outlier detection with the kernelized spatial depth function statistical depth functions provide from the deepest point a center outward ordering of multidimensional data in this sense depth functions can measure the extremeness or outlyingness of a data point with respect to a given data set hence they can detect outliers observations that appear extreme relative to the rest of the observations of the various statistical depths the spatial depth is especially appealing because of its computational efficiency and mathematical tractability in this article we propose a novel statistical depth the kernelized spatial depth ksd which generalizes the spatial depth via positive definite kernels by choosing a proper kernel the ksd can capture the local structure of a data set while the spatial depth fails we demonstrate this by the half moon data and the ring shaped data based on the ksd we propose a novel outlier detection algorithm by which an observation with a depth value less than a threshold is declared as an outlier the proposed algorithm is simple in structure the threshold is the only one parameter for a given kernel it applies to a one class learning setting in which normal observations are given as the training data as well as to a missing label scenario where the training set consists of a mixture of normal observations and outliers with unknown labels we give upper bounds on the false alarm probability of a depth based detector these upper bounds can be used to determine the threshold we perform extensive experiments on synthetic data and data sets from real applications the proposed outlier detector is compared with existing methods the ksd outlier detector demonstrates a competitive performance

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

order restricted score parameters in association models for contingency tables abstract the row effects and column effects models for two way contingency tables have parameters for the row and column categories pertaining to the association between the variables for classifications having ordered categories it is often reasonable to assume that the association parameters have a corresponding ordering this article proposes order restricted estimates of the association parameters in these models the maximum likelihood solution can be determined by the solution of a simple isotonic regression of some of the model sufficient statistics the models are primarily log linear in form and can be expressed in terms of odds ratios for 2 2 subtables consisting of adjacent rows and adjacent columns for the order restricted solution these local log odds ratios have uniform sign goodness of fit statistics for this solution are related to corresponding statistics for collapsed tables and to statistics for testing equality of sets of the parameters the row effects model discussed in this art

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

online estimation of the geometric median in hilbert spaces nonasymptotic confidence balls estimation procedures based on recursive algorithms are interesting and powerful techniques that are able to deal rapidly with very large samples of high dimensional data the collected data may be contaminated by noise so that robust location indicators such as the geometric median may be preferred to the mean in this context an estimator of the geometric median based on a fast and efficient averaged nonlinear stochastic gradient algorithm has been developed by bernoulli19 2013 18 43 this work aims at studying more precisely the nonasymptotic behavior of this nonlinear algorithm by giving nonasymptotic confidence balls in general separable hilbert spaces this new result is based on the derivation of improved l 2 rates of convergence as well as an exponential inequality for the nearly martingale terms of the recursive nonlinear robbins monro algorithm

the multivariate l1 median and associated data depth this paper gives three related results i a new simple fast monotonically converging algorithm for deriving the l1 median of a data cloud in d a problem that can be traced to fermat and has fascinated applied mathematicians for over three centuries ii a new general definition for depth functions as functions of multivariate medians so that different definitions of medians will correspondingly give rise to different dept functions and iii a simple closed form formula of the l1 depth function for a given data cloud in d

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

general notions of statistical depth function statistical depth functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data here we introduce several general structures for depth functions classify many existing examples as special cases and establish results on the possession or lack thereof of four key properties desirable for depth functions in general roughly speaking these properties may be described as affine invariance maximality at center monotonicity relative to deepest point and vanishing at infinity this provides a more systematic basis for selection of a depth function in particular from these and other considerations it is found that the halfspace depth behaves very well overall in comparison with various competitors

monge kantorovich depth quantiles ranks and signs we propose new concepts of statistical depth multivariate quantiles ranks and signs based on canonical transportation maps between a distributionof interest on ird and a reference distribution on the d dimensionalunit ball the new depth concept called monge kantorovich depth specializesto halfspace depth in the case of elliptical distributions but for more generaldistributions differs from the latter in the ability for its contours to account fornon convex features of the distribution of interest we propose empirical counterpartsto the population versions of those monge kantorovich depth contours quantiles ranks and signs and show their consistency by establishing a uniformconvergence property for transport maps which is of independent interest

on local intrinsic dimension estimation and its applications in this paper we present multiple novel applications for local intrinsic dimension estimation there has been much work done on estimating the global dimension of a data set typically for the purposes of dimensionality reduction we show that by estimating dimension locally we are able to extend the uses of dimension estimation to many applications which are not possible with global dimension estimation additionally we show that local dimension estimation can be used to obtain a better global dimension estimate alleviating the negative bias that is common to all known dimension estimation algorithms we illustrate local dimension estimation s uses towards additional applications such as learning on statistical manifolds network anomaly detection clustering and image segmentation

stability of 2 d systems described by the fornasini marchesini first model a sufficient condition for the stability of linear two dimensional 2 d systems described by the fornasini marchesini 1976 first model is presented the condition is compared with previously reported conditions

on the fixed poles for disturbance rejection we propose a geometric characterization of the fixed poles for the disturbance rejection problem by static state feedback and in the particular case when the system is controllable a structural characterization in terms of finite invariant zeros of certain open loop subsystems we propose solutions through which all the other poles can be freely assigned

on the cayley hamilton theorem for two dimensional systems an alternate proof of the 2 d cayley hamilton theorem is supplied together with an extension to derived polynomials

robust eigenstructure assignment in geometric control theory in this paper we employ the rosenbrock system matrix pencil for the computation of output nulling subspaces of linear time invariant systems which appear in the solution of a large number of control and estimation problems we also consider the problem of finding friends of these output nulling subspaces i e the feedback matrices that render such subspaces invariant with respect to the closed loop map and output nulling with respect to the output map and which at the same time deliver a robust closed loop eigenstructure we show that the methods presented in this paper offer considerably more robust eigenstructure assignment than the other commonly used methods and algorithms

a geometric approach to the theory of 2 d systems the authors develop a geometric approach to the theory of 2 d two dimensional systems defining in a suitable way the notion of a sub 1 2 b sub 1 2 invariant subspaces and of controlled invariant subspaces such subspaces are shown to have good computational and feedback properties which make them useful in application in particular sufficient conditions and constructive procedures are obtained for the solutions of disturbance decoupling and model matching problems moreover it is shown that certain structural properties of a 2 d system can be described by means of a set of indexes defined in geometric terms and that such structural indexes can be used to reformulate the sufficient condition for model matching

an iterative procedure for obtaining i projections onto the intersection of convex sets abstract a frequently occuring problem is to find that probability distribution pd lying within a convex set which minimizes the i divergence between it and given pd r this document proposes an iterative procedure which requires only that the set be convex and not necessarily linear which under general conditions will converge to the desired i projection

extremal depth for functional data and applications abstractwe propose a new notion called extremal depth ed for functional data discuss its properties and compare its performance with existing concepts the proposed notion is based on a measure of extreme outlyingness ed has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces in particular a the central region achieves the nominal desired simultaneous coverage probability b there is a correspondence between ed based simultaneous central regions and appropriate pointwise central regions and c the method is resistant to certain classes of functional outliers the article examines the performance of ed and compares it with other depth notions its usefulness is demonstrated through applications to constructing central regions functional boxplots outlier detection and simultaneous confidence bands in regression problems supplementary materials for this article are availab

transforming contingency tables abstract we present a general theorem on transforming contingency tables and several applications where the transformation technique has allowed us to take advantage of the iterative proportional fitting procedure and has resulted in simple and useful procedures a further advantage of this technique is that it is sometimes possible to recognize closed form estimates in the transformed problem while they would be overlooked in the original setting we shall view the estimation problem as one of minimizing the kullback leibler information distance between two probability mass functions and will roughly follow the notation of csiszar 1976 although we have adopted the information distance point of veiw the duality between maximum likelihood estimation and minimum information estimation see e g darroch and ratcliff 1972 implies that the results of this paper can just as well be interpreted from the maximum likelihood point of view

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

speeding up mcmc by efficient data subsampling we propose subsampling markov chain monte carlo mcmc an mcmc framework where the likelihood function for n observations is estimated from a random subset of m observations we introduce a highly

nonparametric imputation by data depth abstractwe present single imputation method for missing values which borrows the idea of data depth a measure of centrality defined for an arbitrary point of a space with respect to a probability d

permutation tests for equality of distributions in high dimensional settings motivated by applications in high dimensional settings we suggest a test of the hypothesis h 0 that two sampled distributions are identical it is assumed that two independent datasets are drawn from the respective populations which may be very general in particular the distributions may be multivariate or infinite dimensional in the latter case representing for example the distributions of random functions from one euclidean space to another our test uses a measure of distance between data this measure should be symmetric but need not satisfy the triangle inequality so it is not essential that it be a metric the test is based on ranking the pooled dataset with respect to the distance and relative to any fixed data value and repeating this operation for each fixed datum a permutation argument enables a critical point to be chosen such that the test has concisely known significance level conditional on the set of all pairwise distances

a geometric approach to visualization of variability in functional data abstractwe propose a new method for the construction and visualization of boxplot type displays for functional data we use a recent functional data analysis framework based on a representation of functions called square root slope functions to decompose observed variation in functional data into three main components amplitude phase and vertical translation we then construct separate displays for each component using the geometry and metric of each representation space based on a novel definition of the median the two quartiles and extreme observations the outlyingness of functional data is a very complex concept thus we propose to identify outliers based on any of the three main components after decomposition we provide a variety of visualization tools for the proposed boxplot type displays including surface plots we evaluate the proposed method using extensive simulations and then focus our attention on three real data applications including exploratory data analysis of sea surface tempe

on the concept of depth for functional data the statistical analysis of functional data is a growing need in many research areas in particular a robust methodology is important to study curves which are the output of many experiments in applied statistics as a starting point for this robust analysis we propose analyze and apply a new definition of depth for functional observations based on the graphic representation of the curves given a collection of functions it establishes the centrality of an observation and provides a natural center outward ordering of the sample curves robust statistics such as the median function or a trimmed mean function can be defined from this depth definition its finite dimensional version provides a new depth for multivariate data that is computationally feasible and useful for studying high dimensional observations thus this new depth is also suitable for complex observations such as microarray data images and those arising in some recent marketing and financial studies natural properties of these

an lmi based algorithm for designing suboptimal static cal h_2 cal h_ infty output feedback controllers we consider the problem of designing a suboptimal cal h 2 cal h infty feedback control law for a linear time invariant control system when a complete set of state variables is not available this problem can be necessarily restated as a nonconvex optimization problem with a bilinear multiobjective functional under suitably chosen linear matrix inequality lmi constraints to solve such a problem we propose an lmi based procedure which is a sequential linearization programming approach the properties and the convergence of the algorithm are discussed in detail finally several numerical examples for static cal h 2 cal h infty output feedback problems demonstrate the applicability of the considered algorithm and also verify the theoretical results numerically

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

estimation of a regression model on two or more sets of differently grouped data abstract one dimensional grouped survey data are made available to the public but the cross classified data are usually not two methods to estimate a contingency table from the known margins are investigated one method is to fit goodman s correlation model and the other is a bayesian method that incorporates vague outside information both methods are used to estimate a regression model on two or more sets of differently grouped data

spatial medians depth functions and multivariate jensen s inequality for any given partial order in a d dimensional euclidean space under mild regularity assumptions we show that the intersection of closed generalized intervals containing more than 1 2 of the probability mass is a non empty compact interval this property is shared with common intervals on real line where the intersection is the median set of the underlying probability distribution so obtained multivariate medians with respect to a partial order can be observed as special cases of centers of distribution in the sense of type d depth functions introduced by y zuo and r serfling em ann stat bf 28 2000 461 482 we show that the halfspace depth function can be realized via compact convex sets or for example closed balls in place of halfspaces and discuss structural properties of halfspace and related depth functions and their centers among other things we prove that in general the maximal guaranteed depth is frac 1 d 1 as an application of these results we provide a jensen s type inequality for functions of several variables with medians in place of expectations which is an extension of the previous work by m merkle em stat prob letters bf 71 2005 277 281

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

asymptotic data analysis on manifolds given an m dimensional compact submanifold m of euclidean space r s the concept of mean location of a distribution related to mean or expected vector is generalized to more general r s valued functionals including median location which is derived from the spatial median the asymptotic statistical inference for general functionals of distributions on such submanifolds is elaborated convergence properties are studied in relation to the behavior of the underlying distributions with respect to the cutlocus an application is given in the context of independent but not identically distributed samples in particular to a multisample setup

simultaneous estimation of intrarater and interrater agreement for multiple raters under order restrictions for a binary trait it is valuable in many studies to assess both intrarater and interrater agreement most measures of intrarater agreement do not adjust for unequal estimates of prevalence between the separate rating occasions for a given rater and measures of interrater agreement typically ignore data from the second set of assessments when raters make duplicate assessments in the event when both measures are assessed there are instances where interrater agreement is larger than at least one of the corresponding intrarater agreements this implies that a rater agrees less with him herself and more with another rater in the situation of multiple raters making duplicate assessments on all subjects the authors propose properties for an agreement measure based on the odds ratio for a dichotomous trait i estimate a single prevalence across two reading occasions for each rater ii estimate pairwise interrater agreement from all available data iii bound the pairwise interrater agreement above by the corresponding intrarater agreements estimation of odds ratios under these properties is done by maximizing the multinomial likelihood with constraints using generalized log linear models in combination with a generalization of the lemke dykstra iterative incremental algorithm an example from a mammography examination reliability study is used to demonstrate the new method

global properties and duality in 2 d systems the paper is concerned with structural properties of the global stale of 2 d systems global reachability and observability are related to the existence of the inverses over rings of the reachability and observability matrices this leads to introduce the concept of dual system of a 2 d system in terms of a system defined over a suitable ring of polynomials finally global reachability and observability conditions are proved to be equivalent to the existence of bezout identities in two variables

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

structural invariants of two dimensional systems in this paper some fundamental structural properties of two dimensional 2 d systems which remain invariant under feedback and output injection transformation groups are identified and investigated for the first time as is well known structural invariants that follow from the definition of controlled and conditioned invariance output nulling input containing self bounded and self hidden subspaces play pivotal roles in many theoretical studies of systems theory and in the solution of several control estimation problems these concepts are developed and studied within a 2 d context in this paper

estimation of the rate distortion function motivated by questions in lossy data compression and by theoretical considerations the problem of estimating the rate distortion function of an unknown not necessarily discrete valued source from empirical data is examined the focus is the behavior of the so called ldquoplug inrdquo estimator which is simply the rate distortion function of the empirical distribution of the observed data sufficient conditions are given for its consistency and examples are provided demonstrating that in certain cases it fails to converge to the true rate distortion function the analysis of its performance is complicated by the fact that the rate distortion function is not continuous in the source distribution the underlying mathematical problem is closely related to the classical problem of establishing the consistency of maximum likelihood estimators mles general consistency results are given for the plug in estimator applied to a broad class of sources including all stationary and ergodic ones a more general class of estimation problems is also considered arising in the context of lossy data compression when the allowed class of coding distributions is restricted analogous results are developed for the plug in estimator in that case finally consistency theorems are formulated for modified e g penalized versions of the plug in and for estimating the optimal reproduction distribution

robust functional estimation using the median and spherical principal components summary we present robust estimators for the mean and the principal components of a stochastic process in l2 r robustness and asymptotic properties of the estimators are studied theoretically by simulation and by example it is shown that the proposed estimators are generally more robust to outliers than the commonly used sample mean and principal components although their properties depend on the spacings of the eigenvalues of the covariance function

an iterative procedure for general probability measures to obtain i projections onto intersections of convex sets the iterative proportional fitting procedure ipfp was introduced formally by deming and stephan in 1940 for bivariate densities this procedure has been investigated by kullback and ruschendorf it is well known that the ipfp is a sequence of successive i projections onto sets of probability measures with fixed marginals however when finding the i projection onto the intersection of arbitrary closed convex sets e g marginal stochastic orders a sequence of successive i projections onto these sets may not lead to the actual solution addressing this situation we present a new iterative i projection algorithm under reasonable assumptions and using tools from fenchel duality convergence of this algorithm to the true solution is shown the cases of infinite dimensional ipfp and marginal stochastic orders are worked out in this context

the spatial distribution in infinite dimensional spaces and related quantiles and depths the spatial distribution has been widely used to develop various nonparametric procedures for finite dimensional multivariate data in this paper we investigate the concept of spatial distribution for data in infinite dimensional banach spaces many technical difficulties are encountered in such spaces that are primarily due to the non compactness of the closed unit ball in this work we prove some glivenko cantelli and donsker type results for the empirical spatial distribution process in infinite dimensional spaces the spatial quantiles in such spaces can be obtained by inverting the spatial distribution function a bahadur type asymptotic linear representation and the associated weak convergence results for the sample spatial quantiles in infinite dimensional spaces are derived a study of the asymptotic efficiency of the sample spatial median relative to the sample mean is carried out for some standard probability distributions in function spaces the spatial distribution can be used to define the spatial depth in infinite dimensional banach spaces and we study the asymptotic properties of the empirical spatial depth in such spaces we also demonstrate the spatial quantiles and the spatial depth using some real and simulated functional data

self bounded subspaces for nonstrictly proper systems and their application to the disturbance decoupling with direct feedthrough matrices in this paper the concept of self bounded controlled invariance is extended to nonstrictly proper systems moreover its use in connection with the disturbance decoupling problem with internal stability is investigated in the case where the feedthrough matrices from the control input and from the disturbance to the output to be decoupled are possibly nonzero

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

penalty based aggregation of multidimensional data abstract research in aggregation theory is nowadays still mostly focused on algorithms to summarize tuples consisting of observations in some real interval or of diverse general ordered structures of course in practice of information processing many other data types between these two extreme cases are worth inspecting this contribution deals with the aggregation of lists of data points in r d for arbitrary d 1 even though particular functions aiming to summarize multidimensional data have been discussed by researchers in data analysis computational statistics and geometry there is clearly a need to provide a comprehensive and unified model in which their properties like equivariances to geometric transformations internality and monotonicity may be studied at an appropriate level of generality the proposed penalty based approach serves as a common framework for all idempotent information aggregation methods including componentwise functions pairwise distance minimizers and data depth based medians it also allows for deriving many new practically useful tools

a survey of strategies for modeling cross classifications having ordinal variables abstract a survey is given of the main strategies for modeling cross classifications that contain ordinal variables models are described for two way tables in which one or both classifications are ordered and for multidimensional tables in which at least one classification is ordered primary emphasis is given to construction interpretation and implications of loglinear and logit models

optimally weighted l2 distance for functional data many techniques of functional data analysis require choosing a measure of distance between functions with the most common choice being l2 distance in this article we show that using a weighted l2 distance with a judiciously chosen weight function can improve the performance of various statistical methods for functional data including k medoids clustering nonparametric classification and permutation testing assuming a quadratically penalized e g spline basis representation for the functional data we consider three nontrivial weight functions design density weights inverse variance weights and a new weight function that minimizes the coefficient of variation of the resulting squared distance by means of an efficient iterative procedure the benefits of weighting in particular with the proposed weight function are demonstrated both in simulation studies and in applications to the berkeley growth data and a functional magnetic resonance imaging data set

control systems analysis for the fornasini marchesini 2d systems model progress after four decades the development of a control systems theory for multidimensional linear systems i e systems with more than one independent variable is an area where a very significant volume of research is based

fault detection and isolation of two dimensional 2d systems abstract in this work we develop a novel fault detection and isolation fdi scheme for discrete time two dimensional 2d systems that are represented by the fornasini marchesini model ii fmii this is accomplished by generalizing the basic invariant subspaces including unobservable conditioned invariant and unobservability subspaces of 1d systems to 2d models these extensions have been achieved and facilitated by representing a 2d model as an infinite dimensional inf d system on a banach vector space and by particularly constructing algorithms that compute these subspaces in a finite and known number of steps by utilizing the introduced subspaces the fdi problem is formulated and necessary and sufficient conditions for its solvability are provided sufficient conditions for solvability of the fdi problem for 2d systems using both deadbeat and lmi based filters have also been developed moreover the capabilities and advantages of our proposed approach are demonstrated by performing an analytical comparison with the currently available 2d geometric methods in the literature

trend representation based log density regularization system for portfolio optimization abstract portfolio optimization po has been catching more and more attention in the artificial intelligence and the machine learning communities in this paper we propose a novel trend representation based log density regularization trlr system for portfolio optimization its novelty falls into two aspects first it introduces a log density regularization to the increasing factor of portfolio which is seldom addressed by previous po systems it reflects a relationship between the portfolio and the price relative at an equilibrium point second trlr exploits a novel trend representation by taking the time variable as regressor in a weighted ridge regression hence trlr captures price trend patterns effectively extensive experiments conducted on 5 benchmark datasets from real world financial markets demonstrate that trlr achieves significantly better performance than other state of the art strategies and runs fast which shows its effectiveness and efficiency for large scale applications

collapsed two way contingency tables and the chi square reduction principle summary the value of the chi square statistic for homogeneity of rows and columns in a contingency table remains unchanged if the table is collapsed grouped over homogeneous rows and columns the difference between the chi square values pertaining to the original table and to the collapsed table the chi square reduction is shown to have a meaningful canonical decomposition which can guide the researcher in detecting homogeneous rows and columns the methodology proposed generalizes an earlier methodology suggested by gilula for the same problem

geometric theory for the singular roesser model a e b invariant and e a b invariant subspaces for the two dimensional singular roesser model are investigated these subspaces are related to the existence of the solutions when the boundary conditions are in these subspaces also the existence of a solution sequence in certain subspaces derived from the invariant subspaces is shown the boundary conditions that appear in the solution when some semistates in the solution are restricted to zero are also investigated

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

critical angles in polyhedral convex cones numerical and statistical considerations this work concerns the numerical computation of critical angles in polyhedral convex cones the set of proper critical angles is evaluated explicitly by solving a series of generalized eigenvalue problems involving the generators of the cone the local maximal angles are identified by using a necessary condition for local maximality the expected numbers of critical angles in random polyhedral convex cones are estimated experimentally

convergence analysis of generalized iteratively reweighted least squares algorithms on convex function spaces the computation of robust regression estimates often relies on minimization of a convex functional on a convex set in this paper we discuss a general technique for a large class of convex functionals to compute the minimizers iteratively which is closely related to majorization minimization algorithms our approach is based on a quadratic approximation of the functional to be minimized and includes the iteratively reweighted least squares algorithm as a special case we prove convergence on convex function spaces for general coercive and convex functionals f and derive geometric convergence in certain unconstrained settings the algorithm is applied to total variation tv penalized quantile regression and is compared with a step size corrected newton raphson algorithm it is found that typically in the first steps the iteratively reweighted least squares algorithm performs significantly better whereas the newton type method outpaces the former only after many iterations finally in the setting of bivariate regression with unimodality constraints we illustrate how this algorithm allows one to utilize highly efficient algorithms for special quadratic programs in more complex settings

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