normalisers in limit groups let gamma be a limit group s subset gamma a non trivial subgroup and n the normaliser of s if h 1 s mathbb q has finite mathbb q dimension then s is finitely generated and either n s is finite or n is abelian this result has applications to the study of subdirect products of limit groups

stallings foldings and subgroups of free groups we re cast in a more combinatorial and computational form the topological approach of j stallings to the study of subgroups of free groups

the hanna neumann conjecture for demushkin groups abstract we confirm the hanna neumann conjecture for topologically finitely generated closed subgroups u and w of a nonsolvable demushkin group g namely we show that g u g w d u g w g 1 d u d w where d k max d k 1 0 and d k is the least cardinality of a topological generating set for the group k

tableau algorithms for factor analysis by instrumental variable methods simple tableau algorithms are given for the noniterative instrumental variable fabin 2 and two stage regression fabin 3 factor loading estimates of hagglund corresponding generalized least squares estimates of factor covariances and unique variances are introduced an example is given for the purpose of illustration and comparison

linear biseparating maps between spaces of vector valued differentiable functions and automatic continuity abstract we give a complete description of linear biseparating maps between spaces of vector valued differentiable functions this description automatically implies continuity of such maps

group cocycles and the ring of affiliated operators in this article we study cocycles of discrete countable groups with values in 2 g and the ring of affiliated operators ug we clarify properties of the first cohomology of a group g with coefficients in 2 g and answer several questions from de cornulier et al transform groups 13 1 125 147 2008 moreover we obtain strong results about the existence of free subgroups and the subgroup structure provided the group has a positive first 2 betti num ber we give numerous applications and examples of groups which satisfy our assumptions

factor analysis by instrumental variables methods three alternative estimation procedures for factor analysis based on the instrumental variables method are presented these procedures are justified by the method of least squares formulas for asymptotic standard errors of factor loadings are derived the procedures are empirically compared to the method of maximum likelihood the conclusion based on the data used in this study is that two of the procedures seem to work well

weighted composition operators ofc0 x s abstract in this paper we prove that into isometries and disjointness preserving linear maps from c 0 x into c 0 y are essentially weighted composition operators tf h f for some continuous map and some continuous scalar valued function h

a polychoric instrumental variable piv estimator for structural equation models with categorical variables this paper presents a new polychoric instrumental variable piv estimator to use in structural equation models sems with categorical observed variables the piv estimator is a generalization of bollen s psychometrika 61 109 121 1996 2sls iv estimator for continuous variables to categorical endogenous variables we derive the piv estimator and its asymptotic standard errors for the regression coefficients in the latent variable and measurement models we also provide an estimator of the variance and covariance parameters of the model asymptotic standard errors for these and test statistics of overall model fit we examine this estimator via an empirical study and also via a small simulation study our results illustrate the greater robustness of the piv estimator to structural misspecifications than the system wide estimators that are commonly applied in sems

model implied instrumental variable generalized method of moments miiv gmm estimators for latent variable models the common maximum likelihood ml estimator for structural equation models sems has optimal asymptotic properties under ideal conditions e g correct structure no excess kurtosis etc that are rarely met in practice this paper proposes model implied instrumental variable generalized method of moments miiv gmm estimators for latent variable sems that are more robust than ml to violations of both the model structure and distributional assumptions under less demanding assumptions the miiv gmm estimators are consistent asymptotically unbiased asymptotically normal and have an asymptotic covariance matrix they are distribution free robust to heteroscedasticity and have overidentification goodness of fit j tests with asymptotic chi square distributions in addition miiv gmm estimators are scalable in that they can estimate and test the full model or any subset of equations and hence allow better pinpointing of those parts of the model that fit and do not fit the data an empirical example illustrates miiv gmm estimators two simulation studies explore their finite sample properties and find that they perform well across a range of sample sizes

an alternative two stage least squares 2sls estimator for latent variable equations the maximum likelihood estimator dominates the estimation of general structural equation models noniterative equation by equation estimators for factor analysis have received some attention but little has been done on such estimators for latent variable equations i propose an alternative 2sls estimator of the parameters in lisrel type models and contrast it with the existing ones the new 2sls estimator allows observed and latent variables to originate from nonnormal distributions is consistent has a known asymptotic covariance matrix and is estimable with standard statistical software diagnostics for evaluating instrumental variables are described an empirical example illustrates the estimator

a characterisation of large finitely presented groups in this paper we will consider finitely presented groups that have a finite index subgroup which admits a surjective homomorphism onto a non abelian free group gromov called these groups large 4 large groups have particularly nice properties for example super exponential subgroup growth they also play an important role in lowdimensional topology it is a major conjecture that the fundamental group of any closed hyperbolic 3 manifold is large our main theorem is a characterisation of these groups in terms of the existence of a normal series where successive quotients are finite abelian groups with sufficiently large rank and order

ascending chains of finitely generated subgroups abstract we show that a nonempty family of n generated subgroups of a pro p group has a maximal element this suggests that noetherian induction can be used to discover new features of finitely generated subgroups of pro p groups to demonstrate this we show that in various pro p groups e g free pro p groups nonsolvable demushkin groups the commensurator of a finitely generated subgroup h 1 is the greatest subgroup of containing h as an open subgroup we also show that an ascending chain of n generated subgroups of a limit group must terminate this extends the analogous result for free groups proved by takahasi higman and kapovich myasnikov

subgroups of direct products of limit groups if ti tn are limit groups and s c t x x tn is of type fp q then s contains a subgroup of finite index that is itself a direct product of at most n limit groups this answers a question of sela

noniterative estimation and the choice of the number of factors in exploratory factor analysis based on the usual factor analysis model this paper investigates the relationship between improper solutions and the number of factors and discusses the properties of the noniterative estimation method of ihara and kano in exploratory factor analysis the consistency of the ihara and kano estimator is shown to hold even for an overestimated number of factors which provides a theoretical basis for the rare occurrence of improper solutions and for a new method of choosing the number of factors the comparative study of their estimator and that based on maximum likelihood is carried out by a monte carlo experiment

robustness of statistical inference in factor analysis and related models summary a class of latent variable models which includes the unrestricted factor analysis model is considered it is shown that minimum discrepancy test statistics and estimators derived under normality assumptions retain their asymptotic properties when the common factors are not normally distributed but the unique factors do have a multivariate normal distribution the minimum discrepancy test statistics and estimators considered include the usual likelihood ratio test statistic and maximum likelihood estimators

conjugate gradient acceleration of the em algorithm the em algorithm is a very popular and widely applicable algorithm for the computation of maximum likelihood estimates although its implementation is generally simple the em algorithm often exhibits slow convergence and is costly in some areas of application past attempts to accelerate the em algorithm have most commonly been based on some form of aitken acceleration here we propose an alternative method based on conjugate gradients the key as we show is that the em step can be viewed approximately at least as a generalized gradient making it natural to apply generalized conjugate gradient methods in an attempt to accelerate the em algorithm the proposed method is relatively simple to implement and can handle problems with a large number of parameters an important feature of most em algorithms to demonstrate the effectiveness of the proposed acceleration method we consider its application to several problems in each of the following areas estimation of a covariance matrix from incomplete mu

nonconvergence improper solutions and starting values in lisrel maximum likelihood estimation in the framework of a robustness study on maximum likelihood estimation with lisrel three types of problems are dealt with nonconvergence improper solutions and choice of starting values the purpose of the paper is to illustrate why and to what extent these problems are of importance for users of lisrel the ways in which these issues may affect the design and conclusions of robustness research is also discussed

some contributions to efficient statistics in structural models specification and estimation of moment structures current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments e g means and covariances and to distribution theory based on multivariate normality in psychometrics the multinormality assumption is often incorrect so that statistical tests on parameters or model goodness of fit will frequently be incorrect as well it is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary structural representations are developed for generalizations of the bentler weeks joreskog keesling wiley and factor analytic models some asymptotically distribution free efficient estimators for such arbitrary structural models are developed limited information estimators are obtained as well the special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail the argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds many open research areas are described

varieties of finite supersolvable groups with the m hall property the varieties in the title are shown to be precisely the product varieties gp ab d for some prime p and some positive integer d dividing p 1 here gp denotes the variety of all finite p groups and ab d the variety of all finite abelian groups of exponent dividing d it turns out that these are exactly those varieties h of supersolvable groups for which all finitely generated free pro h groups are freely indexed in the sense of lubotzky and van den dries several alternative characterizations of these varieties are presented some applications to formal language theory and finite monoid theory are also given among these is the determination of all supersolvable solutions h to the equations ph j h and j h jopen image in new windowh which is to the present date the most complete solution to a problem raised by pin another consequence of our results is that for each such variety h the monoid variety ph j h jopen image in new windowh has decidable membership

simultaneous equation systems as moment structure models with an introduction to latent variable models abstract an introduction to latent variable covariance structure models is provided estimation and testing of such models with normal and non normal variables is reviewed and a relatively inexpensive asymptotically distribution free estimator is introduced the traditional econometric simultaneous equation system is reconceptualized as a random vector structural equation model extensions of the model to deal with latent variables and a wider variety of structural phenomena are made via the joreskog keesling wiley lisrel approach and a simpler approach due to bentler and weeks these representation systems are extended via first and second moments about the origin of measured variables explained in terms of the structural coefficients and the moments of explanatory variables citations to further literature are provided

a gauss newton algorithm for exploratory factor analysis it is shown that the scoring algorithm for maximum likelihood estimation in exploratory factor analysis can be developed in a way that is many times more efficient than a direct development based on information matrices and score vectors the algorithm offers a simple alternative to current algorithms and when used in one step mode provides the simplest and fastest method presently available for moving from consistent to efficient estimates perhaps of greater importance is its potential for extension to the confirmatory model the algorithm is developed as a gauss newton algorithm to facilitate its application to generalized least squares and to maximum likelihood estimation

biseparating maps between lipschitz function spaces for complete metric spaces x and y a description of linear biseparating maps between spaces of vector valued lipschitz functions defined on x and y is provided in particular it is proved that x and y are bi lipschitz homeomorphic and the automatic continuity of such maps is derived in some cases besides these results are used to characterize the separating bijections between scalar valued lipschitz function spaces when y is compact