finite dimensional backward shift invariant subspaces of arveson spaces a description is given of finite dimensional backward shift invariant subspaces of arveson spaces which are certain multivariable analogues of the hardy space of the unit disk

superconvergent patch recovery with equilibrium and conjoint interpolant enhancements the superconvergent patch derivative recovery method of zienkiewicz and zhu is enhanced by adding the squares of the residuals of the equilibrium equation and natural boundary conditions in addition a new conjoint polynomial for interpolating the local patch stresses over the element which significantly improves the local projection scheme is presented results show that in the 4 node quadrilateral the equilibrium and boundary condition residuals usually improve accuracy but not the rate of convergence whereas in the 9 node quadrilateral results are mixed the conjoint polynomial always improves the accuracy of the derivative field within the element as compared to the standard nodal interpolation particularly in 4 node quadrilaterals

bootstrap confidence bands for shrinkage estimators empirical application of shrinkage estimators has been limited by the inability to estimate confidence intervals we investigate confidence band estimators based on edgeworth expansions and bootstrapping our monte carlo results suggest that both efron s bias correction method with acceleration and the simple percentile bootstrap methods generate reasonable confidence bands approximations based on edgeworth expansions performed poorly we then use the percentile method with a single bootstrap to generate bands for predictions of gnp growth rates from a leading indicators model our study shows that simple percentile bootstrap confidence bands perform well enough to support empirical applications of shrinkage estimators

patch recovery based on superconvergent derivatives and equilibrium in this paper a postprocessing technique is developed for determining first order derivatives fluxes stresses at nodal points based on derivatives in superconvergent points it is an extension of the superconvergent patch recovery technique presented by zienkiewicz and zhu in contrast to that technique all flux or stress components are interpolated at the same time coupled by equilibrium equations at the superconvergent points the equilibrium equations and use of one order higher degree of interpolation polynomials of stress give a dramatic decrease in error of recovered derivatives even at boundaries

can the random walk model be beaten in out of sample density forecasts evidence from intraday foreign exchange rates abstract it has been documented that random walk outperforms most economic structural and time series models in out of sample forecasts of the conditional mean dynamics of exchange rates in this paper we study whether random walk has similar dominance in out of sample forecasts of the conditional probability density of exchange rates given that the probability density forecasts are often needed in many applications in economics and finance we first develop a nonparametric portmanteau test for optimal density forecasts of univariate time series models in an out of sample setting and provide simulation evidence on its finite sample performance then we conduct a comprehensive empirical analysis on the out of sample performances of a wide variety of nonlinear time series models in forecasting the intraday probability densities of two major exchange rates euro dollar and yen dollar it is found that some sophisticated time series models that capture time varying higher order conditional moments such as markov regime switching models have better density forecasts for exchange rates than random walk or modified random walk with garch and student t innovations this finding dramatically differs from that on mean forecasts and suggests that sophisticated time series models could be useful in out of sample applications involving the probability density

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

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

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

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

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

derivative superconvergence of rectangular finite elements for the reissner mindlin plate abstract the finite element method with rectangular meshes for the reissner mindlin plate is analyzed for a plate with thickness bounded below by a positive constant moderately thick plate derivative superconvergence of the finite element solution at the gaussian points is justified and optimal error estimates for both rotation and displacement are established

testing for causality in real time a framework for testing in real time on line the statistical significance of the causality between nonstationary random processes is developed the process representation is that of transfer function tf arma models the causality parameters are prediction error variances and dynamic multipliers the estimation algorithm is that of recursive nonlinear least squares rnls the basic step is made by analyzing the asymptotic distribution of this estimator under an assumption of stationary but in operative conditions given by discounting past observations with exponential weights ew an empirical example based on real economic time series illustrates and checks the method of on line inference

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

the schur algorithm and reproducing kernel hilbert spaces in the ball abstract using reproducing kernel hilbert spaces methods we develop a schur type algorithm for a subclass of the functions analytic and contractive in the ball we also consider the nevanlinna pick interpolation problem in that class

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

backward shift operator and finite dimensional de branges rovnyak spaces in the ball recently bolotnikov and rodman characterized finite dimensional backward shift invariant subspaces of the arveson space in this note we study finite dimensional backward shift invariant hilbert spaces contractively included in the arveson space to that purpose we redefine in an appropriate way the backward shift operators in terms of power series expansions

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

boundary interpolation in the ball we solve a boundary interpolation problem in the reproducing kernel hilbert space of functions analytic in the unit ball of cn with reproducing kernel 1 1 1nzkwk we introduce the notion of brune factor or blaschke potapov factor of the third kind in this setting

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

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

comparing dynamic equilibrium models to data a bayesian approach abstract this paper studies the properties of the bayesian approach to estimation and comparison of dynamic equilibrium economies both tasks can be performed even if the models are nonnested misspecified and nonlinear first we show that bayesian methods have a classical interpretation asymptotically the parameter point estimates converge to their pseudotrue values and the best model under the kullback leibler distance will have the highest posterior probability second we illustrate the strong small sample behavior of the approach using a well known application the u s cattle cycle bayesian estimates outperform maximum likelihood results and the proposed model is easily compared with a set of bvars

forecasting and turning point predictions in a bayesian panel var model we provide methods for forecasting variables and predicting turning points in panel bayesian vars we specify a flexible model which accounts for both interdependencies in the cross section and time variations in the parameters posterior distributions for the parameters are obtained for hierarchical and for minnesota type priors formulas for multistep multiunit point and average forecasts are provided an application to the problem of forecasting the growth rate of output and of predicting turning points in the g 7 illustrates the approach a comparison with alternative forecasting methods is also provided

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

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

a full 3d finite element analysis using adaptive refinement and pcg solver with back interpolation in this paper adaptive refinement finite element analyses were carried out for full 3d problems in order to achieve an optimal computation cost and to eliminate the effects of singular points the adaptive refinement procedure was applied in conjunction with a back interpolation for the construction of a good initial guess for the solution of the linear equations system the combined use of the adaptive refinement procedure the back interpolation scheme and the preconditioned conjugate gradient pcg solver lead to a significant reduction in the operations for the solution of the simultaneous linear equations in the adaptive refinement analysis in many cases the number of iterations needed by the pcg solver to reach a converged solution is independent of the number of equations in the global system the numerical results obtained indicated that for a series of carefully designed adaptive meshes the computational cost required to solve the linear system could be made only proportional to the number of degrees of freedom in the mesh to our knowledge this is the first time that the global stiffness equations in 3d stress analysis have been solved with this efficiency the same set of numerical results also showed that in general the total computational cost of the adaptive refinement procedure can usually be minimized by gradually reducing the target relative error of the solution during successive refinements rather than employing a constant target relative error throughout the whole adaptive analysis

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

caratheodory fejer interpolation in the ball with mixed derivatives we use reproducing kernel hilbert space methods to solve a caratheodory fejer type interpolation problem with mixed derivatives corresponding to a so called lower inclusive set in the class of schur multipliers

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

forecasting with nonstationary dynamic factor models abstract in this paper we analyze the structure and the forecasting performance of the dynamic factor model it is shown that the forecasts obtained by the factor model imply shrinkage pooling terms similar to the ones obtained from hierarchical bayesian models that have been applied successfully in the econometric literature thus the results obtained in this paper provide an additional justification for these and other types of pooling procedures the expected decrease in mse for using a factor model versus univariate arima and shrinkage models are studied for the one factor model monte carlo simulations are presented to illustrate this result a factor model is also built to forecast gnp of european countries and it is shown that the factor model can provide a substantial improvement in forecasts with respect to both univariate and shrinkage univariate forecasts

error estimates and convergence rates for various incompressible elements this note reports numerical experiments on the efficiency of simple error estimates derived earlier1 applied to incompressible mixed or related penalty type formulations the rate of convergence and performance of various mixed elements is compared numerical results from a driven cavity and an incompressible elastic problem demonstrate that the t6b1 3d and t6 3c elements give a faster rate of convergence than the t6 1d element however in the case of a plane extrusion analysis stronger singularity the rate of convergence for the t6b1 3d element drops and is inferior to that of the t6 1d while the t6 3c element still proves superior to the other two elements

the curvature of a hilbert module over ℂ z1 zd a notion of curvature is introduced in multivariable operator theory the curvature invariant of a hilbert module over z1 zd is a nonnegative real number which has significant extremal properties which tends to be an integer and which is hard to compute directly it is shown that for graded hilbert modules the curvature agrees with the euler characteristic of a certain finitely generated algebraic module over the appropriate polynomial ring this result is a higher dimensional operator theoretic counterpart of the gauss bonnet formula which expresses the average gaussian curvature of a compact oriented riemann surface as the alternating sum of the betti numbers of the surface and it solves the problem of calculating the curvature of graded hilbert modules the proof of that result is based on an asymptotic formula which expresses the curvature of a hilbert module in terms that allow its comparison to a corresponding asymptotic expression for the euler characteristic

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

on constructing accurate recovered stress fields for the finite element solution of reissner mindlin plate bending problems the effectiveness and reliability of three local least squares fit procedures for the construction of smoothed moments and shear forces for the solution of the reissner mindlin rm thick plate model are reviewed the three procedures considered are namely the superconvergent patch recovery technique spr the recovery by equilibrium in patches rep and the recovery procedure suggested by lee park and lee lp numerical studies are carried out by applying these three recovery procedures for the construction of smoothed stress fields for various rm plate bending problems the results obtained indicate that if the order of polynomial used in the stress recovery is the same as that for the finite element analysis all three procedures produce recovered stress fields with very similar accuracy and convergence rate however when the order of polynomial is raised if the exact solution is smooth without any strong boundary layers or singularities both the rep and lp procedures can produce more accurate stress fields than the spr in case that singularities or boundary layers are present the lp procedure often outperforms the rep procedure and results in more stable recovery matrices and more accurate recovered stress fields

rational hyperholomorphic functions in r4 we introduce the notion of rationality for hyperholomorphic functions functions in the kernel of the cauchy fueter operator following the case of one complex variable we give three equivalent definitions the first in terms of cauchy kovalevskaya quotients of polynomials the second in terms of realizations and the third in terms of backward shift invariance also introduced and studied are the counterparts of the arveson space and blaschke factors

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

common correlated effects estimation of heterogeneous dynamic panel data models with weakly exogenous regressors abstract this paper extends the common correlated effects cce approach developed by pesaran 2006 to heterogeneous panel data models with lagged dependent variables and or weakly exogenous regressors we show that the cce mean group estimator continues to be valid but the following two conditions must be satisfied to deal with the dynamics a sufficient number of lags of cross section averages must be included in individual equations of the panel and the number of cross section averages must be at least as large as the number of unobserved common factors we establish consistency rates derive the asymptotic distribution suggest using covariates to deal with the effects of multiple unobserved common factors and consider jackknife and recursive de meaning bias correction procedures to mitigate the small sample time series bias theoretical findings are accompanied by extensive monte carlo experiments which show that the proposed estimators perform well so long as the time series dimension of the panel is sufficiently large

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

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

dynamic hierarchical models an analysis of a time series of cross sectional data is considered under a bayesian perspective information is modelled in terms of prior distributions and stratified parametric linear models developed by lindley and smith and dynamic linear models developed by harrison and stevens are merged into a general framework this is shown to include many models proposed in econometrics and experimental design properties of the model are derived and shrinkage estimators reassessed evolution smoothing and passage of data information through the levels of the hierarchy are discussed inference with an unknown scalar observation variance is drawn and an extension to the non linear case is proposed

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

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

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

error estimates and adaptive refinement for plate bending problems the zienkiewicz zhu error estimator is shown to be effective in problems of plate flexure when used in conjunction with triangular elements and an adaptive mesh generator allowing a prescribed size of elements to be developed very fast adaptive convergence for results of specified accuracy is achieved

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

application of the zienkiewicz zhu error estimator for plate and shell analysis the global error in energy norm is computed by summing all the elemental errors the method is well suited for adaptive mesh refinement as the error contribution for each element is known demonstration examples using uniform and adaptive refinement schemes for both the plate and shell analysis show the effectiveness of the method proposed

invariant subspaces and nevanlinna pick kernels abstract a theorem of beurling lax halmos represents a subspace m of h2 c d the hardy space of analytic functions with values in the hilbert space e and square summable power series invariant for multiplication by z as h2 f where f is a subspace of e and is an inner function with values in l f e when the hardy space is replaced by the hilbert space h k determined by a nevanlinna pick kernel k such as the dirichlet kernel or the row contraction kernel on the ball in c d the blh theorem survives with f an auxiliary hilbert space and a l f e valued function which is inner in the sense that the operator m of multiplication by is a partial isometry under mild additional hypotheses when e c mz the operator of multiplication by z is cellularly indecomposable and has the codimension one property however if m is invariant for mz m mz m need not be a cyclic subspace for mz restricted to m

a study of boundary layers in plates using mindlin reissner and 3 d elements finite elements based on mindlin reissner theory and three dimensional theory are used to study the distribution of shear forces and twisting moments in plates with various simple support conditions differences between the results obtained using these two theories are highlighted a crude adaptive mesh refinement procedure is applied to improve the accuracy of the finite element analysis

complementation in krein spaces a generalization of the concept of orthogonal complement is introduced in complete and decomposable complex vector spaces with scalar product complementation is a construction in the geometry of hilbert space which was applied to the invariant subspace theory of contractive transformations in hilbert space by james rovnyak and the author 6 the concept was later formalized by the author 3 continuous and contractive transformations in krein spaces appear in the estimation theory of riemann mapping functions 4 it is therefore of interest to know whether a generalization of complementation theory applies in krein spaces such a generalization is now obtained the results are also of interest in the invariant subspace theory of continuous and contractive transformations in krein spaces 5 the vector spaces considered are taken over the complex numbers a scalar product for a vector space 1 is a complex valued function a b of a and b in 1 which is linear symmetric and nondegenerate linearity means that the identity aa 3b c a a c 3 b c holds for all elements a b and c of 1 when a and are complex numbers symmetry means that the identity b a a b holds for all elements a and b of 1 nondegeneracy means that an element a of 1 is zero if the scalar product a b is zero for every element b of 1 every element b of 1 determines a linear functional bon 1 which is defined by b a a b for every element a of 1 the weak topology of 1 is the weakest topology with respect to which bis a continuous linear functional on 1 for every element b of 1 the weak topology of 1 is a locally convex topology having the property that every continuous linear functional on 1 is of the form bfor an element b of 1 the element b is then unique the antispace of a vector space with scalar product is the same vector space considered with the negative of the given scalar product a fundamental example of a vector space with scalar product is a hilbert space a krein space is a vector space with scalar product which is the orthogonal sum of a hilbert space and the antispace of a hilbert space received by the editors october 10 1986 and in revised form february 23 1987 the results of the paper were presented to the department of mathematics indiana and purdue university in indianapolis on march 27 1987 as the ernest j johnson colloquium 1980 mathematics subject classification 1985 revision primary 46d05 research supported by the national science foundation 1988 american mathematical society 0002 9947 88 1 00 25 per page

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

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

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

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