including the electricite de france operational model supplementary materials for this article are available online

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

peter hall functional data analysis and random objects functional data analysis has become a major branch of nonparametric statistics and is a fast evolving field peter hall has made fundamental contributions to this area and its theoretical underpinnings he wrote more than 25 papers in functional data analysis between 1998 and 2016 and from 2005 on was a tenured faculty member with a 25 appointment in the department of statistics at the university of california davis this article describes aspects of his appointment and academic life in davis and also some of his major results in functional data analysis along with a brief history of this area it concludes with an outlook on new types of functional data and an emerging field of random objects that subsumes functional data analysis as it deals with more complex data structures

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

an application of gauge theory to four dimensional topology soit x une u variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee q est definie positive alors cette forme est equivalente sur les entiers a la forme diagonale standard soit dans une base q u 1 u 2 u 2 u 2 1 u 2 2 u 2 2