tests for regulability of 2 d systems regulability tests of 2 d systems are transformed into stability tests of one variable polynomials in this paper the method can be used in regulability tests of multi dimensional systems without any substantial modification

2 d exact model matching the exact model matching problem in single input single output 2 d systems is solved by applying polyaomial techniques all solutions are described in a parametric form natural solvability conditions for causal and or stable solutions are given and a simple design procedure is proposed it consists in solving a linear 2 d polynomial equation which directly yields a suitable compensator

on the coefficient assignment of two dimensional systems in this note we prove that in two dimensional 2 d systems the arbitrary coefficient assignment cannot be achieved by using causal output feedbacks the problem however can be transformed into the design of systems over rings in order to find conditions guaranteeing the existence of a solution some related problems are also discussed

common principal components in k groups abstract this article generalizes the method of principal components to so called common principal components as follows consider the hypothesis that the covariance matrices i for k populations are simultaneously diagonalizable that is there is an orthogonal matrix such that i is diagonal for i 1 k i derive the normal theory maximum likelihood estimates of the common component i matrices and the log likelihood ratio statistics for testing this hypothesis the solution has some favorable properties that do not depend on normality assumptions numerical examples illustrate the method applications to data reduction multiple regression and nonlinear discriminant analysis are sketched

choosing an optimal method to combine p values fisher 1925 was the first to suggest a method of combining the p values obtained from several statistics and many other methods have been proposed since then however there is no agreement about what is the best method motivated by a situation that now often arises in genetic epidemiology we consider the problem when it is possible to define a simple alternative hypothesis of interest for which the expected effect size of each test statistic is known and we determine the most powerful test for this simple alternative hypothesis based on the proposed method we show that information about the effect sizes can be used to obtain the best weights for liptak s method of combining p values we present extensive simulation results comparing methods of combining p values and illustrate for a real example in genetic epidemiology how information about effect sizes can be deduced

random matrix theory filters in portfolio optimisation a stability and risk assessment abstract random matrix theory rmt filters applied to covariance matrices of financial returns have recently been shown to offer improvements to the optimisation of stock portfolios this paper studies the effect of three rmt filters on the realised portfolio risk and on the stability of the filtered covariance matrix using bootstrap analysis and out of sample testing we propose an extension to an existing rmt filter based on krzanowski stability which is observed to reduce risk and increase stability when compared to other rmt filters tested we also study a scheme for filtering the covariance matrix directly as opposed to the standard method of filtering correlation where the latter is found to lower the realised risk on average by up to 6 7 we consider both equally and exponentially weighted covariance matrices in our analysis and observe that the overall best method out of sample was that of the exponentially weighted covariance with our krzanowski stability based filter applied to the correlation matrix we also find that the optimal out of sample decay factors for both filtered and unfiltered forecasts were higher than those suggested by riskmetrics j p morgan reuters riskmetrics technical document technical report 1996 http www riskmetrics com techdoc html with those for the latter approaching a value of 1 in conclusion rmt filtering reduced the realised risk on average and in the majority of cases when tested out of sample but increased the realised risk on a marked number of individual days in some cases more than doubling it

the sylvester resultant with applications to systems over rings the sylvester resultant is studied in this paper for systems over rings the systems over rings may have zero coprime fractions fractor coprime fractions and fraction with common factors the sylvester resultant can be used to test these situations it can also be used to achieve the design of coefficient assignment in the first case to test the regulability in the second case and to find the fractor coprime fractions in the third case

on the effects of moderate multivariate nonnormality on roy s largest root test abstract the asymptotic distribution of roy s largest root statistic in multivariate edgeworth populations is expanded to terms of the first order to this order the effects of non normality are expressed by mardia s measures of multivariate skewness and kurtosis together with a supplementary skewness measure tables of corrections to the nominal significance level are presented for the k sample manova situation comparison with simulation results indicates that the correction terms provide a useful indication both of the magnitude and the direction of the effect of nonnormality on the nominal 5 percent type i error even when the underlying population is not well represented by an edgeworth expansion provided that the skewness and kurtosis are not too large

distributions of singular values for some random matrices the singular value decomposition is a matrix decomposition technique widely used in the analysis of multivariate data such as complex space time images obtained in both physical and biological systems in this paper we examine the distribution of singular values of low rank matrices corrupted by additive noise past studies have been limited to uniform uncorrelated noise using diagrammatic and saddle point integration techniques we extend these results to heterogeneous and correlated noise sources we also provide perturbative estimates of error bars on the reconstructed low rank matrix obtained by truncating a singular value decomposition 1999 the american physical society

a parametric meta analysis in a meta analysis we assemble a sample of independent nonidentically distributed p values the fisher s combination procedure provides a chi squared test of whether the p values were sampled from the null uniform distribution after rejecting the null uniform hypothesis we are faced with the problem of how to combine the assembled p values we first derive a distribution for the p values the distribution is parameterized by the standardized mean difference smd and the sample size it includes the uniform as a special case the maximum likelihood estimate mle of the smd can then be obtained from the independent nonidentically distributed p values the mle can be interpreted as a weighted average of the study specific estimate of the effect size with a shrinkage the method is broadly applicable to p values obtained in the maximum likelihood framework simulation studies show that our method can effectively estimate the effect size with as few as 6 p values in the meta analyses we also present a bayes estimator for smd and a method to account for publication bias we demonstrate our methods on several meta analyses that assess the potential benefits of citicoline for patients with memory disorders or patients recovering from ischemic stroke

random matrix theory for portfolio optimization a stability approach we apply random matrix theory rmt to an empirically measured financial correlation matrix c and show that this matrix contains a large amount of noise in order to determine the sensitivity of the spectral properties of a random matrix to noise we simulate a set of data and add different volumes of random noise having ascertained that the eigenspectrum is independent of the standard deviation of added noise we use rmt to determine the noise percentage in a correlation matrix based on real data from s p500 eigenvalue and eigenvector analyses are applied and the experimental results for each of them are presented to identify qualitatively and quantitatively different spectral properties of the empirical correlation matrix to a random counterpart finally we attempt to separate the noisy part from the non noisy part of c we apply an existing technique to cleaning c and then discuss its associated problems we propose a technique of filtering c that has many advantages from the stability point of view over the existing method of cleaning

a class of asymptotic tests for principal component vectors in this paper the hypothesis that a set of vectors lie in the subspace spanned by a prescribed subset of the principal component vectors for a normal population is considered a class of invariant asymptotic tests based on the sample covariance matrix is derived tests in this class are shown to be consistent and their local power functions are given the arguments used in deriving the class of tests are not heavily dependent on the assumption of normality nor on the use of the sample covariance matrix the results are shown to generalize when the procedures are based on any affine invariant m estimate of scatter and when the population is elliptical

on confidence regions in canonical variate analysis it is argued that confidence circles as traditionally drawn on canonical variate diagrams are incorrect because no allowance is made in their construction for the sampling variability of the canonical variate axes a series of approximations is employed to obtain tractable expressions for the correct regions despite the rather broad approximations involved empirical assessment via bootstrapping shows the new regions to have much more accurate probability content than the traditional circles an illustrative example highlights the differences between the two types of region

analysis of linear combinations with extreme ratios of variance abstract if the covariance matrices 1 and 2 of two multivariate populations are not identical insight into the differences between 1 and 2 can often be gained by analyzing the linear combinations with extreme ratios of variances that is those defined by the eigenvectors associated with the extreme roots of 1 1 2 this article gives a descriptive method similar to variable selection procedures in regression for screening and simplifying these linear combinations a hypothesis of redundancy of variables is defined and a statistic for testing this hypothesis is derived the method is illustrated by an example

comments on 2 d exact model matching two examples are given to indicate that in 2 d coefficient assignment model matching some cancellations are unavoidable in the author s belief and the split condition not only the zero coprimeness is necessary

regulation of split linear systems over rings coefficient assignment and observers a theory of regulators is developed for finite free split linear systems over a commutative ring k this is achieved by developing a theory of coefficient assignment and observers it is shown that the problem of coefficient assignment can be solved for reachable systems by using dynamic state feedback for strongly observable systems it is shown that observers with arbitrary dynamics can be constructed internal stability of observer and state feedback configuration is considered explicitly some examples are given to illustrate these techniques

asymptotic inference for eigenvectors abstract asymptotic procedures are given for testing certain hypotheses concerning eigenvectors and for constructing confidence regions for eigenvectors these asymptotic procedures are derived under fairly general conditions on the estimates of the matrix whose eigenvectors are of interest applications of the general results to principal components analysis and canonical variate analysis are given author

how many variables should be entered in a regression equation abstract the optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points as the number of regressors grows large the sp criterion provides an asymptotically optimal rule for the number of variables to enter