even sectors of lie superalgebras as locally convex lie algebras let g be a finite dimensional lie superalgebra over a graded commutative local augmented arens michael ground algebra a lie group is associated with a number of pleasant properties to the even sector g0 viewed as an ordinary complete locally convex lie algebra which is in general infinite dimensional

a likelihood ratio test for mtp_2 within binary variables multivariate totally positive mtp 2 binary distributions have been studied in many fields such as statistical mechanics computer storage and latent variable models we show that mtp 2 is equivalent to the requirement that the parameters of a saturated log linear model belong to a convex cone and we provide a fisher scoring algorithm for maximum likelihood estimation we also show that the asymptotic distribution of the log likelihood ratio is a mixture of chi squares a distribution known as chi bar squared in the literature on order restricted inference for this we derive tight bounds which turn out to have very simple forms a potential application of this method is for item response theory irt models which are used in educational assessment to analyse the responses of a group of subjects to a collection of questions items an important issue within irt is whether the joint distribution of the manifest variables is compatible with a single latent variable representation satisfying local independence and monotonicity which in turn imply that the joint distribution of item responses is mtp 2

asymptotic stability of the mmse linear filter for systems with uncertain observations corresp sufficient conditions for uniform asymptotic stability in the large of the optimal minimum mean square error mmse linear filter are developed for discrete linear systems whose observations may contain noise alone and where only the probability of occurrence of such cases is known to the estimator conditions for existence uniqueness and stability of the steady state optimal filter are also considered for the case when the system is time invariant

superconformal change of variables for n 1 neveu schwarz vertex operator superalgebras abstract superconformal change of variables formulas for n 1 neveu schwarz vertex operator superalgebras are presented for general invertible superconformal changes of variables using the underlying worldsheet supergeometry of propagating superstrings geometric proofs of the change of variables formulas are given for the case of convergent superconformal changes of variables more general formal algebraic proofs of the change of variables formulas in the case of formal superconformal changes of variables are then given finally isomorphic families of n 1 ns vosas are derived from the superconformal change of variables formulas

superspaces and supersymmetries a theory of graded banach modules over a banach grassmann algebra is developed and applied to differential geometry of super manifolds the explicit structure of superspaces carrying poincare supersymmetry and extended supersymmetry including central charges is described

lqg homing in two dimensions in this note we consider the problem of the optimal control of a set of two independent gaussian white noises first in the upper half plane and then in the first quadrant in both cases the objective is to leave the continuation region either as soon as possible or through the origin depending on the form of the cost function

the theory of g supermanifolds on developpe une theorie des supervarietes dans laquelle une supervariete est une variete ordinaire associee a une g structure d ordre 2 integrable on demontre un theoreme de structure

likelihood inference for a class of latent markov models under linear hypotheses on the transition probabilities summary for a class of latent markov models for discrete variables having a longitudinal structure we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process for the maximum likelihood estimation of a latent markov model under hypotheses of this type we outline an em algorithm that is based on well known recursions in the hidden markov literature we also show that under certain assumptions the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent markov model against a less stringent linear hypothesis on the transition probabilities of the same model is of x2 type as a particular case we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent markov version which may be used to test the hypothesis of absence of transition between latent states the approach is illustrated through a series of simulations and two applications the first of which is based on educational testing data that have been collected within the national assessment of educational progress 1996 and the second on data concerning the use of marijuana which have been collected within the national youth survey 19761980

superconformal primary fields on a graded riemann sphere primary superfields for a two dimensional euclidean superconformal field theory are constructed as sections of a sheaf over a graded riemann sphere the transformation law is found to be the same as that of an o n extended primary field the construction is then applied to the n 3 neveu schwarz case various quantities in the n 3 theory are calculated such as elements of the super mobius group and the two point function applications of the construction to calculate three point functions and fusion rules in a manifestly supersymmetric fashion are discussed

discrete supergroups and super riemann surfaces the properties of discrete supergroups that represent the homotopy groups of super riemann surfaces are emphasized after the study of the superforms invariant with respect to these supergroups the set of superconformal differentials are defined and an example is given of those by defining poincare s super theta functions some remarks on a possible definition of the jacobi variety of a super riemann surface are given

likelihood inference on the underlying structure of irt models the assumptions underlying item response theory irt models may be expressed as a set of equality and inequality constraints on the parameters of a latent class model it is well known that the same assumptions imply that the parameters of the manifest distribution have to satisfy a more complicated set of inequality constraints which however are necessary but not sufficient in this paper we describe how the theory for likelihood based inference under equality and inequality constraints may be used to test the underlying assumptions of irt models it turns out that the analysis based directly on the latent structure is simpler and more flexible in particular we indicate how several interesting extensions of the rasch model may be obtained by partial relaxation of the basic constraints an application to a data set provided by educational testing service is used to illustrate the approach

convergence of optimal linear estimator with multiplicative and time correlated additive measurement noises in this paper the problem of convergence for the optimal linear estimator of discrete time linear systems with multiplicative and time correlated additive measurement noises is studied by defining a new random vector that consists of the innovation error and part of the noise in the new measurement obtained from the measurement differencing method we obtain convergence conditions of the optimal linear estimator by equivalently studying the convergence of the expectation of a random matrix where the random matrix is the product of the new vector and its transpose it is also shown that the state error covariance matrix of the optimal linear estimator converges to a unique fixed point under appropriate conditions and moreover this fixed point can be obtained by solving a set of matrix equations

a new recursive filter for systems with multiplicative noise an optimal linear recursive minimum mean square error estimator was previously developed by the authors see ieee trans autom control vol 34 no 5 p 568 74 may 1989 for a zero mean signal corrupted by multiplicative noise in its measurement model this recursive filter cannot be obtained by the recursive structure of a conventional kalman filter where the new estimate is a linear combination of the previous estimate and the new data instead the recursive structure was achieved by combining the previous estimate with recursive innovation a linear combination of the most recent two data samples and the previous estimate in this work the signal is extended to be nonzero mean in the conventional kalman filter the superposition principle can be applied to both the signal and the measurement models for this nonzero mean extension however when multiplicative noise exists the measurement model becomes nonlinear therefore a new recursive structure for the innovation process needs to be developed to achieve a recursive filter

an inequality for correlations in unidimensional monotone latent variable models for binary variables it is shown that a unidimensional monotone latent variable model for binary items implies a restriction on the relative sizes of item correlations the negative logarithm of the correlations satisfies the triangle inequality this inequality is not implied by the condition that the correlations are nonnegative the criterion that coefficient h exceeds 0 30 or manifest monotonicity the inequality implies both a lower bound and an upper bound for each correlation between two items based on the correlations of those two items with every possible third item it is discussed how this can be used in mokken s a theory and procedure of scale analysis mouton the hague 1971 scale analysis

identification of non minimum phase linear stochastic systems abstract the identification of time invariant non minimum phase stochastic systems driven by non gaussian white noise is considered given only the noisy observations of the system output a two step procedure is proposed in the first step a spectrally equivalent system is estimated using a standard technique that exploits only the second order statistics of the measurements in the second step a partial set of 4th order cumulants of the measurements is exploited to resolve the location of the system zeros knowledge of the probability distribution of the driving noise is not required strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are also presented in support of the theory

semiparametric estimation in the rasch model and related exponential response models including a simple latent class model for item analysis abstract the rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects leading to the failure of the usual likelihood methodology both conditional likelihood methods and mixture model techniques have been used to circumvent these problems in this article we show that these seemingly unrelated analyses are in fact closely linked to each other despite dramatic structural differences between the classes of models implied by each approach we show that the finite mixture model for j dichotomous items having t latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if t j 1 2 unconditional maximum likelihood estimators for the finite mixture model can be viewed as keifer wolfowitz estimators for the random effects version of the rasch model latent class versions of the model are especially attractive when t is

super poincare algebras space times and supergravities ii the presentation of supergravity theories of our previous paper super poincare algebras space times and supergravities i is re formulated in the language of berezin leites kostant theory of supermanifolds it is also shown that the equations of cremmer julia and scherk s theory of 11d supergravity are equivalent to manifestly covariant equations on a supermanifold

optimal filtering for discrete time linear systems with multiplicative white noise perturbations and periodic coefficients in this technical brief the problem of the estimation of a remote signal generated by a discrete time dynamical system with periodic coefficients subject to multiplicative and additive white noise perturbations is investigated to measure the quality of the estimation achieved by an admissible filter we introduced a performance criterion described by the cesaro limit of the mean square of the deviation between the estimated signal zf t and the remote signal z t the dimension of the state space of the admissible filters is not prefixed the state space representation of the optimal filter is constructed based on the unique periodic solution of a discrete time linear equation together with the stabilizing solution of a suitable discrete time riccati equation with periodic coefficients

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

consistent superspace integration the standard berezin method for integration over odd variables is combined in a new way with de witt s contour method for integration over even grassmann variables to give a new method of superspace integration it is shown that this integral unlike the standard superspace integral is invariant under coordinate transformations in superspace the relation between the new method and the standard method is discussed

the geometry of super riemann surfaces we define super riemann surfaces as smooth 2 2 dimensional supermanifolds equipped with a reduction of their structure group to the group of invertible upper triangular 2 2 complex matrices the integrability conditions for such a reduction turn out to be most of the torsion constraints of 2d supergravity we show that they are both necessary and sufficient for a frame to admit local superconformal coordinates the other torsion constraints are merely conditions to fix some of the gauge freedom in this description or to specify a particular connection on such a manifold analogous to the levi civita connection in riemannian geometry unlike ordinary riemann surfaces a super riemann surface cannot be regarded as having only one complex dimension nevertheless in certain important aspects super riemann surfaces behave as nicely as if they had only one dimension in particular they posses an analog widehat partial of the cauchy riemann operator on ordinary riemann surfaces a differential operator taking values in the bundle of half volume forms this operator furnishes a short resolution of the structure sheaf making possible a quillen theory of determinant line bundles finally we show that the moduli space of super riemann surfaces is embedded in the larger space of complex curves of dimension 1 1

conditional association and unidimensionality in monotone latent variable models latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables usually assuming the conditional independence of the observable variables given the latent variables these models play an important role in educational measurement and psychometrics in sociology and in population genetics and are implicit in some work on systems reliability we study a broad class of latent variable models namely the monotone unidimensional models in which the latent variable is a scalar the observable variables are conditionally independent given the latent variable and the conditional distribution of the observables given the latent variable is stochastically increasing in the latent variable all models in this class imply a new strong form of positive dependence among the observable variables namely conditional positive association this positive dependence condition may be used to test whether any model in this class can provide an adequate fit to observed data various applications generalizations and a numerical example are discussed

optimal filtering for discrete time linear systems with time correlated multiplicative measurement noises in this note the filtering problem for discrete time linear systems with time correlated multiplicative measurement noises is considered where the vector consisting of all the multiplicative measurement noises can be described by a linear system model with white noise by introducing several new recursive terms a novel algorithm for optimal filtering of the system under consideration is proposed in the sense of linear minimum mean square error the proposed algorithm is recursive and has time independent complexity computer simulations are provided to illustrate the performance of the proposed algorithm

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

positive quadrant dependence and marginal modeling in two way tables with ordered margins for a collection of two way tables where subjects are cross classified according to the same pair of ordinal categorical variables conditionally on the value of one or more discrete explanatory variables we propose a general approach to likelihood inference that combines marginal modeling with fitting and testing of inequality constraints such as those implied by the assumption that one marginal distribution is stochastically larger than the other positive dependence and stronger positive dependence the approach is based on parameterizing bivariate conditional distributions with global logits and global log odds ratios and we provide a general framework for handling models defined by equality and inequality constraints on these parameters in this way such models as marginal homogeneity proportional odds among row or columns margins and plackett distribution may be treated together with various models defined by inequality constraints on the same parameters such as for instance those implied by

a characterization of monotone unidimensional latent variable models recently the problem of characterizing monotone unidimensional latent variable models for binary repeated measures was studied by ellis and van den wollenberg and by junker we generalize their work with a de finetti like characterization of the distribution of repeated measures x x 1 x 2 that can be represented with mixtures of likelihoods of independent but not identically distributed random variables where the data satisfy a stochastic ordering property with respect to the mixing variable the random variables x j may be arbitrary real valued random variables we show that the distribution of x can be given a monotone unidimensional latent variable representation that is useful in the sense of junker if and only if this distribution satisfies conditional association ca and a vanishing conditional dependence vcd condition which asserts that finite subsets of the variables in x become independent as we condition on a larger and larger segment of the remaining variables in x it is also interesting that the mixture representation is in a certain ordinal sense unique when ca and vcd hold the characterization theorem extends and simplifies the main result of junker and generalizes methods of ellis and van den wollenberg to a much broader class of models exchangeable sequences of binary random variables also satisfy both ca and vcd as do exchangeable sequences arising as location mixtures in the same way that de finetti s theorem provides a path toward justifying standard i i d mixture components in hierarchical models on the basis of our intuitions about the exchangeability of observations this theorem justifies one dimensional latent variable components in hierarchical models in terms of our intuitions about positive association and redundancy between observations because these conditions are on the joint distribution of the observable data x they may also be used to construct asymptotically power 1 tests for unidimensional latent variable models

manifest characterization and testing for certain latent properties work due to junker and more recently due to junker and ellis characterized desired latent properties of an educational testing procedure in terms of a collection of other manifest properties this is important because one can only propose tests for manifest quantities not latent ones here we complete the conversion of a pair of latent properties to equivalent conditions in terms of four manifest quantities and identify a general method for producing tests for manifest properties 1 introduction item response theory irt is the statistical theory of standardized tests which are commonly used in educational testing applications the goal is to combine the data generated by many examinees answering a collection of test items so as to estimate the value of a parameter or trait say for each of the examinees the parameter is intended to quantify a latent trait such as mathematics ability the traits are latent in the sense that they cannot be measured directly more specifically desired properties of suchtesting procedures are called latent when their statement depends explicitly on the the latent trait being estimated most efforts at modeling involve the introduction of latent parameters one specifies parameters to reflect aspects of the physical problem such as the individual achievement of each examinee the difficulty of each test item specialized knowledge that certain examinees might possess etc this is in contrast to the manifest properties of a testing procedure which can be phrased in a way that does not explicitly depend on the latent trait the limitation of a latent model is that it contains parameters for the latent trait the experimenter wants to estimate each examinee s parameter value and so cannot perform hypothesis tests on a conjectured model in the usual way the solution to this problem is to convert latent models or latent statements about them to physically meaningful manifest properties which are provably mathematically equivalent to the latent properties actually wanted manifest statements are amenable to conventional hypothesis testing and the problem then becomes the identification of optimal hypothesis tests for the manifest quantities in this way one can test hypotheses that are independent of the latent structure at least in principle the goal of characterizing latent properties in terms of manifest properties to be tested begins with stout 1987 stout considers the requirement that

optimal estimation for discrete time linear systems in the presence of multiplicative and time correlated additive measurement noises in this paper the state estimation problem for discrete time linear systems influenced by multiplicative and time correlated additive measurement noises is considered where the multiplicative noises are zero mean white noise sequences and the time correlated additive noise is described by a linear system model with white noise an optimal linear estimator for the system under consideration is proposed which does not require computing the inverse of state transition matrix the proposed estimator has a recursive structure and has time independent computation and storage load computer simulations are carried out to demonstrate the performance of the proposed estimator the simulation results show the superiority of the proposed estimator

cohomology of supermanifolds the aim of this chapter is to unfold a basic cohomological theory for supermanifolds which will be exploited in the next chapter to study the structure of superbundles in particular to build a theory of characteristic classes this cohomology theory does not embody only trivial extensions of results valid for differentiable manifolds for instance the natural analogue of the de rham theorem does not hold in general and similarly in the case of complex supermanifolds there is generally speaking no analogue of the dolbeault theorem these features are consequences of the fact that the structure sheaf of a supermanifold does not need to be cohomologically trivial related to this is also the fact that the cohomology of the complex of global graded differential forms on a g supermanifold m a i e the super de rham cohomology of m a depends on the g supermanifold structure of m a so that homeomorphic and even smoothly diffeomorphic g supermanifolds may have a different super de rham cohomology that is super de rham cohomology is a fine invariant of the supermanifold structure

a unified approach to likelihood inference on stochastic orderings in a nonparametric context abstract for data in a two way contingency table with ordered margins we consider various hypotheses of stochastic orders among the conditional distributions considered by rows and show that each is equivalent to requiring that an invertible transformation of the vectors of conditional row probabilities satisfies an appropriate set of linear inequalities this leads to the construction of a general algorithm for maximum likelihood estimation under multinomial sampling and provides a simple framework for deriving the asymptotic distribution of log likelihood ratio tests the usual stochastic ordering and the so called uniform and likelihood ratio orderings are considered as special cases in particular for each of these three orderings we determine the transformation required to apply the estimation algorithm we then consider testing the hypothesis that the rows are identically distributed against the alternative that they are stochastically ordered as well as testing each stochastic order against an u

stability of optimum linear estimators of stochastic signals in white multiplicative noise conditions for uniform asymptotic stability in the large of the optimal minimum mean square error linear filter are developed for linear systems whose observations are corrupted by white multiplicative noise in addition to white additive noise both discrete time as well as continuous time systems are considered the multiplicative noise model may be useful in problems associated with phenomena such as fading or reflection of the transmitted signal from the ionosphere and also certain situations involving sampling gating or amplitude modulation conditions for existence uniqueness and stability of the steady state optimal filter are also considered for time invariant systems

a new structure of recursive estimator a novel structure of a linear recursive estimator minimizing the mean square error is derived for a system with a multiplicative noise in the measurement model the conventional form of a recursive estimator the new estimate is a linear combination of the new data and the previous estimate is not appropriate for the above system in contrast according to presented form of estimator the new estimate and the new innovation which is recursively obtained by a linear combination of the new data the previous data and the previous innovation

asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints summary the analysis of moment structural models has become an important tool of investigation in behavioural educational and economic studies the chi squared largesample test is routinely employed to assess the goodness of fit of the model considered however in order to invoke the standard asymptotic distribution theory certain regularity conditions have to be met here we consider the case where the population value of the parameter vector is a boundary point of the feasible region we show that in this case the asymptotic distribution of test statistic is a mixture of chi squared distributions the problem of finding the corresponding weights is discussed

extended rc association models allowing for order restrictions and marginal modeling in the context of two way contingency tables the rc model may be seen as a way of modeling the set of log odds ratios for adjacent 2 2 subtables through row and column scores this article presents an extended class of rc models that allows simultaneous modeling of the marginal distributions and the association between two categorical variables these components are parameterized with logits and log odds ratios that may be of different types e g global or continuation to suit the nature of the data and the type of dependence of interest an algorithm for maximum likelihood estimation under equality and inequality constraints is presented the asymptotic distribution of the likelihood ratio statistic to test some interesting hypotheses is derived and extensions to multiway tables are outlined three examples are presented to highlight the features of the new approach

a multidimensional item response model constrained latent class analysis using the gibbs sampler and posterior predictive checks in this paper it will be shown that a certain class of constrained latent class models may be interpreted as a special case of nonparametric multidimensional item response models the parameters of this latent class model will be estimated using an application of the gibbs sampler it will be illustrated that the gibbs sampler is an excellent tool if inequality constraints have to be taken into consideration when making inferences model fit will be investigated using posterior predictive checks checks for manifest monotonicity the agreement between the observed and expected conditional association structure marginal local homogeneity and the number of latent classes will be presented

marginal regression models for the analysis of positive association of ordinal response variables given a set of discrete response variables some of which are ordinal and an arbitrary set of discrete explanatory variables we propose a simple matrix formulation for parameterising the saturated model as in glonek 1996 this is such that within a hierarchical structure marginal logits and log odds ratios of various possible types together with the remaining log linear interactions of high order may be modelled by equality and inequality constraints inequality constraints are particularly relevant for specifying models of positive association efficient algorithms are provided for computing maximum likelihood estimates under such constraints the asymptotic distribution of the likelihood ratio test is derived and an extension of the usual analysis of deviance is outlined which incorporates inequality constraints

graded manifolds supermanifolds and infinite dimensional grassmann algebras a new approach to superdifferentiable functions of grassmann variables is developed which avoids ambiguities in odd derivatives this is used to give an improved definition of supermanifold over a finite dimensional grassmann algebra a natural embedding of super manifolds over grassmann algebras with increasing number l of generators is developed and thus a limit asl tends to infinity is possible a correspondence between graded manifolds and supermanifolds is constructed extending results of 5 and 8

on extensions of superconformal algebras starting from vector fields that preserve a differential form on a riemann sphere with grassmann variables one can construct a superconformal algebra by considering central extensions of the algebra of vector fields in this paper the n 4 case is analyzed closely where the presence of weight zero operators in the field theory forces the introduction of noncentral extensions how this modifies the existing field theory representation theory and gelfand fuchs constructions is discussed it is also discussed how graded riemann sphere geometry can be used to give a geometrical description of the central charge in the n 1 theory

testing inequality constraints in linear econometric models abstract this paper develops three asymptotically equivalent tests for examining the validity of imposing linear inequality restrictions on the parameters of linear econometric models first we consider the model y x e where e is n 0 and the hypothesis test h r r versus k rk later we generalize this testing framework to the linear simultaneous equations model we show that the joint asymptotic distribution of these test statistics and the test statistics from the hypothesis test h r r versus k r r is a weighted sum of two sets of independent 2 distributions we also derive a useful duality relation between the multivariate inequality constraints test developed here and the multivariate one sided hypothesis test in small samples these three test statistics satisfy inequalities similar to those derived by berndt and savin 1977 for the case of equality constraints the paper also contains an illustrative application of this testing technique

derivation of linear estimation algorithms from measurements affected by multiplicative and additive noises this paper addresses the problem of estimating signals from observation models with multiplicative and additive noises assuming that the state space model is unknown the multiplicative noise is non white and the signal and additive noise are correlated recursive algorithms are derived for the least squares linear filter and fixed point smoother the proposed algorithms are obtained using an innovation approach and taking into account the information provided by the covariance functions of the process involved

brief paper optimal estimation of linear discrete time systems with stochastic parameters this paper considers optimal linear state estimation in the general case of linear discrete time systems with stochastic parameters which are statistically independent with respect to time the estimator is derived by transforming the system to one with deterministic parameters and state dependent additive system and observation noise it is shown that mean square stability of the system is a sufficient and almost necessary condition for the existence uniqueness and stability of the time invariant estimator