improved stability robustness bounds using state transformation for linear discrete systems abstract sufficient condition bounds on the linear time varying perturbations for robust stability of an asymptotically stable linear time invariant discrete time system have been reported recently the development involves both schwartz and triangular inequalities and tends to give conservative results this paper uses state transformation to obtain improvement in these bounds both unstructured and structured perturbation bounds are shown to improve using transformations the proposed analysis is applied to a fourth order macroeconomic system model

internal consistency of tests analyses old and new a coefficient derived from communalities of test parts has been proposed as greatest lower bound to guttman s immediate retest reliability the communalities have at times been calculated from covariances between itemsets which tends to underestimate appreciably when items are experimentally independent a consistent estimate of the greatest defensible internal consistency coefficient is obtained by factoring item covariances in samples of modest size this analysis capitalizes on chance an estimate subject to less upward bias is suggested for estimating alternate forms reliability communality based coefficients are less appropriate than stratified alpha

sample size requirements for estimating intraclass correlations with desired precision a method is developed to calculate the approximate number of subjects required to obtain an exact confidence interval of desired width for certain types of intraclass correlations in one way and two way anova models the sample size approximation is shown to be very accurate

weak amenability of fourier algebras and local synthesis of the anti diagonal abstract we show that for a connected lie group g its fourier algebra a g is weakly amenable only if g is abelian our main new idea is to show that weak amenability of a g implies that the anti diagonal g g g 1 g g is a set of local synthesis for a g g we then show that this cannot happen if g is non abelian we conclude for a locally compact group g that a g can be weakly amenable only if it contains no closed connected non abelian lie subgroups in particular for a lie group g a g is weakly amenable if and only if its connected component of the identity g e is abelian

hyper tauberian algebras and weak amenability of figa talamanca herz algebras abstract we study certain commutative regular semisimple banach algebras which we call hyper tauberian algebras we first show that they form a subclass of weakly amenable tauberian algebras then we investigate the basic and hereditary properties of them moreover we show that if a is a hyper tauberian algebra then the linear space of bounded derivations from a into any banach a bimodule is reflexive we apply these results to the figa talamanca herz algebra a p g of a locally compact group g for p 1 we show that a p g is hyper tauberian if the principal component of g is abelian finally by considering the quantization of these results we show that for any locally compact group g a p g equipped with an appropriate operator space structure is a quantized hyper tauberian algebra this in particular implies that a p g is operator weakly amenable

optimal stochastic control for performance and stability robustness a design method for discrete time control systems that maintain stability with minimum performance degradation in the presence of a variety of deterministic and stochastic perturbation disturbances is presented deterministic perturbation and modeling errors are represented by maximum deviations from a nominal linear discrete time system and stochastic perturbations are modeled by generalization of the sector bound nonlinearity concept to the stochastic case based on the given bounds on deterministic and stochastic perturbations an upper bound on the quadratic performance index which is useful in assessing the performance deterioration according to the feedback gain used is found then the optimal feedback gain which minimizes this bound on the performance index is derived in the time invariant case the existence of a stabilizing property of the bound optimal controller which is obtained by minimizing an average cost per stage is shown

the asymptotic bias of minimum trace factor analysis with applications to the greatest lower bound to reliability in theory the greatest lower bound g l b to reliability is the best possible lower bound to the reliability based on single test administration yet the practical use of the g l b has been severely hindered by sampling bias problems it is well known that the g l b based on small samples even a sample of one thousand subjects is not generally enough may severely overestimate the population value and statistical treatment of the bias has been badly missing the only results obtained so far are concerned with the asymptotic variance of the g l b and of its numerator the maximum possible error variance of a test based on first order derivatives and the asumption of multivariate normality the present paper extends these results by offering explicit expressions for the second order derivatives this yields a closed form expression for the asymptotic bias of both the g l b and its numerator under the assumptions that the rank of the reduced covariance matrix is at or above the ledermann bound and that the nonnegativity constraints on the diagonal elements of the matrix of unique variances are inactive it is also shown that when the reduced rank is at its highest possible value i e the number of variables minus one the numerator of the g l b is asymptotically unbiased and the asymptotic bias of the g l b is negative the latter results are contrary to common belief but apply only to cases where the number of variables is small the asymptotic results are illustrated by numerical examples

asymptotic permutation tests in general factorial designs summary in general factorial designs where no homoscedasticity or a particular error distribution is assumed the well known wald type statistic is a simple asymptotically valid procedure however it is well known that it suffers from a poor finite sample approximation since the convergence to its 2 limit distribution is quite slow this becomes even worse with an increasing number of factor levels the aim of the paper is to improve the small sample behaviour of the wald type statistic maintaining its applicability to general settings as crossed or hierarchically nested designs by applying a modified permutation approach in particular it is shown that this approach approximates the null distribution of the wald type statistic not only under the null hypothesis but also under the alternative yielding an asymptotically valid permutation test which is even finitely exact under exchangeability finally its small sample behaviour is compared with competing procedures in an extensive simulation study

lower bounds to the reliabilities of factor score estimators under the general common factor model the reliabilities of factor score estimators might be of more interest than the reliability of the total score the unweighted sum of item scores in this paper lower bounds to the reliabilities of thurstone s factor score estimators bartlett s factor score estimators and mcdonald s factor score estimators are derived and conditions are given under which these lower bounds are equal the relative performance of the derived lower bounds is studied using classic example data sets the results show that estimates of the lower bounds to the reliabilities of thurstone s factor score estimators are greater than or equal to the estimates of the lower bounds to the reliabilities of bartlett s and mcdonald s factor score estimators

reliability of test scores in nonparametric item response theory three methods for estimating reliability are studied within the context of nonparametric item response theory two were proposed originally by mokken 1971 and a third is developed in this paper using a monte carlo strategy these three estimation methods are compared with four classical lower bounds to reliability finally recommendations are given concerning the use of these estimation methods

operator space structure and amenability for figa talamanca herz algebras column and row operator spaces which we denote by col and row respectively over arbitrary banach spaces were introduced by the first named author for hilbert spaces these definitions coincide with the usual ones given a locally compact group g and p p 1 with 1p 1p 1 we use the operator space structure on cb col lp g to equip the figa talamanca herz algebra ap g with an operator space structure turning it into a quantized banach algebra moreover we show that for p q 2 or 2 q p and amenable g the canonical inclusion aq g ap g is completely bounded with cb norm at most kg2 where kg is grothendieck s constant as an application we show that g is amenable if and only if ap g is operator amenable for all and equivalently for one p 1 this extends a theorem by ruan

covariate free and covariate dependent reliability classical test theory reliability coefficients are said to be population specific reliability generalization a meta analysis method is the main procedure for evaluating the stability of reliability coefficients across populations a new approach is developed to evaluate the degree of invariance of reliability coefficients to population characteristics factor or common variance of a reliability measure is partitioned into parts that are and are not influenced by control variables resulting in a partition of reliability into a covariate dependent and a covariate free part the approach can be implemented in a single sample and can be applied to a variety of reliability coefficients

weak and cyclic amenability for fourier algebras of connected lie groups abstract using techniques of non abelian harmonic analysis we construct an explicit non zero cyclic derivation on the fourier algebra of the real a x b group in particular this provides the first proof that this algebra is not weakly amenable using the structure theory of lie groups we deduce that the fourier algebras of connected semisimple lie groups also support non zero cyclic derivations and are likewise not weakly amenable our results complement earlier work of johnson 1994 15 plymen 2001 18 and forrest samei and spronk 2009 9 as an additional illustration of our techniques we construct an explicit non zero cyclic derivation on the fourier algebra of the reduced heisenberg group providing the first example of a connected nilpotent group whose fourier algebra is not weakly amenable

models and methods for the analysis of correlation coefficients abstract the normal distribution plays a very prominant role in statistics and in multivariate analysis the multinormal model is even more dominant than in the classical univariate or bivariate situations in this paper we show that the assumption of continuous multinormal observations can be relaxed in various ways for continuous multivariate analysis most of the existing large sample theory can be applied without assuming multivariate normality we also develop several discrete multinormal models the first one is the classical pearson model which results from discreticizing multinormal variables the second one is inspired by correspondence analysis and the third one by loglinear analysis the models are presented in terms of correlation coefficients and applied to the spearman model of factor analyses using an example from political science

constrained least squares estimators of oblique common factors an expression is given for weighted least squares estimators of oblique common factors constrained to have the same covariance matrix as the factors they estimate it is shown that if as in exploratory factor analysis the common factors are obtained by oblique transformation from the lawley rao basis the constrained estimators are given by the same transformation finally a proof of uniqueness is given

alpha dimension free and model based internal consistency reliability as pointed out by sijtsma in press coefficient alpha is inappropriate as a single summary of the internal consistency of a composite score better estimators of internal consistency are available in addition to those mentioned by sijtsma an old dimension free coefficient and structural equation model based coefficients are proposed to improve the routine reporting of psychometric internal consistency the various ways to measure internal consistency are also shown to be appropriate to binary and polytomous items

robustness of discrete time systems for unstructured stochastic perturbations several stochastic stability robustness measures are presented for nominally exponentially stable linear discrete time systems with unstructured perturbations having second moment bounds dependence of these measures on the stability degree of the nominal system and other parameters used in the procedure is illustrated by using the time evolution of the second moment of the system state and stochastic lyapunov stability results positive super martingale convergence theorems the ability of nominally exponentially stable systems to maintain stability in the presence of unstructured stochastic linear and nonlinear perturbations is demonstrated quantitative results are given to determine the maximum modeling uncertainty which can be tolerated in design upper bounds on the second moments of stochastic perturbations to maintain the mean square and almost sure stability of these systems in the presence of unstructured perturbations are obtained

reducibility and unobservability of markov processes the linear system case a vector markov process will be called stochastically unobservable by the measurement process if there exists an initial distribution such that some marginal conditional distributions equal the corresponding unconditional ones it will be called reducible if there exists an invertible transformation such that the transformed process is stochastically unobservable necessary and sufficient conditions are derived in the context of linear diffusions it is also shown that reducibility can be regarded as a natural extension of the concept of estimability defined for linear stochastic systems

coefficients alpha beta omega and the glb comments on sijtsma there are three fundamental problems in sijtsma psychometrika 2008 1 contrary to the name the glb is not the greatest lower bound of reliability but rather is systematically less than t mcdonald test theory a unified treatment erlbaum hillsdale 1999 2 we agree with sijtsma that when considering how well a test measures one concept is not appropriate but recommend t rather than the glb and 3 the end user needs procedures that are readily available in open source software

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

weak amenability for fourier algebras of 1 connected nilpotent lie groups a special case of a conjecture raised by forrest and runde 2005 10 asserts that the fourier algebra of every non abelian connected lie group fails to be weakly amenable this was already known to hold in the non abelian compact cases by earlier work of johnson 1994 13 and plymen unpublished note in recent work choi and ghandehari 2014 4 the authors verified this conjecture for the real ax b group and hence by structure theory for any semisimple lie group in this paper we verify the conjecture for all 1 connected non abelian nilpotent lie groups by reducing the problem to the case of the heisenberg group as in our previous paper an explicit non zero derivation is constructed on a dense subalgebra and then shown to be bounded using harmonic analysis en route we use the known fusion rules for schrodinger representations to give a concrete realization of the dual convolution for this group as a kind of twisted operator valued convolution we also give some partial results for solvable groups which give further evidence to support the general conjecture

robust stability of discrete time systems under parametric perturbations stability robustness analysis of a system under parametric perturbations is concerned with characterizing a region in the parameter space in which the system remains stable in this paper two methods are presented to estimate the stability robustness region of a linear time invariant discrete time system under multiparameter additive perturbations an inherent difficulty which originates from the nonlinear appearance of the perturbation parameters in the inequalities defining the robustness region is resolved by transforming the problem to stability of a higher order continuous time system this allows for application of the available results on stability robustness of continuous time systems to discrete time systems the results are also applied to stability analysis of discrete time interconnected systems where the interconnections are treated as perturbations on decoupled stable subsystems

robust stabilization of uncertain systems in this paper we consider the systems described by dx axdt budt sum i sigma i f i xd beta i qquad text or qquad dot x ax bu sum i b i f i x t c i x and we will derive conditions under which there exists a feedback control law u kx such that the closed loop system is stable for all sigma i or smooth nonlinearities f i the nonlinearities f i and the noisy gains sigma i d beta i are unknown uncertainties in the system and the problem considered is to obtain a control law which is robust against these uncertainties as far as stability is concerned

the greatest lower bound to the reliability of a test and the hypothesis of unidimensionality to assess the reliability of congeneric tests specifically designed reliability measures have been proposed this paper emphasizes that such measures rely on a unidimensionality hypothesis which can neither be confirmed nor rejected when there are only three test parts and will invariably be rejected when there are more than three test parts jackson and agunwamba s 1977 greatest lower bound to reliability is proposed instead although this bound has a reputation for overestimating the population value when the sample size is small this is no reason to prefer the unidimensionality based reliability firstly the sampling bias problem of the glb does not play a role when the number of test parts is small as is often the case with congeneric measures secondly glb and unidimensionality based reliability are often equal when there are three test parts and when there are more test parts their numerical values are still very similar to the extent that the bias problem of the greatest lower bound does play a role unidimensionality based reliability is equally affected although unidimensionality and reliability are often thought of as unrelated this paper shows that from at least two perspectives they act as antagonistic concepts a measure based on the same framework that led to the greatest lower bound is discussed for assessing how close is a set of variables to unidimensionality it is the percentage of common variance that can be explained by a single factor an empirical example is given to demonstrate the main points of the paper

exact and asymptotically robust permutation tests given independent samples from p and q two sample permutation tests allow one to construct exact level tests when the null hypothesis is p q on the other hand when comparing or testing particular parameters of p and q such as their means or medians permutation tests need not be level or even approximately level in large samples under very weak assumptions for comparing estimators we provide a general test procedure whereby the asymptotic validity of the permutation test holds while retaining the exact rejection probability in finite samples when the underlying distributions are identical a quite general theory is possible based on a coupling construction as well as a key contiguity argument for the binomial and hypergeometric distributions the ideas are broadly applicable and special attention is given to a nonparametric k sample behrens fisher problem whereby a permutation test is constructed which is exact level under the hypothesis of identical distributions but has asymptotic rejection probability under the more general null hypothesis of equality of means a monte carlo simulation study is performed 2010 msc subject classifications primary 62e20 secondary 62g10

on deriving the inverse of a sum of matrices available expressions are reviewed and new ones derived for the inverse of the sum of two matrices one of them being nonsingular particular attention is given to text bf a text bf ubv 1 where textbf a is nonsingular and textbf u b and textbf v may be rectangular generalized inverses of textbf a textbf ubv are also considered several statistical applications are discussed

a general structural equation model with dichotomous ordered categorical and continuous latent variable indicators a structural equation model is proposed with a generalized measurement part allowing for dichotomous and ordered categorical variables indicators in addition to continuous ones a computationally feasible three stage estimator is proposed for any combination of observed variable types this approach provides large sample chi square tests of fit and standard errors of estimates for situations not previously covered two multiple indicator modeling examples are given one is a simultaneous analysis of two groups with a structural equation model underlying skewed likert variables the second is a longitudinal model with a structural model for multivariate probit regressions

cronbach s α revelle s β and mcdonald s ωh their relations with each other and two alternative conceptualizations of reliability we make theoretical comparisons among five coefficients cronbach s revelle s mcdonald s h and two alternative conceptualizations of reliability though many end users and psychometricians alike may not distinguish among these five coefficients we demonstrate formally their nonequivalence specifically whereas there are conditions under which and h are equivalent to each other and to one of the two conceptualizations of reliability considered here we show that equality with this conceptualization of reliability and between and h holds only under a highly restrictive set of conditions and that the conditions under which equals h are only somewhat more general the nonequivalence of and h suggests that important information about the psychometric properties of a scale may be missing when scale developers and users only report as is almost always the case

on the connection between sets of operator synthesis and sets of spectral synthesis for locally compact groups we extend the results by froelich and spronk and turowska on the connection between operator synthesis and spectral synthesis for a g to second countable locally compact groups g this gives us another proof that one point subset of g is a set of spectral synthesis and that any closed subgroup is a set of local spectral synthesis furthermore we show that non triangular sets are strong operator ditkin sets and we establish a connection between operator ditkin sets and ditkin sets these results are applied to prove that any closed subgroup of g is a local ditkin set

new robustness bounds for discrete systems with random perturbations some new stochastic stability robustness bounds for state space models are reported nominally exponentially stable discrete time systems are assumed to be subject to random parameter perturbations and novel bounds are obtained on the maximum variances of these random perturbations to maintain stability robustness the methods employed in the analysis are the existing ones used in the deterministic framework after transforming the stochastic robustness problem to a deterministic one the results are compared with each other and with the exact stability region in an example

parametrization of all linear compensators for discrete time stochastic parameter systems abstract for discrete time stochastic parameter systems this paper presents a characterization of all state covariances assignable by a linear controller and a parametrization of all controllers that achieves a desired covariance these results indirectly provide the parametrization of all linear fixed order compensators which are mean square stabilizing for this class of systems the paper also includes robustification of the derived compensators and an example to illustrate the results

coefficients alpha and reliabilities of unrotated and rotated components it has been shown by kaiser that the sum of coefficients alpha of a set of principal components does not change when the components are transformed by an orthogonal rotation in this paper kaiser s result is generalized first the invariance property is shown to hold for any set of orthogonal components next a similar invariance property is derived for the reliability of any set of components both generalizations are established by considering simultaneously optimal weights for components with maximum alpha and with maximum reliability respectively a short cut formula is offered to evaluate the coefficients alpha for orthogonally rotated principal components from rotation weights and eigenvalues of the correlation matrix finally the greatest lower bound to reliability and a weighted version are discussed

stochastic robustness of linear time invariant control systems a simple numerical procedure for estimating the stochastic robustness of a linear time invariant system is described monte carlo evaluation of the system s eigenvalues allows the probability of instability and the related stochastic root locus to be estimated this analysis approach treats not only gaussian parameter uncertainties but also nongaussian cases including uncertain but bound variations confidence intervals for the scalar probability of instability address computational issues inherent in monte carlo simulation trivial extensions of the procedure admit consideration of alternate discriminants thus the probabilities that stipulated degrees of instability will be exceeded or that closed loop roots will leave desirable regions can also be estimated results are particularly amenable to graphical presentation

quantile lower bounds to reliability based on locally optimal splits extending the theory of lower bounds to reliability based on splits given by guttman in psychometrika 53 63 70 1945 this paper introduces quantile lower bound coefficients 4 q that refer to cumulative proportions of potential locally optimal split half coefficients that are below a particular point q in the distribution of split halves based on different partitions of variables into two sets interesting quantile values are q 0 05 0 50 0 95 1 00 with 4 0 05 4 0 50 4 0 95 4 1 0 only the global optimum 4 1 0 guttman s maximal 4 has previously been considered to be interesting but in small samples it substantially overestimates population reliability the three coefficients 4 0 05 4 0 50 and 4 0 95 provide new lower bounds to reliability the smallest 4 0 05 provides the most protection against capitalizing on chance associations and thus overestimation 4 0 50 is the median of these coefficients while 4 0 95 tends to overestimate reliability but also exhibits less bias than previous estimators computational theory algorithm and publicly available code based in r are provided to compute these coefficients simulation studies evaluate the performance of these coefficients and compare them to coefficient alpha and the greatest lower bound under several population reliability structures

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

robustness results in linear quadratic gaussian based multivariable control designs the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity in particular robustness results associated with multivariable control systems designed on the basis of linear quadratic lq and the linear quadratic gaussian lqg design methodologies are presented

on the distribution of the maximum likelihood estimator of cronbach s alpha the asymptotic normal distribution of the maximum likelihood estimator of cronbach s alpha under normality is derived for the case when no assumptions are made about the covariances among items the asymptotic distribution is also considered for the special case of compound symmetry and compared to the exact distribution

tests for equality of several alpha coefficients when their sample estimates are dependent in a variety of measurement situations the researcher may wish to compare the reliabilities of several instruments administered to the same sample of subjects this paper presents eleven statistical procedures which test the equality ofm coefficient alphas when the sample alpha coefficients are dependent several of the procedures are derived in detail and numerical examples are given for two since all of the procedures depend on approximate asymptotic results monte carlo methods are used to assess the accuracy of the procedures for sample sizes of 50 100 and 200 both control of type i error and power are evaluated by computer simulation two of the procedures are unable to control type i errors satisfactorily the remaining nine procedures perform properly but three are somewhat superior in power and type i error control

computational aspects of the greatest lower bound to the reliability and constrained minimum trace factor analysis in the last decade several algorithms for computing the greatest lower bound to reliability or the constrained minimum trace communality solution in factor analysis have been developed in this paper convergence properties of these methods are examined instead of using lagrange multipliers a new theorem is applied that gives a sufficient condition for a symmetric matrix to be gramian whereas computational pitfalls for two methods suggested by woodhouse and jackson can be constructed it is shown that a slightly modified version of one method suggested by bentler and woodward can safely be applied to any set of data a uniqueness proof for the solution desired is offered

resampling based inference methods for comparing two coefficients alpha the two sample problem for cronbach s coefficient formula see text as an estimate of test or composite score reliability has attracted little attention compared to the extensive treatment of the one sample case it is necessary to compare the reliability of a test for different subgroups for different tests or the short and long forms of a test in this paper we study statistical procedures of comparing two coefficients formula see text and formula see text the null hypothesis of interest is formula see text which we test against one or two sided alternatives for this purpose resampling based permutation and bootstrap tests are proposed for two group multivariate non normal models under the general asymptotically distribution free adf setting these statistical tests ensure a better control of the type i error in finite or very small sample sizes when the state of affairs adf large sample test may fail to properly attain the nominal significance level by proper choice of a studentized test statistic the resampling tests are modified in order to be valid asymptotically even in non exchangeable data frameworks moreover extensions of this approach to other designs and reliability measures are discussed as well finally the usefulness of the proposed resampling based testing strategies is demonstrated in an extensive simulation study and illustrated by real data applications

on the relationship between the higher order factor model and the hierarchical factor model the relationship between the higher order factor model and the hierarchical factor model is explored formally we show that the schmid leiman transformation produces constrained hierarchical factor solutions using a generalized schmid leiman transformation and its inverse we show that for any unconstrained hierarchical factor model there is an equivalent higher order factor model with direct effects loadings on the manifest variables from the higher order factors therefore the class of higher order factor models without direct effects of higher order factors is nested within the class of unconstrained hierarchical factor models in light of these formal results we discuss some implications for testing the higher order factor model and the issue of general factor an interesting aspect concerning the efficient fitting of the higher order factor model with direct effects is noted

stability robustness of linear discrete time systems in the presence of uncertainty the stability robustness problem is considered for nominally stable linear discrete time systems using time domain analysis methods and lyapunov theory bounds on the norms of the time varying non linear perturbations are given to maintain the asymptotic stability of these systems in the presence of such perturbations

robustness of feedback stabilized systems in the presence of non linear and random perturbations the general robustness problem is discussed for a controlled discrete time system subject to a lur e type feedback non linearity together with random multiplicative noises effective on state input and the non linearity a sufficient condition is given utilizing the discrete stochastic version of the second method of lyapunov to guarantee that any stabilizing controller designed for the deterministic linear part of the system renders the closed loop system with perturbations asymptotically stable with probability one then specializations to systems given in controllability and controller canonical forms are made independent noise signals are assumed to be effective on individual parameters of these canonical forms whose inputs are designed to assign the closed loop poles to zero in these cases stronger results are obtained in terms of system parameters and known characteristics of perturbations

stability robustness bounds for linear state space models with structured uncertainty in this note we consider the robust stability analysis problem in linear state space models we consider systems with structured uncertainty some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived these bounds are shown to be less conservative than the existing ones

the influence of finite word length on digital optimal control this paper is concerned with the performance of linear discrete time systems controlled by a finite word length computer with floating point arithmetic and of which the state is directly measurable with an a d converter of the same word length the effect of using finite word length is twofold first roundings are made after addition or multiplication of two rounded numbers second the control parameters are represented in the controller s memory by rounded numbers the first effect can be accounted for by considering the control parameters stochastic the second effect is deterministic after a description of the stochastlcs of the roundoff errors has been derived the influence of both effects on the optimality and stability of digital control systems in the steady state in relation to a quadratic cost function is considered

some new results on correlation preserving factor scores prediction methods anderson and rubin and mcdonald have proposed a correlation preserving method of factor scores prediction which minimizes the trace of a residual covariance matrix for variables green has proposed a correlation preserving method which minimizes the trace of a residual covariance matrix for factors krijnen wansbeek and ten berge have proposed minimizing the determinant rather than the trace of the latter covariance matrix and offered an iterative procedure to that effect in the present paper it is shown that the iterative procedure can be replaced by a closed form solution when all unique variances are strictly positive this solution is the same as mcdonald s the solution coincides with green s solution in certain special cases for instance when the factors are orthogonal

minimum rank and minimum trace of covariance matrices this paper considers some mathematical aspects of minimum trace factor analysis mtfa the uniqueness of an optimal point of mtfa is proved and necessary and sufficient conditions for a point x to be optimal are established finally some results about the connection between mtfa and the classical minimum rank factor analysis will be presented

rank reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis one of the intriguing questions of factor analysis is the extent to which one can reduce the rank of a symmetric matrix by only changing its diagonal entries we show in this paper that the set of matrices which can be reduced to rankr has positive lebesgue measure if and only ifr is greater or equal to the ledermann bound in other words the ledermann bound is shown to bealmost surely the greatest lower bound to a reduced rank of the sample covariance matrix afterwards an asymptotic sampling theory of so called minimum trace factor analysis mtfa is proposed the theory is based on continuous and differential properties of functions involved in the mtfa convex analysis techniques are utilized to obtain conditions for differentiability of these functions

improved bounds for linear discrete time systems with structured perturbations a time domain analysis of the stability robustness of linear discrete time systems subject to time varying structured perturbations is considered the lyapunov stability theory is used to obtain bounds on the perturbation such that the systems remain stable it is shown that these bounds are less conservative than the existing ones this is illustrated via two numerical examples

full and reduced order observer design for discrete stochastic bilinear systems the author considers a general discrete time stochastic bilinear system model and derives the mean square optimal linear unbiased observer equations to be used in reconstructing a prespecified linear combination of state variables based on noisy output measurements

weighted generalized estimating functions for longitudinal response and covariate data that are missing at random longitudinal studies often feature incomplete response and covariate data it is well known that biases can arise from naive analyses of available data but the precise impact of incomplete data depends on the frequency of missing data and the strength of the association between the response variables and covariates and the missing data indicators various factors may influence the availability of response and covariate data at scheduled assessment times and at any given assessment time the response may be missing covariate data may be missing or both response and covariate data may be missing here we show that it is important to take the association between the missing data indicators for these two processes into account through joint models inverse probability weighted generalized estimating equations offer an appealing approach for doing this here we develop these equations for a particular model generating intermittently missing at random data empirical studies demonstrate that the consistent e

deterministic and stochastic robustness measures for discrete systems deterministic and stochastic lyapunov theorems are used to demonstrate the robustness of a stable linear time variant discrete time nominal system to both unknown deterministic and stochastic perturbations time domain conditions are presented on the appropriate deterministic or random characteristics of perturbations to maintain the proper stability behavior of the overall system it is concluded that the novel robustness conditions proposed can find application in the feedback design of control systems where the closed loop system is known to be stable with a certain degree e g as in the case of linear quadratic optimal control with alpha degree of prescribed stability

stability and criticality analysis for integer linear programs with markovian problem data this paper presents the stability and criticality analysis of integer linear programs with respect to perturbations in stochastic data given as markov chains these perturbations affect the initial distribution the transition matrix or the stationary distribution of markov chains stability analysis is concerned with obtaining the set of all perturbations for which a solution remains optimal this paper gives expressions for stability regions for perturbations in the initial distribution the transition matrix the stationary distribution and the product of elements of the transition matrix and the stationary distribution furthermore criticality measures that describe the sensitivity of the objective function with respect to an element of the problem data are derived stability regions that preserve the stochasticity of the problem data are given finally stability regions for perturbations of elements of the transition matrix given that the problem is not linear in the initial distribution or the transition matrix are obtained using a small perturbation analysis the results are applied to sensor placement problems and numerical examples are given

a numerical approach to the approximate and the exact minimum rank of a covariance matrix a concept of approximate minimum rank for a covariance matrix is defined which contains the exact minimum rank as a special case a computational procedure to evaluate the approximate minimum rank is offered the procedure yields those proper communalities for which the unexplained common variance ignored in low rank factor analysis is minimized the procedure also permits a numerical determination of the exact minimum rank of a covariance matrix within limits of computational accuracy a set of 180 covariance matrices with known or bounded minimum rank was analyzed the procedure was successful throughout in recovering the desired rank

generalized estimating equations for ordinal categorical data arbitrary patterns of missing responses and missingness in a key covariate summary we propose methods for regression analysis of repeatedly measured ordinal categorical data when there is nonmonotone missingness in these responses and when a key covariate is missing depending on observables the methods use ordinal regression models in conjunction with generalized estimating equations gees we extend the gee methodology to accommodate arbitrary patterns of missingness in the responses when this missingness is independent of the unobserved responses we further extend the methodology to provide correction for possible bias when missingness in knowledge of a key covariate may depend on observables the approach is illustrated with the analysis of data from a study in diagnostic oncology in which multiple correlated receiver operating characteristic curves are estimated and corrected for possible verification bias when the true disease status is missing depending on observables

commentary on coefficient alpha a cautionary tale the general use of coefficient alpha to assess reliability should be discouraged on a number of grounds the assumptions underlying coefficient alpha are unlikely to hold in practice and violation of these assumptions can result in nontrivial negative or positive bias structural equation modeling was discussed as an informative process both to assess the assumptions underlying coefficient alpha and to estimate reliability

reliability of summed item scores using structural equation modeling an alternative to coefficient alpha a method is presented for estimating reliability using structural equation modeling sem that allows for nonlinearity between factors and item scores assuming the focus is on consistency of summed item scores this method for estimating reliability is preferred to those based on linear sem models and to the most commonly reported estimate of reliability coefficient alpha

amenability and the structure of the algebras _ a number of characterizations are given of the class of amenable locally compact groups in terms of the ideal structure of the algebras ap g an almost connected group is amenable if and only if for some 1 p oo and some closed ideal i of ap g i has a bounded approximate identity furthermore g is amenable if and only if every derivation of ap g into a banach ap g bimodule is continuous

modeling individualized coefficient alpha to measure quality of test score data individualized coefficient alpha is defined it is item and subject specific and is used to measure the quality of test score data with heterogenicity among the subjects and items a regression model is developed based on 3 sets of generalized estimating equations the first set of generalized estimating equation models the expectation of the responses the second set models the response s variance and the third set is proposed to estimate the individualized coefficient alpha defined and used to measure individualized internal consistency of the responses we also use different techniques to extend our method to handle missing data asymptotic property of the estimators is discussed based on which inference on the coefficient alpha is derived performance of our method is evaluated through simulation study and real data analysis the real data application is from a health literacy study in hunan province of china

amenability and weak amenability of the fourier algebra let g be a locally compact group we show that its fourier algebra a g is amenable if and only if g has an abelian subgroup of finite index and that its fourier stieltjes algebra b g is amenable if and only if g has a compact abelian subgroup of finite index we then show that a g is weakly amenable if the component of the identity of g is abelian and we prove some partial results towards the converse

comments on improved bounds for linear discrete time systems with structured perturbations in this note we clarify a few issues that are not addressed in the above paper by x niu ibid vol 37 p 1170 3 1992 to expand the applications of its results