statistical and stabilizability properties of equivalent discrete time systems with stochastic parameters this paper considers the influence of the statistics of a scalar continuous time system with white stochastic parameters on the statistics the correlation and the stabilizability of the corresponding scalar equivalent discrete time system by means of numerical examples some insight into the behaviour of the equivalent discrete time system is given furthermore these examples illustrate the crucial influence of the correlation between the state and control dependent noise of the continuous time system on the stabilizability of the equivalent discrete time system

stability and stabilizability of chemical reactors modelled with stochastic parameters abstract chemical reactors are considered where unknown parameter variations are model led by stochastic parameters the continuous time process is transformed to an equivalent discrete time system with stochastic parameters which is a natural approach in the context of digital control making the analysis much easier a stabilizability test for this discrete time model is used to analyse three cases from the chemical engineering literature it is shown that stability in a mean sense is too weak from an engineering point of view one should study stability at least in a mean square sense which is the approach given here

characterizing the manifest probabilities of latent trait models the problem of characterizing the manifest probabilities of a latent trait model is considered the item characteristic curve is transformed to the item passing odds curve and a corresponding transformation is made on the distribution of ability this results in a useful expression for the manifest probabilities of any latent trait model the result is then applied to give a characterization of the rasch model as a log linear model for a 2 j contingency table partial results are also obtained for other models the question of the identifiability of guessing parameters is also discussed

limited and full information estimation and goodness of fit testing in 2n contingency tables high dimensional contingency tables tend to be sparse and standard goodness of fit statistics such as x2 cannot be used without pooling categories as an improvement on arbitrary pooling for goodness of fit of large 2n contingency tables we propose classes of quadratic form statistics based on the residuals of margins or multivariate moments up to order r these classes of test statistics are asymptotically chi squared distributed under the null hypothesis further the marginal residuals are useful for diagnosing lack of fit of parametric models we show that when r is small r 2 3 the proposed statistics have better small sample properties and are asymptotically more powerful than x2 for some useful multivariate binary models related to these test statistics is a class of limited information estimators based on low dimensional margins we show that these estimators have high efficiency for one commonly used latent trait model for binary data

analysis of residuals for the multinomial item response model using the item response model as developed on the multinomial distribution asymptotic variances are obtained for residuals associated with response patterns and first and second order marginal frequencies of manifest variables when the model does not fit well an examination of these residuals may reveal the source of the poor fit finally a limited information test of fit for the model is developed by using residuals defined for the first and second order marginals model evaluation based on residuals for these marginals is particularly useful when the response pattern frequencies are sparse

some properties of projective modules over discrete hodge algebras all rings in this paper are assumed to be commutative with 1 and all modules finitely generated let b be a discrete hodge algebra over a r ing a by definition this means that b r i where r a xi x and i is an ideal in r generated by monomials t vorst showed in 1 12 that thebehavior of projective modules over such b is very similar to the case of an ordinary polynomial ring in the following sense if all projective modules over any polynomial ring with ground ring a are extended from a then every projective module over a discrete hodge algebra over a is extended from a let b be a discrete hodge algebra over a noetherian ring a and p a projective module over b s mandal proved in 7 that if rank p dim b dim a 1 then

extensions of the partial credit model the partial credit model developed by masters 1982 is a unidimensional latent trait model for responses scored in two or more ordered categories in the present paper some extensions of the model are presented first a marginal maximum likelihood estimation procedure is developed which allows for incomplete data and linear restrictions on both the item and the population parameters secondly two statistical tests for evaluating model fit are presented the former test has power against violation of the assumption about the ability distribution the latter test offers the possibility of identifying specific items that do not fit the model

affine representability results in mathbb a 1 homotopy theory i vector bundles we establish a general affine representability result in a1 homotopy theory over a general base we apply this result to obtain representability results for vector bundles in a1 homotopy theory our results simplify and significantly generalize morel s a1 representability theorem for vector bundles

the nilpotence conjecture in k theory of toric varieties it is shown that all nontrivial elements in higher k groups of toric varieties are annihilated by iterations of the natural frobenius type endomorphisms this is a higher analog of the triviality of vector bundles on affine toric varieties

testing goodness of fit with multinomial data abstract several new test procedures are proposed for assessing the goodness of fit of a postulated multinomial distribution the new tests are neyman smooth type tests with orders selected adaptively from the data they are shown through fourier and large sample analyses to provide potential improvements over classical methods in terms of their ability to detect certain types of alternatives simulation results and a real example illustrate the finite sample validity of the large sample theory and the practical utility of the proposed methods

stabilization of linear systems by noise it is proved that the biggest lyapunov number lambda max of the system dot x a f t x where a is a fixed d times d matrix and f t is a zero mean strictly stationary matrix valued stochastic process satisfies 1 d trace a leqq lambda max on the other hand for each varepsilon 0 there is a process f t for which lambda max leqq 1 d trace a varepsilon in particular the system dot x ax can be stabilized by zero mean stationary parameter noise if and only if trace a 0 the stabilization can be accomplished by a one dimensional noise source the results carry over to the case where a is a stationary process they are also true for f t white noise

mean and covariance structure analysis theoretical and practical improvements abstract the most widely used multivariate statistical models in the social and behavioral sciences involve linear structural relations among observed and latent variables in practice these variables are generally nonnormally distributed hence classical multivariate analysis based on multinomial error free variables having no simultaneous interrelations is not adequate to deal with such data a promising alternative based on asymptotically distribution free adf covariance structure analysis has been found to be virtually useless in practical model evaluation at finite sample sizes with nonnormal data we take a new look at the basic statistical theory of structural models under arbitrary distributions using the methodology of nonlinear regression and generalized least squares estimation for example we adopt the use of residual weight matrices from regression theory we develop a series of estimators and tests based on arbitrary distribution theory we obtain a type of probabilistic bartlett co

brief paper optimal reduced order compensation of time varying discrete time systems with deterministic and white parameters the finite horizon optimal compensation problem is considered in the case of linear time varying discrete time systems with deterministic and white stochastic parameters and quadratic criteria the dimensions of the compensator are a priori fixed and may be time varying also the dimensions of the system may be time varying strengthened discrete time optimal projection equations sdope are developed which within the class of minimal compensators are equivalent to the first order necessary optimality conditions based on the sdope and their associated boundary conditions two numerical algorithms are presented to solve the two point boundary value problem one is a homotopy algorithm while the second iterates the sdope repeatedly forward and backward in time the latter algorithm is much more efficient and constitutes a generalization of the single iteration of the control and estimation riccati equations associated with the full order problem for systems with deterministic parameters the algorithms are illustrated with a numerical example the case of systems with deterministic parameters will be treated as a special case of systems with white parameters

the equivalent discrete time optimal control problem for continuous time systems with stochastic parameters this paper considers the transformation of the digital optimal control problem to an equivalent discrete time optimal control problem for linear continuous time systems with continuous time white stochastic parameters and additive continuous time white noise the observations available at the sampling instants are in general non linear and corrupted by discrete time noise the equivalent discrete time system has white stochastic parameters expressions are derived for the first and second moments of these parameters and for the cost criterion parameters which are explicit in the parameters and the statistics of the continuous time system

a general family of limited information goodness of fit statistics for multinomial data maydeu olivares and joe j am stat assoc 100 1009 1020 2005 psychometrika 71 713 732 2006 introduced classes of chi square tests for sparse multidimensional multinomial data based on low order marginal proportions our extension provides general conditions under which quadratic forms in linear functions of cell residuals are asymptotically chi square the new statistics need not be based on margins and can be used for one dimensional multinomials we also provide theory that explains why limited information statistics have good power regardless of sparseness we show how quadratic form statistics can be constructed that are more powerful than x2 and yet have approximate chi square null distribution in finite samples with large models examples with models for truncated count data and binary item response data are used to illustrate the theory

a composite likelihood inference in latent variable models for ordinal longitudinal responses the paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model the model considers time dependent latent variables and item specific random effects to be accountable for the interdependencies of the multivariate ordinal items time dependent latent variables are linked with an autoregressive model simulation results have shown composite likelihood estimators to have a small amount of bias and mean square error and as such they are feasible alternatives to full maximum likelihood model selection criteria developed for composite likelihood estimation are used in the applications furthermore lower order residuals are used as measures of fit for the selected models

the serre problem for discrete hodge algebras all rings in this paper will be commutative and noetherian let a b be a split injection of rings a finitely generated projective b module is called extended from a if there exists a finitely generated projective a module q such that p q b furthermore we call an c eglr b resp slr b extended from a if can be written as f i with fi glr a resp slr a and 7 e b the group of elementary matrices now let a be a ring in this paper we will consider a algebras of the following type a x1 xn i where i is an ideal generated by monomials such an a algebra is called a discrete hodge algebra over a and vice versa every discrete hodge algebra over a is of this type 5 for the proofs of most of our results we can restrict ourselves to the special class of square free discrete hodge algebras over a by which is meant that i can be generated by square free monomials the varieties over a corresponding to these square flee discrete hodge algebras are unions of intersections of coordinate hyperplanes h i x 1 xn anixi 0 i 1 n typical examples are a x 1 xn and a x 1 x 2 x i x 2 the main result of this paper is the following

the optimal projection equations for fixed order sampled data dynamic compensation with computation delay for an lqg type sampled data regulator problem which accounts for computational delay and utilizes an averaging a d device the equivalent discrete time problem is shown to be of increased order due to the inclusion of delayed measurement states the optimal projection equations for reduced order discrete time compensation are applied to the augmented problem to characterize low order controllers the design results are illustrated on a tenth order flexible beam example

how should we assess the fit of rasch type models approximating the power of goodness of fit statistics in categorical data analysis we investigate the performance of three statistics r 1 r 2 glas in psychometrika 53 525 546 1988 and m 2 maydeu olivares joe in j am stat assoc 100 1009 1020 2005 psychometrika 71 713 732 2006 to assess the overall fit of a one parameter logistic model 1pl estimated by marginal maximum likelihood ml r 1 and r 2 were specifically designed to target specific assumptions of rasch models whereas m 2 is a general purpose test statistic we report asymptotic power rates under some interesting violations of model assumptions different item discrimination presence of guessing and multidimensionality as well as empirical rejection rates for correctly specified models and some misspecified models all three statistics were found to be more powerful than pearson s x 2 against two and three parameter logistic alternatives 2pl and 3pl and against multidimensional 1pl models the results suggest that there is no clear advantage in using goodness of fit statistics specifically designed for rasch type models to test these models when marginal ml estimation is used

limited information goodness of fit testing in multidimensional contingency tables we introduce a family of goodness of fit statistics for testing composite null hypotheses in multidimensional contingency tables these statistics are quadratic forms in marginal residuals up to order r they are asymptotically chi square under the null hypothesis when parameters are estimated using any asymptotically normal consistent estimator for a widely used item response model when r is small and multidimensional tables are sparse the proposed statistics have accurate empirical type i errors unlike pearson s x2 for this model in nonsparse situations the proposed statistics are also more powerful than x2 in addition the proposed statistics are asymptotically chi square when applied to subtables and can be used for a piecewise goodness of fit assessment to determine the source of misfit in poorly fitting models

an inar 1 negative multinomial regression model for longitudinal count data this paper discusses a regression model for the analysis of longitudinal count data observed in a panel study an integer valued first order autoregressive inar 1 poisson process is adapted to represent time dependent correlations among the counts by combining the inar 1 representation with a random effects approach a new negative multinomial distribution is derived that includes the bivariate negative binomial distribution proposed by edwards and gurland 1961 and subrahmaniam 1966 as a special case a detailed analysis of the relationship between personality factors and daily emotion experiences illustrates the approach

the derivation of some tests for the rasch model from the multinomial distribution the present paper is concerned with testing the fit of the rasch model it is shown that this can be achieved by constructing functions of the data on which model tests can be based that have power against specific model violations it is shown that the asymptotic distribution of these tests can be derived by using the theoretical framework of testing model fit in general multinomial and product multinomial models the model tests are presented in two versions one that can be used in the context of marginal maximum likelihood estimation and one that can be applied in the context of conditional maximum likelihood estimation

limited information estimation and testing of discretized multivariate normal structural models discretized multivariate normal structural models are often estimated using multistage estimation procedures the asymptotic properties of parameter estimates standard errors and tests of structural restrictions on thresholds and polychoric correlations are well known it was not clear how to assess the overall discrepancy between the contingency table and the model for these estimators it is shown that the overall discrepancy can be decomposed into a distributional discrepancy and a structural discrepancy a test of the overall model specification is proposed as well as a test of the distributional specification i e discretized multivariate normality also the small sample performance of overall distributional and structural tests as well as of parameter estimates and standard errors is investigated under conditions of correct model specification and also under mild structural and or distributional misspecification it is found that relatively small samples are needed for parameter estimates standard errors and structural tests larger samples are needed for the distributional and overall tests furthermore parameter estimates standard errors and structural tests are surprisingly robust to distributional misspecification

tailor made tests of goodness of fit summary we examine a large class of distributional tests equivalent to tests based on degenerate u statistics the factors which influence the performance of these tests are isolated an analysis of the factors leads us to suggest tests with improved power properties against certain types of alternatives one such test is based on a chi squared statistic which employs overlapping cells rather than disjoint cells it is shown that this test has power superior to that of the classical chi squared statistic

stability theorems for overrings of polynomial rings let r be a polynomial ring over a field projective modules over rings of the type r ix y r x y where r is a non zero element of r have been considered by murthy swan weibel see mu and w these rings lie between r x and r x x 1 and even when they are regular projective modules over them need not be free mu example 6 2 this leads us to study stability properties of projective modules over rings a which lie between r x and r x x 1 when r is any commutative noetherian ring we prove stability theorems for projective modules over such rings a in w these results theorems 4 2 and 4 3 have been proved for a r x by plumstead p and for a r x x 1 by mandal ma in w we prove similar results for the allied class of rings d of the type r x y xy stability theorems for gl a and gl d are proved in w when a r x or r x x 1 our theorems 6 2 i and 6 4 i had already been proved by suslin s finally in w 7 we study pic r x y r xy when r is a pid theorem 7 1 extends a result of murthy mu corollary 5 3 it would be interesting to know whether theorems 4 1 and 4 2 can be extended to the polynomial ring a t 1 tm where a lies between r x and r x x 1 more precisely for a projective a t 1 t module p of rank dim a we would like to know if the following statements are true i p has a unimodular element ii p has the cancellation property we have been able to show that when a r x the statement i is true b r theorem 3 1