association models and the bivariate normal for contingency tables with ordered categories summary association models considered by goodman 1979 for contingency tables with ordered categories are presented here in a somewhat different form to facilitate comparison with the bivariate normal association models can be applied when an underlying bivariate normal is assumed and also under more general conditions and they provide alternatives to tetrachoric and polychoric correlation these models agree more closely with the bivariate normal than does plackett s model 1965 when the row and column classifications arise from underlying univariate normal distributions the general utility of the association models is illustrated here

testing dependence among serially correlated multicategory variables the contingency table literature on tests for dependence among discrete multicategory variables is extensive standard tests assume however that draws are independent and only limited results exist on the effect of serial dependency a problem that is important in areas such as economics finance medical trials and meteorology this article proposes new tests of independence based on canonical correlations from dynamically augmented reduced rank regressions the tests allow for an arbitrary number of categories as well as multiway tables of arbitrary dimension and are robust in the presence of serial dependencies that take the form of finite order markov processes for three way or higher order tables we propose new tests of joint and marginal independence monte carlo experiments show that the proposed tests have good finite sample properties an empirical application to microeconomic survey data on firms forecasts of changes to their production and prices demonstrates the importance of correcting fo

models for the analysis of association in multivariate contingency tables abstract the present work describes a family of models that can be used for the analysis of association in multiway cross classifications the models are complementary to the usual i e the so called hierarchical log linear models an advantage of this family of models is that it is frequently possible to give a more parsimonious description of the association than is possible with the usual log linear models approach the models will be especially useful when some or all of the variables are ordinal the models are derived from a reparameterization of the saturated model based on singular value decompositions of interaction terms in the log linear parameterization multivariate association models given in goodman 1979 1986 clogg 1982a b agresti and kezouh 1983 gilula and haberman 1988 and becker and clogg 1989 are obtained as special cases the utility of the models developed in this article is demonstrated with the analysis of two examples the first example a cross classification of

multivariate normal integrals and contingency tables with ordered categories ak dimensional multivariate normal distribution is made discrete by partitioning thek dimensional euclidean space with rectangular grids the collection of probability integrals over the partitioned cubes is ak dimensional contingency table with ordered categories it is shown that loglinear model with main effects plus two way interactions provides an accurate approximation for thek dimensional table the complete multivariate normal integral table is computed via the iterative proportional fitting algorithm from bivariate normal integral tables this approach imposes no restriction on the correlation matrix comparisons with other numerical integration algorithms are reported the approximation suggests association models for discretized multivariate normal distributions and contingency tables with ordered categories

on generalized m quasi einstein manifolds with constant scalar curvature abstract we study generalized m quasi einstein manifolds with constant scalar curvature first we establish a classification of generalized m quasi einstein manifolds with parallel ricci tensor second and particularly if an m quasi einstein manifold possesses constant scalar curvature then we determine the scalar curvature in explicit form and show that which values are attainable by presenting examples

delay estimation and the estimation of coherence and phase the method of delay estimation given in hamon and hannan 1 is reviewed and a modification involving autoregressive model fitting is proposed it is shown how numerical problems associated with the optimization of the criterion used in both the original and modified procedures can be circumvented the modified procedure and a procedure due to chan riley and plant 2 are compared to the hamon hannan procedure by simulations for moderate to large signal to noise ratios the modified hamon hannan procedure appears to provide better estimates in the case of low signal to noise ratios with the smaller size the chan riley and plant procedure performed best

analysis of sets of two way contingency tables using association models abstract a class of models is introduced for the analysis of group differences in the association between two discrete variables the rc m association model for two way tables is reviewed and alternative weighting systems for identifying interaction parameters are presented this model is generalized for the setting where a two way contingency table is available for two or more groups various restricted models can be used to examine possible sources of intergroup heterogeneity in the association these sources pertain to heterogeneity in the intrinsic association and or in the scores for the row and column variables the importance of weights used to identify the row and column scores is emphasized a classical set of data previously analyzed by many authors is used to illustrate the advantages of the models and methods developed here

linear modeling and the coherence function in this paper a tutorial introduction to the magnitude squared ms coherence function and its relation to linear modeling is interleaved with new methods for characterizing bidirectional and unidirectional linear association between two time series a new method for characterizing bidirectional linear association is based on the new concept of an ms coherence sequence which is the inverse z transform of the ms coherence function the ms coherence function is approximated as a single real valued ratio of polynominals in z the ratio is determined by a matrix equation whose entries are convolutions of correlation functions solutions for the corresponding ms coherence parameters employ an eigenvalue eigenvector decomposition the algorithm is compared to a traditional periodogram based method using computer simulations the computer simulations also demonstrate the effects of parameter overdetermination and overordering the sensitivity of the matrix equations for the computer simulations is computed via the numerical linear algebra concept of condition number

generalized quasi einstein manifolds with harmonic weyl tensor in this paper we introduce the notion of generalized quasi einstein manifold that generalizes the concepts of ricci soliton ricci almost soliton and quasi einstein manifolds we prove that a complete generalized quasi einstein manifold with harmonic weyl tensor and with zero radial weyl curvature is locally a warped product with n 1 dimensional einstein fibers in particular this implies a local characterization for locally conformally flat gradient ricci almost solitons similar to that proved for gradient ricci solitons

on asymptotic power and efficiency of tests of independence in contingency tables with ordered classifications abstract asymptotic power formulas for tests of independence against simple association models in i j contingency tables with ordered categories are presented yates s score correlation test and spearman s tied rank correlation test are compared with a likelihood ratio test proposed by s j haberman for testing independence in log linear models with ordered classifications asymptotic power and relative efficiencies are derived under local alternatives that need not be included in the likelihood model assumed by haberman s procedure some computations for real and fictitious data are presented

ordinal association in contingency tables some interpretive aspects abstract two families of models for ordered contingency tables goodman s association models and canonical correlation models are investigated and compared with respect to the interpretation of their parameters we show that the two families of models actually refer to different kinds of ordinal association stochastic order extremity for correlation models and stochastic order entropy for association models this difference is related to the way the two models scale interaction the scale difference is proven to be of substantial consequence especially under strong association

a compact gradient generalized quasi einstein metric with constant scalar curvature abstract in this paper we shall show that a compact gradient generalized m quasi einstein metric m n g f with constant scalar curvature must be isometric to a standard euclidean sphere s n with the potential f well determined

association models and canonical correlation in the analysis of cross classifications having ordered categories abstract the association models considered in goodman 1979a for the analysis of cross classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach both the association models and the canonical correlation approach can provide meaningful scores for the row and column categories and these scores can be used to partition into relevant components the usual chi squared statistic for testing the null hypothesis of statistical independence between the row classification and column classification however while the usual procedure for testing the statistical significance of chi squared components is invalid when these components are based on the canonical correlations a corresponding procedure is valid when these components are obtained with the association models the components of association obtained with the association mo

model determination for categorical data with factor level merging we deal with contingency table data that are used to examine the relationships between a set of categorical variables or factors we assume that such relationships can be adequately described by the conditional independence structure that is imposed by an undirected graphical model if the contingency table is large a desirable simplified interpretation can be achieved by combining some categories or levels of the factors we introduce conditions under which such an operation does not alter the markov properties of the graph implementation of these conditions leads to bayesian model uncertainty procedures based on reversible jump markov chain monte carlo methods the methodology is illustrated on a 2 x 3 x 4 and up to a 4 x 5 x 5 x 2 x 2 contingency table

some applications of quasisymmetry summary we give three applications of quasisymmetry the first two applications involve derived conditional distributions in a study involving matched individuals where the parameters associated with the matching are eliminated by appropriate conditioning extensions to matched triplets or to larger blocks lead to generalizations of quasisymmetry the third application involves reversibility of markov chains where the connexion between reversibility and quasisymmetry is exploited to construct tests for reversibility and tests for homogeneity of several reversible chains

magnitude squared conherence function estimation an adaptive approach this paper concerns an adaptive approach for estimating the magnitude squared coherence msc function via widrow s least mean square lms algorithm analytical expressions for the bias and variance of the estimate so obtained are derived for the case when the input signals are stationary some computer simulation results are also included for both stationary and nonstationary signals

duality of i projections and maximum likelihood estimation for log linear models under cone constraints abstract important order restrictions and general log linear models for multinomial experiments can often be expressed by requiring that the vector composed of the logs of the probabilities fall within a closed convex cone here we exhibit a duality relationship by way of a fenchel duality theorem between these types of problems and projections in i divergence geometry we show that many cone constrained maximum likelihood estimation problems are exactly equivalent to an i projection onto a translation of the negative polar cone this duality relationship permits the concise characterization of cone restricted maximum likelihood estimates and the use of iterative algorithms proposed by csiszar 1975 and dykstra 1985b which are analogous to the iterative proportional fitting procedure computational aspects of maximum likelihood estimates are discussed and a relationship with least squares projections onto isotonic cones is presented we discuss examples in detail to exhibit the usefulness and power

generalized bilinear models generalized bilinear models are presented for the statistical analysis of two way arrays these models combine bilinear models and generalized linear modeling and yield a family of models that includes many existing models as well as suggest other potentially useful ones this approach both unifies and extends models for two way arrays including the ability to treat response and explanatory variables differently in the models and the incorporation of external information about the variables directly into the analysis a unifying framework for the generalized bilinear models is provided by considering four particular cases which have been proposed and used in the existing statistical literature a three step procedure is proposed to analyze data sets by generalized bilinear models two data sets of different nature are analyzed

modeling of time delay and its application to estimation of nonstationary delays a method to model a time delay by a finite impulse response filter is presented it is useful in simulation work that involves time delays and transforms the time delay estimation problem into one of parameter estimation the benefits of this approach are the elimination of spectral estimation a choice of many parameter estimation algorithms and the capability to track time varying delays two examples of estimating nonstationary time delays are also given

delayed block transfer function in the frequency domain when the impulse response of a transfer system is long it is difficult for the standard cross spectrum method to obtain an accurate estimate of the transfer function by applying the fast fourier transform fft with a finite length window the bias error in the estimate is large especially around the resonant frequency of the transfer system in the paper therefore the authors propose an alternative new method to obtain an accurate estimate of the transfer function the delayed block transfer function is introduced to detect the components that are correlated to the signal in the input window but leak from the output window based on these transfer functions the total characteristics of the transfer system are estimated accurately in the latter half of the paper the authors derive the theoretical expressions for the bias errors in the transfer functions estimated by the proposed and the standard methods by thoroughly comparing the resultant expressions the superiority and the usefulness of the proposed method are theoretically confirmed finally the simulation experiments show the advantages of the proposed method

some models for the analysis of association in multiway cross classifications having ordered categories abstract goodman recently presented a class of models for the analysis of association between two discrete ordinal variables the association was measured in terms of the odds ratios in 2 2 subtables formed from adjacent rows and adjacent columns of the cross classification and models were devised that allowed the odds ratios to depend on an overall effect on row effects on column effects and on other effects this article presents some generalizations of this approach appropriate for multiway cross classifications including a models for the analysis of conditional association b models for the analysis of partial association and c models for the analysis of symmetric association three cross classifications are analyzed with these models and methods and rather simple interpretations of the association in each are provided

correspondence analysis of incomplete contingency tables correspondence analysis can be described as a technique which decomposes the departure from independence in a two way contingency table in this paper a form of correspondence analysis is proposed which decomposes the departure from the quasi independence model this form seems to be a good alternative to ordinary correspondence analysis in cases where the use of the latter is either impossible or not recommended for example in case of missing data or structural zeros it is shown that nora s reconstitution of order zero a procedure well known in the french literature is formally identical to our correspondence analysis of incomplete tables therefore reconstitution of order zero can also be interpreted as providing a decomposition of the residuals from the quasi independence model furthermore correspondence analysis of incomplete tables can be performed using existing programs for ordinary correspondence analysis

asymmetry models for contingency tables abstract for the quasi symmetry qs model applicable to square contingency tables with commensurable classification variables it is proved that under certain conditions it is the closest model to symmetry in terms of the kullback leibler distance replacing the kullback leibler distance by f divergence we introduce a generalized quasi symmetry model the qs f and develop interpretational aspects for its parameters qs is a special case of qs f whereas the most characteristic of the newly introduced qs type models is the pearsonian qs model we compute maximum likelihood estimates of the parameters of the pearsonian qs model and compare it through examples and simulation studies to the classical qs model in terms of goodness of fit and of the powers of the tests for marginal homogeneity conditional on the qs and pearsonian qs models

estimation of coherence and time delay with arma models magnitude squared coherence msc and time delay are two important quantities needed for passive detection and localization of a radiating source using several sensors this paper presents a novel approach to estimating the msc and time delay from the outputs of two sensors it first models the msc as the product of the transfer functions of two autoregressive moving average arma filters the arma coefficients are then determined by a least squares matrix pseudoinverse solution to the estimation equation time delay estimation follows as a byproduct since both phase and msc estimates are now available simulation results obtained from this modeling approach are compared against those estimated from the traditional periodograms in the majority of cases studied the arma approach appears to be superior giving smaller bias and variances in both msc and time delay estimations

canonical analysis of contingency tables by maximum likelihood abstract canonical analysis has often been employed instead of log linear models to analyze the relationship of two polytomous random variables however until the last few years analysis has been informal in this article models are examined that place nontrivial restrictions on the values of the canonical parameters so that a parsimonious description of association is obtained maximum likelihood is used to obtain parameter estimates for these restricted models approximate confidence intervals are derived for parameters and chi squared tests are used to check adequacy of models the resulting models may be used to determine the appropriateness of latent class analysis or to determine whether a set of canonical scores has specified patterns results are illustrated through analysis of two tables previously analyzed in the statistical literature comparisons are made with alternate methods of analysis based on a log linear parameterization of cell probabilities it is shown that canonical analysis wh