nested generalized linear mixed models an orthodox best linear unbiased predictor approach summary we introduce a new class of generalized linear mixed models based on the tweedie exponential dispersion model distributions accommodating a wide range of discrete continuous and mixed data using the best linear unbiased predictor of random effects we obtain an optimal estimating function for the regression parameters in the sense of godambe allowing an efficient common fitting algorithm for the whole class although allowing full parametric inference our main results depend only on the first and second moment assumptions of unobserved random effects in addition we obtain consistent estimators for both regression and dispersion parameters we illustrate the method by analysing the epilepsy data and cake baking data along with simulations and asymptotic justifications this shows the usefulness of the method for analysis of clustered non normal data

patterns in eigenvalues the 70th josiah willard gibbs lecture typical large unitary matrices show remarkable patterns in their eigenvalue distribution these same patterns appear in telephone encryption the zeros of riemann s zeta function a variety of physics problems and in the study of toeplitz operators this paper surveys these applications and what is currently known about the patterns

asymptotics of eigenvalues of large symmetric toeplitz matrices with smooth simple loop symbols abstract this paper is devoted to the asymptotic behavior of all eigenvalues of the increasing finite principal sections of an infinite symmetric in general non hermitian toeplitz matrix the symbol of the infinite matrix is supposed to be moderately smooth and to trace out a simple loop in the complex plane the main result describes the asymptotic structure of all eigenvalues the asymptotic expansions constructed are uniform with respect to the location of the eigenvalues in the bulk of the spectrum

dynamic stochastic models for time dependent ordered paired comparison systems abstract when paired comparisons are made sequentially over time as for example in chess competitions it is natural to assume that the underlying abilities do change with time previous approaches are based on fixed updating schemes where the increments and decrements are fixed functions of the underlying abilities the parameters that determine the functions have to be specified a priori and are based on rational reasoning we suggest an alternative scheme for keeping track with the underlying abilities our approach is based on two components a response model that specifies the connection between the observations and the underlying abilities and a transition model that specifies the variation of abilities over time the response model is a very general paired comparison model allowing for ties and ordered responses the transition model incorporates random walk models and local linear trend models taken together these two components form a non gaussian state space model based on recent results rec

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

a monte carlo approach to nonnormal and nonlinear state space modeling abstract a solution to multivariate state space modeling forecasting and smoothing is discussed we allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation the observational equation or both an adaptive monte carlo integration technique known as the gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework the methodology is a general strategy for obtaining marginal posterior densities of coefficients in the model or of any of the unknown elements of the state space missing data problems including the k step ahead prediction problem also are easily incorporated into this framework we illustrate the broad applicability of our approach with two examples a problem involving nonnormal error distributions in a linear model setting and a one step ahead prediction problem in a situation where both the state and observational equations are nonlinear and involve unknown parameters

on the rate of convergence of regularized boosting classifiers a regularized boosting method is introduced for which regularization is obtained through a penalization function it is shown through oracle inequalities that this method is model adaptive the rate of convergence of the probability of misclassification is investigated it is shown that for quite a large class of distributions the probability of error converges to the bayes risk at a rate faster than n v 2 4 v 1 where v is the vc dimension of the base class whose elements are combined by boosting methods to obtain an aggregated classifier the dimension independent nature of the rates may partially explain the good behavior of these methods in practical problems under tsybakov s noise condition the rate of convergence is even faster we investigate the conditions necessary to obtain such rates for different base classes the special case of boosting using decision stumps is studied in detail we characterize the class of classifiers realizable by aggregating decision stumps it is shown that some versions of boosting work especially well in high dimensional logistic additive models it appears that adding a limited labelling noise to the training data may in certain cases improve the convergence as has been also suggested by other authors

the scan sampler for time series models summary an algorithm called the scan sampler is developed and discussed the scan sampler has a variety of uses for time series analysis based on the state space model with nongaussian observations the algorithm is based on the kalman filter smoothing algorithm it can be used for bayesian inference using markov chain monte carlo and to find posterior modes

particle filters for state space models with the presence of unknown static parameters particle filters for dynamic state space models handling unknown static parameters are discussed the approach is based on marginalizing the static parameters out of the posterior distribution such that only the state vector needs to be considered such a marginalization can always be applied however real time applications are only possible when the distribution of the unknown parameters given both observations and the hidden state vector depends on some low dimensional sufficient statistics such sufficient statistics are present in many of the commonly used state space models marginalizing the static parameters avoids the problem of impoverishment which typically occurs when static parameters are included as part of the state vector the filters are tested on several different models with promising results

eigenvalues of hermitian toeplitz matrices with smooth simple loop symbols abstract the paper presents higher order asymptotic formulas for the eigenvalues of large hermitian toeplitz matrices with moderately smooth symbols which trace out a simple loop on the real line the formulas are established not only for the extreme eigenvalues but also for the inner eigenvalues the results extend and make more precise existing results which so far pertain to banded matrices or to matrices with infinitely differentiable symbols also given is a fixed point equation for the eigenvalues which may be solved numerically by an iteration method

fuzzy perceptron neural networks for classifiers with numerical data and linguistic rules as inputs this paper presents a novel learning algorithm of fuzzy perceptron neural networks fpnns for classifiers that utilize expert knowledge represented by fuzzy if then rules as well as numerical data as inputs the conventional linear perceptron network is extended to a second order one which is much more flexible for defining a discriminant function in order to handle fuzzy numbers in neural networks level sets of fuzzy input vectors are incorporated into perceptron neural learning at different levels of the input fuzzy numbers updating the weight vector depends on the minimum of the output of the fuzzy perceptron neural network and the corresponding nonfuzzy target output that indicates the correct class of the fuzzy input vector this minimum is computed efficiently by employing the modified vertex method moreover the fuzzy pocket algorithm is introduced into our fuzzy perceptron learning scheme to solve the nonseparable problems simulation results demonstrate the effectiveness of the proposed fpnn model

bayesian forecasting of multinomial time series through conditionally gaussian dynamic models abstract we consider inference in the class of conditionally gaussian dynamic models for nonnormal multivariate time series in such models data are represented as drawn from nonnormal sampling distributions whose parameters are related both through time and hierarchically across several multivariate series a key example the main focus here is time series of multinomial observations a common occurrence in sociological and demographic studies involving categorical count data however we present this development in a more general setting as the resulting methods apply beyond the multinomial context we discuss inference in the proposed model class via a posterior simulation scheme based on appropriate modifications of existing markov chain monte carlo algorithms for normal dynamic linear models and including metropolis hastings components we develop an analysis of time series of flows of students in the italian secondary education system as an illustration of the models and methods

fuzzy analysis of statistical evidence bayesian classifiers are effective methods for pattern classification although their assumptions on the belief structure among attributes are not always justified in this paper we introduce a new classification method based on the possibility measure which does not require a precise belief model and in a sense it includes the bayesian classifiers as special cases this new classification method uses the fuzzy operators to aggregate attributes information evidence and it is referred to as fuzzy analysis of statistical evidence fase fase has several nice properties it is noise tolerant it can handle missing values with ease and it can extract statistical patterns from the data and represent them by knowledge of beliefs which in turn are propositions for an expert system thus from pattern classification to expert systems fase provides a linkage from inductive reasoning to deductive reasoning

on the extreme eigenvalues of hermitian block toeplitz matrices abstract we are concerned with the behavior of the minimum maximum eigenvalue 0 n n n of an n 1 n 1 hermitian toeplitz matrix tn where is an integrable real valued function kac murdoch and szego widom parter and r h chan obtained that 0 n min o 1 n2k in the case where c2k at least locally and inf has a zero of order 2k we obtain the same result under the second hypothesis alone moreover we develop a new tool in order to estimate the extreme eigenvalues of the mentioned matrices proving that the rate of convergence of 0 n to inf depends only on the order not necessarily even or integer or finite of the zero of inf with the help of this tool we derive an absolute lower bound for the minimal eigenvalues of toeplitz matrices generated by nonnegative l1 functions and also an upper bound for the associated euclidean condition numbers finally these results are extended to the case of hermitian block toeplitz matrices with toeplitz blocks generated by a bivariate integrable function

discrete time model reference adaptive control of nonlinear dynamical systems using neural networks a multilayer discrete time neural net nn controller is presented for the direct model reference adaptive control of a class of multi input multi output mim0 nonlinear dynamical systems the nonlinear dynamical system is assumed to be controllable and its state vector is available for measurement the nn controller exhibits learning while functioning features instead of learning then control so that control is immediate with no explicit learning phase needed the tracking error between the output of a nonlinear plant and an ideal linear model converges within a very short time persistence of excitation pe is not needed linearity in the parameters is not required and certainty equivalence is not used this overcomes several limitations of standard adaptive control the novel weight tuning paradigm for the nn controller is based on the well known delta rule but includes a modification to the learning rate parameter plus a correction term it guarantees tracking as well as bounded nn weights in non i

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

auxiliary mixture sampling for parameter driven models of time series of counts with applications to state space modelling we consider parameter driven models of time series of counts where the observations are assumed to arise from a poisson distribution with a mean changing over time according to a latent process estimation of these models is carried out within a bayesian framework using data augmentation and markov chain monte carlo methods we suggest a new auxiliary mixture sampler which possesses a gibbsian transition kernel where we draw from full conditional distributions belonging to standard distribution families only emphasis lies on application to state space modelling of time series of counts but we show that auxiliary mixture sampling may be applied to a wider range of parameter driven models including random effects models and panel data models based on the poisson distribution

asymptotic distribution of the spectra of a class of generalized kac murdock szego matrices we consider symmetric toeplitz matrices tn t r s r s 1n with tr r r where and are real and 0 1 we give formulas for det tn and tn 1 and show that if 1 and 0 then tn has eigenvalues 1n 2n nn such that limn 1n limn nn and 2n n 1 n are equally distributed as n with values of f 1 21 2 cos 2 at n 2 equally spaced points in 0

inside the eigenvalues of certain hermitian toeplitz band matrices while extreme eigenvalues of large hermitian toeplitz matrices have been studied in detail for a long time much less is known about individual inner eigenvalues this paper explores the behavior of the jth eigenvalue of an n by n banded hermitian toeplitz matrix as n tends to infinity and provides asymptotic formulas that are uniform in j for email protected email protected n the real valued generating function of the matrices is assumed to increase strictly from its minimum to its maximum and then to decrease strictly back from the maximum to the minimum having nonzero second derivatives at the minimum and the maximum the results which are of interest in numerical analysis probability theory or statistical physics for example are illustrated and underpinned by numerical examples

outlier models and prior distributions in bayesian linear regression summary bayesian inference in regression models is considered using heavy tailed error distri butions to accommodate outliers the particular class of distributions that can be con structed as scale mixtures of normal distributions are examined and use is made of them as both error models and prior distributions in bayesian linear modelling includ ing simple regression and more complex hierarchical models with structured priors depending on unknown hyperprior parameters the modelling of outliers in nominally normal linear regression models using alternative error distributions which are heavy tailed relative to the normal provides an automatic means of both detecting and accommodating possibly aberrant observations such realistic models do however often lead to analytically intractable analyses with complex posterior distributions in several dimensions that are difficult to summarize and understand in this paper we consider a special yet rather wide class of heavy tailed unimodal and symmetric error distributions for which the analyses though apparently intractable can be examined in some depth by exploiting certain properties of the assumed error form the distributions concerned are those that can be con structed as scale mixtures of normal distributions in his paper concerning location parameters de finetti 1961 discusses such distributions and suggests the hypothetical interpretation that each observation is taken using an instrument with normal error but each time chosen at random from a collection of instruments of different precisions the distribution of the

asymptotics of toeplitz hankel and toeplitz hankel determinants with fisher hartwig singularities we study the asymptotics in n for n dimensional toeplitz determinants whose symbols possess fisher hartwig singularities on a smooth background we prove the general nondegenerate asymptotic behavior as conjectured by basor and tracy we also obtain asymptotics of hankel determinants on a nite interval as well as determinants of toeplitz hankel type our analysis is based on a study of the related system of orthogonal polynomials on the unit circle using the riemann hilbert approach

feedback stabilization using two hidden layer nets the representational capabilities of one hidden layer and two hidden layer nets consisting of feedforward interconnections of linear threshold units are compared it is remarked that for certain problems two hidden layers are required contrary to what might be in principle expected from the known approximation theorems the differences are not based on numerical accuracy or number of units needed nor on capabilities for feature extraction but rather on a much more basic classification into direct and inverse problems the former correspond to the approximation of continuous functions while the latter are concerned with approximating one sided inverses of continuous functions and are often encountered in the context of inverse kinematics determination or in control questions a general result is given showing that nonlinear control systems can be stabilized using two hidden layers but not in general using just one

estimation of median income of four person families a bayesian time series approach abstract this article develops a general methodology for small domain estimation based on data from repeated surveys the results are directly applied to the estimation of median income of four person families for the 50 states and the district of columbia these estimates are needed by the u s department of health and human services hhs to formulate its energy assistance program for low income families the u s bureau of the census by an informal agreement has provided such estimates to hhs through a linear regression methodology since the latter part of the 1970s the current method is an empirical bayes method eb that uses the current population survey cps estimates as well as the most recent decennial census estimates updated by the per capita income estimates of the bureau of economic analysis however with the existing methodology standard errors associated with these estimates are not easy to obtain the eb estimates when used naively can lead to underestimation of standard errors mo

approximation dimension reduction and nonconvex optimization using linear superpositions of gaussians this paper concerns neural network approaches to function approximation and optimization using linear superposition of gaussians or what are popularly known as radial basis function rbf networks the problem of function approximation is one of estimating an underlying function f given samples of the form y sub i x sub i i 1 2 n with y sub i f x sub i when the dimension of the input is high and the number of samples small estimation of the function becomes difficult due to the sparsity of samples in local regions the authors find that this problem of high dimensionality can be overcome to some extent by using linear transformations of the input in the gaussian kernels such transformations induce intrinsic dimension reduction and can be exploited for identifying key factors of the input and for the phase space reconstruction of dynamical systems without explicitly computing the dimension and delay they present a generalization that uses multiple linear projections onto scalars and successive rbf networks mlprbf that estimate the function based on these scaler values they derive some key properties of rbf networks that provide suitable grounds for implementing efficient search strategies for nonconvex optimization within the same framework

a neural net model for prediction abstract in this article we introduce a neural net designed for nonlinear statistical prediction the net is based on a stochastic model featuring a multilayer feedforward architecture with random connections between units and noisy response functions a bayesian inferential procedure for this model based on the kalman filter is derived the resulting learning algorithm generalizes the so called onedimensional newton method an updating algorithm currently popular in the neural net literature a numerical study concerning the prediction of a noisy chaotic time series is presented and the greater predictive accuracy of the new algorithm with respect to the newton algorithm is exhibited

generalized linear models with varying dispersion summary generalized linear models are further generalized to include a linear predictor for the dispersion as well as for the mean it is shown how the convenient structure of generalized linear models can be carried over to this more general setting by considering the mean and dispersion structure separately mean and dispersion submodels are formulated for this the dependent variable for the dispersion submodel being the deviance components of the mean submodel the fact that both submodels are essentially generalized linear models themselves is used to derive simple expressions for the likelihood equations and for asymptotic tests estimation algorithms are proposed which have good convergence properties the results apply mainly to the normal inverse gaussian and gamma distributions but can be extended to discrete distributions by using quasi likelihoods the methods developed are applied to a well known data set

the fisher hartwig conjecture and toeplitz eigenvalues abstract the conjecture of fisher and hartwig published in 1968 describes the asymptotic expansion of toeplitz determinants with singular generating functions for more than twenty years progress was made in extending the validity of the conjecture but recent computer experiments led to counterexamples that show the limits of the original conjecture and pointed the way to a revised conjecture this paper describes the history of the problem several numerical examples and the revised conjecture

markov chain monte carlo for dynamic generalised linear models summary this paper presents a new methodological approach for carrying out bayesian inference about dynamic models for exponential family observations the approach is simulationbased and involves the use of markov chain monte carlo techniques a metropolishastings algorithm is combined with the gibbs sampler in repeated use of an adjusted version of normal dynamic linear models different alternative schemes based on sampling from the system disturbances and state parameters separately and in a block are derived and compared the approach is fully bayesian in obtaining posterior samples with state parameters and unknown hyperparameters illustrations with real datasets with sparse counts and missing values are presented extensions to accommodate more general evolution forms and distributions for observations and disturbances are outlined

prediction using partly conditional time varying coefficients regression models summary data collected longitudinally in time provide the opportunity to develop predictive models of future observations given current data for an individual such models may be of particular value in defining individuals at high risk and thereby in suggesting subgroups for targeting of prevention intervention research efforts in this paper we propose a method for estimating predictive functions the method uses an extension of the marginal regression analysis methods of liang and zeger 1986 biometrika73 13 22 and is implemented using simple estimating equations a key feature of the models is that regression coefficients are modelled as smooth functions of the times both at and for prediction data from a study of obesity in childhood and early adulthood is used to demonstrate the methodology criteria for defining individuals to be at high risk can be defined on the basis of estimated predictive functions we suggest methods for evaluating the diagnostic accuracy sensitivity and specificity of such rules using cross validation the method holds promise as a robust and technically easy way of evaluating information about future prognosis that may be gleaned from a patient s current and past clinical status

observer design based on triangular form generated by injective map a procedure is provided for constructing an injective map as a generalized coordinate change for triangular form transformation based on the triangular form a method is developed for designing nonlinear state observers

a multivariate growth curve model for pregnancy summary a model is proposed for consecutive multivariate observations of pregnancy related quantities for a particular mother assuming proportionality with an underlying univariate growth process apart from the longitudinal aspect of the multivariate time series the cross sectional distribution of growth curves is also discussed the model is examined as regards problems of estimation and model checking and the results are applied to data consisting of bivariate time series of symphyseal fundal distances and fetal weight estimates from 91 mothers we find some evidence in the data on departures from the model

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

linear growth curve analysis based on exponential dispersion models the paper introduces a class of linear growth curve models based on combinations of exponential dispersion models the models have three components namely a latent markov growth process with stationary and independent increments a noise component and a component describing variation between subjects the models allow a wide range of continuous discrete and mixed distributions estimation for the models is based on an estimating equation derived from an em like algorithm combined with kalman smoothing

discrete time neural net controller for a class of nonlinear dynamical systems a family of two layer discrete time neural net nn controllers is presented for the control of a class of mnth order mimo dynamical system no initial learning phase is needed so that the control action is immediate in other words the neural network nn controller exhibits a learning while functioning feature instead of a learning then control feature a two layer nn is used which is linear in the tunable weights the structure of the neural net controller is derived using a filtered error approach it is indicated that delta rule based tuning when employed for closed loop control can yield unbounded nn weights if 1 the net cannot exactly reconstruct a certain required function or 2 there are bounded unknown disturbances acting on the dynamical system certainty equivalence is not used overcoming a major problem in discrete time adaptive control in this paper new online tuning algorithms for discrete time systems are derived which are similar to spl epsiv modification for the case of continuous time systems that include a modification to the learning rate parameter and a correction term to the standard delta rule

dynamic generalized linear models and bayesian forecasting abstract dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters this leads to the calculation of closed standard form predictive distributions for forecasting and model criticism the structure of the models depends on the time evolution of underlying state variables and the feedback of observational information to these variables is achieved using linear bayesian prediction methods data analytic aspects of the models concerning scale parameters and outliers are discussed and some applications are provided dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and

a state space model for multivariate longitudinal count data summary we propose a nonstationary state space model for multivariate longitudinal count data driven by a latent gamma markov process the poisson counts are assumed to be conditionally independent given the latent process both over time and across categories we consider a regression model where time varying covariates may enter via either the poisson model or the latent gamma process estimation is based on the kalman smoother and we consider analysis of residuals from both the poisson model and the latent process a reanalysis of zeger s 1988 polio data shows that the choice between a stationary and nonstationary model is crucial for the correct assessment of the evidence of a long term decrease in the rate of u s polio infection

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

mixture based extension of the ar model and its recursive bayesian identification an extension of the autoregressive ar model is studied which allows transformations and distortions on the regressor to be handled many important signal processing problems are amenable to this extended ar i e ear model it is shown that bayesian identification and prediction of the ear model can be performed recursively in common with the ar model itself the ear model does however require that the transformation be known when it is unknown the associated transformation space is represented by a finite set of candidates what follows is a mixture based ear model i e the mear model an approximate identification algorithm for mear is developed using a restricted variational bayes vb method this restores the elegant recursive update of sufficient statistics the mear model is applied to the robust identification of ar processes corrupted by outliers and burst noise respectively and to click removal for speech

predicting neutron diffusion eigenvalues with a query based adaptive neural architecture a query based approach for adaptively retraining and restructuring a two hidden layer artificial neural network ann has been developed for the speedy prediction of the fundamental mode eigenvalue of the neutron diffusion equation a standard nuclear reactor core design calculation which normally requires the iterative solution of a large scale system of nonlinear partial differential equations pdes the approach developed focuses primarily upon the adaptive selection of training and cross validation data and on artificial neural network ann architecture adjustments with the objective of improving the accuracy and generalization properties of ann based neutron diffusion eigenvalue predictions for illustration the performance of a bare bones feedforward multilayer perceptron mlp is upgraded through a variety of techniques namely nonrandom initial training set selection adjoint function input weighting teacher student membership and equivalence queries for generation of appropriate training data and a dynamic node architecture dna implementation the global methodology is flexible in that it ran wrap around any specific training algorithm selected for the static calculations i e training iterations with a fixed training set and architecture finally the improvements obtained are carefully contrasted against past works reported in the literature

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

toeplitz eigenvalues for radon measures abstractit is well known that for toeplitz matrices generated by a suf ciently smooth real valuedsymbol the eigenvalues behave asymptotically as the values of the symbol on uniform mesheswhile the singular values even for complex valued functions do as those values in modulus these facts are expressed analytically by the szego and szego like formulas and as is provedrecently the smoothness assumptions are as mild as those of l 1 in this paper it is shownthat the szego like formulas hold true even for toeplitz matrices generated by the so calledradon measures 2002 elsevier science inc all rights reserved ams classi cation 15a12 65f10 65f15 65t10keywords toeplitz matrices eigenvalues singular values szego formulas radon measures 1 introductionwe consider a sequence of toeplitz matrices cf 3 a n a kl a kl a k l 0 k l n 1 1 constructed from the coef cients of a formal fourier series f x k a k e i kx 2 supported by the russian fund of basic research under grant 99 01 00017 and completed while the rst author was a guest professor at the university of saarland germany under support of daad

eigenvectors of hermitian toeplitz matrices with smooth simple loop symbols abstract the paper is devoted to the structure and the asymptotics of the eigenvector matrix of hermitian toeplitz matrices with moderately smooth symbols which trace out a simple loop on the real line the results extend existing results on banded toeplitz matrices to full toeplitz matrices with temperate decay of the entries in the first row and column we establish formulas for both the exact and the asymptotic computation of arbitrarily prescribed individual components of arbitrarily prescribed individual eigenvectors these formulas are in terms of the wiener hopf factorization of a function which depends solely on the symbol and the corresponding eigenvalue or even only on an approximation to this eigenvalue the paper does not aim at providing numerical algorithms its main purpose is rather to reveal the structure underneath the eigenvectors which are shown to be the sum of two harmonics and certain edge corrections

a generalization of the kalman filter for models with state dependent observation variance abstract the kalman filter is generalized to cover state space models in which the variance of the observation error depends on the state vector derivations of the filter yielding minimum mean squared error linear estimators and associated error covariance matrices are obtained from two differing viewpoints linear bayes theory and gauss markov theory the results are applied to a model for which y t t 1 2 n follow a poisson distribution with corresponding intensities t t 1 2 n that are assumed to follow an autoregressive process of order 1 namely the steady state generalized kalman filter algorithm in the case for which 1 gives a generalization of exponential smoothing for a poisson process with time varying intensity

robust recursive estimation in the presence of heavy tailed observation noise a first order approximation is derived for the conditional prior distribution of the state of a discrete time stochastic linear dynamic system in the presence of contaminated normal observation noise this distribution is then used to derive a first order approximation of the conditional mean minimum variance estimator if the observation noise distribution can be represented as a member of the e contaminated normal neighborhood then the conditional prior is also to first order an analogous perturbation from a normal distribution whose first two moments are given by the kalman filter moreover the perturbation is itself of a special form combining distributions whose parameters are given by banks of parallel kalman filters and optimal smoothers

leave k out diagnostics for time series abstract the authors propose diagnostics for arima model fitting for time series formed by deleting observations from the data and measuring the change in the estimates of the parameters the use of leave one out diagnostics is a well established tool in regression analysis this document demonstrates the efficacy of observation deletion based diagnostics for arima models addressing issues special to the time diagnostics based on the innovations variance it is shown that the dependency aspect of time series data gives rise to a smearing effect which confounds the diagnostics for the coefficients it is also shown that the diagnostics based on the innovations variance are much clearer and more sensitive than those for the coefficients a leave k out diagnostics approach is proposed to deal with patches of outliers and problems caused by masking are handled by use of iterative deletion an overall strategy for arima model fitting is given and applied to two data sets

dispersion models and longitudinal data analysis dispersion models provide a flexible class of non normal distributions with many potential applications in biostatistics accommodating a wide range of continuous discrete and mixed data starting with liang and zeger s generalized estimating equation method we review some recent applications of dispersion models in longitudinal data analysis including state space models based on the tweedie class of exponential dispersion models in medical applications the latent process of a state space model may often be interpreted as an unobserved potential morbidity process which is modelled as a function of time varying covariates by allowing a multivariate response vector of symptoms the model integrates several response variables of mixed types into a single model for growth curve models the latent process reflects the true growth

a review of some extensions to generalized linear models although generalized linear models are reasonably well known they are not as widely used in medical statistics as might be appropriate with the exception of logistic log linear and some survival models at the same time the generalized linear modelling methodology is decidedly outdated in that more powerful methods involving wider classes of distributions non linear regression censoring and dependence among responses are required limitations of the generalized linear modelling approach include the need for the iterated weighted least squares iwls procedure for estimation and deviances for inferences these restrict the class of models that can be used and do not allow direct comparisons among models from different distributions powerful non linear optimization routines are now available and comparisons can more fruitfully be made using the complete likelihood function the link function is an artefact necessary for iwls to function with linear models but that disappears once the class is extended to truly non linear models restricting comparisons of responses under different treatments to differences in means can be extremely misleading if the shape of the distribution is changing this may involve changes in dispersion or of other shape related parameters such as the skewness in a stable distribution with the treatments or covariates any exact likelihood function defined as the probability of the observed data takes into account the fact that all observable data are interval censored thus directly encompassing the various types of censoring possible with duration type data in most situations this can now be as easily used as the traditional approximate likelihood based on densities finally methods are required for incorporating dependencies among responses in models including conditioning on previous history and on random effects one important procedure for constructing such likelihoods is based on kalman filtering

forecasting turning points in international output growth rates using bayesian exponentially weighted autoregression time varying parameter and pooling techniques abstract in this paper two variants of an autoregressive leading indicator arli model are employed to forecast turning points in the growth rates of 18 countries annual real output for the years 1974 1986 bayesian predictive densities have been employed to compute probabilities of downturns and upturns and they have been employed in a bayesian decision theoretic framework to obtain optimal turning point forecasts various versions of the arli model with and without pooling of data across countries produced about 70 to 80 percent correct forecasts for 158 turning points time varying parameter models performed slightly better than others the performance of the arli models in forecasting turning points is shown to be considerably better than that of four naive methods of forecasting turning points

neural network approximation of piecewise continuous functions application to friction compensation one of the most important properties of neural nets nns for control purposes is the universal approximation property unfortunately this property is generally proven for continuous functions in most real industrial control systems there are nonsmooth functions e g piecewise continuous for which approximation results in the literature are sparse examples include friction deadzone backlash and so on it is found that attempts to approximate piecewise continuous functions using smooth activation functions require many nn nodes and many training iterations and still do not yield very good results therefore a novel neural network structure is given for approximation of piecewise continuous functions of the sort that appear in friction deadzone backlash and other motion control actuator nonlinearities the novel nn consists of neurons having standard sigmoid activation functions plus some additional neurons having a special class of nonsmooth activation functions termed jump approximation basis function two types of nonsmooth jump approximation basis functions are determined a polynomial like basis and a sigmoid like basis this modified nn with additional neurons having jump approximation activation functions can approximate any piecewise continuous function with discontinuities at a finite number of known points applications of the new nn structure are made to rigid link robotic systems with friction nonlinearities friction is a nonlinear effect that can limit the performance of industrial control systems it occurs in all mechanical systems and therefore is unavoidable in control systems it can cause tracking errors limit cycles and other undesirable effects often inexact friction compensation is used with standard adaptive techniques that require models that are linear in the unknown parameters it is shown here how a certain class of augmented nn capable of approximating piecewise continuous functions can be used for friction compensation

robust sequential approximate bayesian estimation summary an approximation to the sequential updating of the distribution of location parameters of a linear time series model is developed for non normal observations the behaviour of the resulting non linear recursive filtering algorithm is examined and shown to have certain desirable properties for a variety of non normal error distributions illustrative examples are given and relationships with previous work on robustness and sequential estimation are mentioned we consider here the problem of sequential estimation of the location vector of a linear time series model termed the dynamic linear model by harrison and stevens 1976 the straightforward exact analysis obtained by assuming normal error and prior structure is generally lost when alternative error distributions are adopted and yet considerations of realism or robustness may strongly suggest such non normal assumptions the multi state model of harrison and stevens provides an approximate analysis based on a discrete variance mixture of normal distributions an approach which has been extensively investigated in the engineering literature under the name of gaussian sum approximations see for example alspach and sorenson 1971 our aim in this paper is to provide an approximate tractible recursive updating procedure for the location parameters which is applicable to a wide range of symmetric unimodal error distributions and is both more realistic and more elegant than the discrete gaussian sum approach in particular for heavy tailed distributions our procedures provide approximate bayesian methods for time series analysis which extend considerably the work of masreliez and martin 1977 and have close connections with classical robustness ideas such as m estimation and influence functions

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

cyclic displacements and decompositions of inverse matrices for cupl toeplitz matrices abstract in this paper we deal mainly with a class of cupl toeplitz matrices 32 without toeplitz structure which are close to the toeplitz matrices in the sense that their 1 1 cyclic displacements coincide with cyclic displacement of some toeplitz matrices by constructing the corresponding displacement of the matrices we derive the formulas on representation of the inverses of the cupl toeplitz matrices in the form of sums of products of factor row first plus last right circulants furthermore the inverses of the cupl hankel matrices can be also obtained which benefits from the relation between the cupl toeplitz matrices and the cupl hankel matrices

asymptotic controllability and exponential stabilization of nonlinear control systems at singular points we discuss the relation between exponential stabilization and asymptotic controllability of nonlinear control systems with constrained control range at singular points using a discounted optimal control approach we construct discrete feedback laws minimizing the lyapunov exponent of the linearization thus we obtain an equivalence result between uniform exponential controllability and uniform exponential stabilizability by means of a discrete feedback law

some properties and generalizations of non negative bayesian time series models we study the most basic bayesian forecasting model for exponential family time series the power steady model psm of smith in terms of observable properties of one step forecast distributions and sample paths the psm implies a constraint between location and spread of the forecast distribution including a scale parameter in the models does not always give an exact solution free of this problem but it does suggest how to define related models free of the constraint we define such a class of models which contains the psm we concentrate on the case where observations are non negative probability theory and simulation show that under very mild conditions almost all sample paths of these models converge to some constant making them unsuitable for modelling in many situations the results apply more generally to non negative models defined in terms of exponentially weighted moving averages we use these and related results to motivate define and apply very simple models based on directly specifying the forecast distributions

a neural state estimator with bounded errors for nonlinear systems a neural state estimator is described acting on discrete time nonlinear systems with noisy measurement channels a sliding window quadratic estimation cost function is considered and the measurement noise is assumed to be additive no probabilistic assumptions are made on the measurement noise nor on the initial state novel theoretical convergence results are developed for the error bounds of both the optimal and the neural approximate estimators to ensure the convergence properties of the neural estimator a minimax tuning technique is used the approximate estimator can be designed offline in such a way as to enable it to process on line any possible measure pattern almost instantly

on the linearity of bayesian interpolators for non gaussian continuous time ar 1 processes bayesian estimation problems involving gaussian distributions often result in linear estimation techniques nevertheless there are no general statements as to whether the linearity of the bayesian estimator is restricted to the gaussian case the two common strategies for non gaussian models are either finding the best linear estimator or numerically evaluating the bayesian estimator by monte carlo methods in this paper we focus on bayesian interpolation of non gaussian first order autoregressive ar processes where the driving innovation can admit any symmetric infinitely divisible distribution characterized by the levy khintchine representation theorem we redefine the bayesian estimation problem in the fourier domain with the help of characteristic forms by providing analytic expressions we show that the optimal interpolator is linear for all symmetric stable distributions the bayesian interpolator can be expressed in a convolutive form where the kernel is described in terms of exponential splines we also show that the limiting case of levy type ar 1 processes the system of which has a pole at the origin always corresponds to a linear bayesian interpolator made of a piecewise linear spline irrespective of the innovation distribution finally we show the two mentioned cases to be the only ones within the family for which the bayesian interpolator is linear

a self organizing state space model a self organizing filter and smoother for the general nonlinear non gaussian state space model is proposed an expanded state space model is defined by augmenting the state vector with the unknown parameters of the original state space model the state of the augmented state space model and hence the state and the parameters of the original state space model are estimated simultaneously by either a non gaussian filter smoother or a monte carlo filter smoother in contrast to maximum likelihood estimation of model parameters in ordinary state space modeling for which the recursive filter computation has to be done many times model parameter estimation in the proposed self organizing filter smoother is achieved with only two passes of the recursive filter and smoother operations examples such as automatic tuning of dispersion and the shape parameters adaptation to changes of the amplitude of a signal in seismic data state estimation for a nonlinear state space model with unknown parameters and seasonal adjustment with a nonlinear model with changing variance parameters are shown to exemplify the usefulness of the proposed method

robustification of kalman filter models abstract kalman filter models based on the assumption of multivariate gaussian distributions are known to be nonrobust this means that when a large discrepancy arises between the prior distribution and the observed data the posterior distribution becomes an unrealistic compromise between the two in this article we discuss a rationale for how to robustify the kalman filter specifically we develop a model wherein the posterior distribution will revert to the prior when extreme outlying observations are encountered and we point out that this can be achieved by assuming a multivariate distribution with student t marginals to achieve fully robust results of the kind desired it becomes necessary to forsake an exact distribution theory approach and adopt an approximation method involving poly t distributions a recursive mechanism for implementing the multivariate t based kalman filter is described its properties are discussed and the procedure is illustrated by an example