asymptotic behaviour of some bootstrap estimators the aim of this paper is to present a theoretical analysis of three bootstrap estimators commonly used in system identification the main results concern the local convergence and accuracy properties of the estimators both iterative and on line versions are examined

identification of continuous time models the paper considers the problem of estimation of the transfer function of a continuous time dynamic system in the presence of colored noise the author introduces an operator transformation that allows for keeping a continuous time parametrization whereas the parameter estimation can be made by means of a discrete time maximum likelihood algorithm a comparison is made between the performance of the new method in comparison with a standard identification of an armax model the method is useful in cases where it is important to estimate the coefficients of a continuous time transfer function and where it is important to maintain a physical interpretation of the transfer function results

identification of multivariable errors in variable models with dynamics this note considers the task of identifying a causal linear dynamic multivariable system excited by stationary zero mean noise of unknown spectrum and given measurements of the system inputs and outputs contaminated by independent additive noise also of unknown spectra although the solution is in general not unique finite dimensional parameterizations of the solution set are given even though the various spectra may not be rational

transitional regression models with application to environmental time series abstract environmental epidemiologists often encounter time series data in the form of discrete or other nonnormal outcomes for example in modeling the relationship between air pollution and hospital admissions or mortality rates we present a case study examining the association between pollen counts and meteorologic covariates although such time series data are inadequately described by standard methods for gaussian time series they are often autocorrelated and warrant an analysis beyond those provided by ordinary generalized linear models glms transitional regression models trms signifying nonlinear regression models expressed in terms of conditional means and variances given past observations provide a unifying framework for two mainstream approaches to extending the glm for autocorrelated data the first approach models current outcomes with a glm that incorporates past outcomes as covariates whereas the second models individual outcomes with marginal glms and then couples the error term

comments on transfer function synthesis using frequency response data frequency response data constitute a good basis for transfer function synthesis when using appropriate techniques for frequency response approximation not all of the numerous existing methods yield excellent results whitfield 1986 discussed various methods with the aid of examples his statement that the frequency approximation technique of stahl 1984 often yields divergent results is only correct when using the iterative matrix adaptation method in conjunction with the least squares cost function however applying the direct solution method as introduced by stahl 1984 all the approximation results of whitfield 1986 can be improved

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

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

asymptotic behaviour of transfer function synthesis methods this paper presents an analysis of the asymptotic behaviour of the solutions to various iterative linear least squares methods that synthesize transfer functions from frequency response data the methods of sanathanan and koerner and lawrence and rogers are shown to possess asymptotic solutions that do not coincide with the solution to a fundamental non linear least squares criterion several methods with more appropriate asymptotic behaviour are then suggested the analytical tools presented should allow analysis of conditions for the convergence of iterative linear least squares methods

brief paper frequency domain maximum likelihood estimation of linear dynamic errors in variables models this paper studies the linear dynamic errors in variables problem for filtered white noise excitations first a frequency domain gaussian maximum likelihood ml estimator is constructed that can handle discrete time as well as continuous time models on a part s of the unit circle or imaginary axis next the ml estimates are calculated via a computationally simple and numerically stable gauss newton minimization scheme finally the cramer rao lower bound is derived

plant rational transfer approximation from input output data a rational transfer function model of the plant is generally desirable in feedback system design when only plan input and output data are available over finite sometimes incomplete time intervals this is especially so in a recent exact design technique for highly uncertain time varying and non linear plants here the plants are replaced rigorously by an equivalent linear time invariant plant set existing numerical techniques were found inadequate especially in the high frequency range which is important in the design of feedback systems with large plant uncertainty a technique was developed with excellent results even for noisy data unstable and non minimum phase plants and severely truncated time intervals the transfer function is calculated directly without derivation of the input output signal transforms the operations involve repeated integrations of the data numerous examples are included

brief paper on the identifiability of errors in variables models with white measurement errors we discuss identifiability of dynamic siso errors in variables eiv models with white measurement errors although this class of models turns out to be generically identifiable it has been pointed out that in certain circumstances there may be two eiv models which are indistinguishable from external input output experiments this lack of global identifiability may be prejudicial to identification and needs better understanding the identifiability conditions found in the literature guarantee uniqueness under certain coprimality assumptions on the rational transfer function of the ideal true system and the spectral density of the noiseless true input unfortunately these conditions are not testable since they concern precisely the unknowns of the problem which are not available to the experimenter we provide new identifiability conditions which are instead expressible in terms of the external description of the observable signals namely their joint power spectral densities

frequency domain system identification using arbitrary signals it is the common conviction that frequency domain system identification suffers from the drawback that it cannot handle arbitrary signals without introducing systematic errors this paper shows that it is possible to deal with nonperiodic signals without any approximation and under the same assumptions as in the time domain by estimating simultaneously some initial conditions and the system model parameters

reconstruction of linear and non linear continuous time system models from input output data using the kernel invariance algorithm abstract a new kernel invariance algorithm kia is introduced to determine both the significant model terms and estimate the unknown parameters in non linear continuous time differential equation models of unknown systems

generalized autoregressive moving average models a class of generalized autoregressive moving average garma models is developed that extends the univariate gaussian arma time series model to a flexible observation driven model for non gaussian time series data the dependent variable is assumed to have a conditional exponential family distribution given the past history of the process the model estimation is carried out using an iteratively reweighted least squares algorithm properties of the model including stationarity and marginal moments are either derived explicitly or investigated using monte carlo simulation the relationship of the garma model to other models is shown including the autoregressive models of zeger and qaqish the moving average models of li and the reparameterized generalized autoregressive conditional heteroscedastic garch model providing the formula for its fourth marginal moment not previously derived the model is demonstrated by the application of the garma model with a negative binomial conditional distribution to

strongly consistent coefficient estimate for errors in variables models for the single input single output siso errors in variables system it is assumed that the system input is an arma process and that the driven noise of the system input and the observation noise are jointly gaussian the two dimensional observation made on system input and output is represented as a two dimensional 2d arma system of minimum phase driven by a sequence of 2d i i d gaussian random vectors innovation representation it is shown that the resulting arma system is identifiable i e its coefficients are uniquely defined under reasonable conditions recursive algorithms are proposed for estimating coefficients of the arma representation including those contained in the original siso system the estimates are proved to be convergent to the true values with probability one and the convergence rate is derived as well the theoretical results are justified by numerical simulation

identification of errors in variables systems with arma observation noises abstract the purpose of the paper is to give the recursive estimate for coefficients of the single input single output siso errors in variables eiv system and to prove its strong consistency the observation noises of the eiv system are assumed to be arma processes and the system input is taken to be an iid sequence the recursive estimation algorithm is given with the help of stochastic approximation sa method and the strong consistency is established under reasonable conditions the numerical simulation is consistent with the theoretical analysis

note on the relation between pole zero location and input output behaviour of siso systems and its influence on controller design linear time invariant completely controllable and observable systems can be described for example by state equations transfer functions or time responses due to specific test signals all these descriptions are uniquely related for a given system where different state representations are possible by use of equivalence transformations however a whole class of different systems characterized by an infinite number of different pole zero patterns exhibits the same input output behaviour within drawing accuracy i e the plots coincide to the point of indistinguishability this effect is demonstrated and it may have implications on such fields as system modelling model order reduction and controller design

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

the traveling salesman problem on cubic and subcubic graphs we study the traveling salesman problem tsp on the metric completion of cubic and subcubic graphs which is known to be np hard the problem is of interest because of its relation to the famous 4 3 conjecture for metric tsp which says that the integrality gap i e the worst case ratio between the optimal value of a tsp instance and that of its linear programming relaxation the subtour elimination relaxation is 4 3 we present the first algorithm for cubic graphs with approximation ratio 4 3 the proof uses polyhedral techniques in a surprising way which is of independent interest in fact we prove constructively that for any cubic graph on n vertices a tour of length 4n 3 2 exists which also implies the 4 3 conjecture as an upper bound for this class of graph tsp recently momke and svensson presented an algorithm that gives a 1 461 approximation for graph tsp on general graphs and as a side result a 4 3 approximation algorithm for this problem on subcubic graphs also settling the 4 3 conjecture for this class of graph tsp the algorithm by momke and svensson is initially randomized but the authors remark that derandomization is trivial we will present a different way to derandomize their algorithm which leads to a faster running time all of the latter also works for multigraphs

a nonstationary negative binomial time series with time dependent covariates enterococcus counts in boston harbor boston harbor has a history of poor water quality including contamination by enteric pathogens we conduct a statistical analysis of data collected by the massachusetts water resources authority mwra between 1996 and 2002 to evaluate the effects of court mandated improvements in sewage treatment motivated by the ineffectiveness of standard poisson mixture models and their zero inflated counterparts we propose a new negative binomial model for time series of enterococcus counts in boston harbor where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor without further restrictions this function is not identifiable in the presence of time dependent covariates consequently we use a basis orthogonal to the space spanned by the covariates and use penalized quasi likelihood pql for estimation we conclude that enterococcus counts were greatly reduced near the nut island treatment plant nitp outfalls following the transfer of wastewaters fro

dynamic errors in variables systems with three variables abstract errors in variables problems are considered for the case of three variables where the underlying relations among the noise free variables are linear and covariance information for the noisy variables is available the static problem where the variables are complex which can arise when narrowband filtering is used is analysed in detail some results are also presented for the case when the linear relations among the variables are defined by dynamic transfer functions

integral equation approach to system identification this paper presents an integral equation approach to the problem of parameter identification in continuous linear siso mimo and linear in parameters nonlinear systems parameter estimates are deduced from an appropriate set of overdetermined equations which are solved in a least squares sense the effects of deterministic disturbances at system input and output are also included in the analysis

frequency response computation via trigonometric continued fraction an efficient algorithm for computing the frequency response of discrete time systems described by rational transfer functions is presented the algorithm is simple fast recursive and can be used for equally or unequally spaced frequencies based on an initial expansion of the system transfer function to a novel jacobi type trigonometric continued fraction the algorithm proposed permits all operations to be performed by real arithmetic guarantees real results saves a number of operations and produces accurate results the algorithm is easily programmable and needs only 2nn real multiplications divisions for evaluating the frequency response of an nth order system at n different frequencies

stochastic system identification with noisy input output measurements using polyspectra two new classes of parametric frequency domain approaches are proposed for estimation of the parameters of scalar linear errors in variables models i e linear systems where measurements of both input and output of the system are noise contaminated the first approach consists of linear estimators where using the bispectrum or the integrated polyspectrum of the input and the cross bispectrum or the integrated cross polyspectrum the system transfer function is first estimated at a number of frequencies exceeding one half the number of unknown parameters the estimated transfer function is then used to estimate the unknown parameters using an overdetermined linear system of equations in the second class of approaches quadratic transfer function matching criteria are optimized by using the results of the linear estimators as initial guesses both classes of the parameter estimators are shown to be consistent in any measurement noise that has symmetric probability density function when the bispectral approaches are used the proposed parameter estimators are shown to be consistent in gaussian measurement noise when trispectral approaches are used

identification of dynamic errors in variables models this paper deals with the identifiability of scalar dynamic errors in variables models characterized by rational spectra the hypothesis of causality for the underlying dynamic system is taken into account by making use of stochastic realization theory and of the structural properties of state space representations it is shown that under mild assumptions the model is uniquely identified

monte carlo maximum likelihood estimation for non gaussian state space models state space models are considered for observations which have non gaussian distributions we obtain accurate approximations to the loglikelihood for such models by monte carlo simulation devices are introduced which improve the accuracy of the approximations and which increase computational efficiency the loglikelihood function is maximised numerically to obtain estimates of the unknown hyperparameters standard errors of the estimates due to simulation are calculated details are given for the important special cases where the observations come from an exponential family distribution and where the observation equation is linear but the observation errors are non gaussian the techniques are illustrated with a series for which the observations have a poisson distribution and a series for which the observation errors have a t distribution

certain models from uncertain data the algebraic case abstract the problem of deriving possible linear relations from data affected by additive noise has received remarkable attention in recent years particularly regarding the assumptions prejudices behind the procedures leading to unique models unlike traditional approaches leading to unique solutions least squares maximum likelihood etc the frisch scheme belonging to the family of errors in variables ev schemes leads to a whole family of models compatible with a set of noisy data and is considered as mildly affected by prejudices this paper shows how also under the assumptions of the frisch scheme it is possible to obtain a unique model from uncertain data and also to derive the actual amount of noise when the noiseless data are linked by a single linear relation the more general ev case of non independent additive noises is then considered and it is shown how also under these assumptions it is possible to obtain the unique set of parameters linking the noiseless data and how the family of compatible noise covariance matrices is defined in this case by the infinite elements of a linear variety

improved approximations for cubic bipartite and cubic tsp we show improved approximation guarantees for the traveling salesman problem on cubic bipartite graphs and cubic graphs for connected cubic bipartite graphs with n nodes we improve on recent results of karp and ravi by giving a local improvement algorithm that finds a tour of length at most 5 4n 2 for 2 connected cubic graphs we show that the techniques of momke and svensson can be combined with the techniques of correa larre and soto to obtain a tour of length at most 4 3 1 8754 n

numerical integration approach to on line identification of continuous time systems abstract the problem of estimating the parameters in linear continuous differential equation models from sampled data is treated using a linear integral filter we can obtain an identification model that is parametrized directly in the continuous time model parameters the unknown initial states of the system do not require estimation the choice of the sampling interval and the design of the linear integral filter are discussed considering the accuracy of parameter estimates and the computational burden by applying the results from discrete time model identification with the obtained identification model a discrete time parameter estimation method is developed and the necessary condition as well as the sufficient condition on the input for consistency are explicitly derived and discussed in particular situations a simulation study is also included to confirm the theoretical results

recursive identification of transfer function matrix in continuous systems via linear integral filter a method is presented for identifying the transfer function matrix of a continuous time multivariate system with unknown initial conditions from sampled data of input output measurements using the so called linear integral filter an operation of numerical integration for handling time derivatives of measurements leads to an identification model without involving the unknown initial conditions and thus they do not require estimation together with the system parameters both a theoretical analysis and simulation study show that the least squares estimates are asymptotically biased even when the system outputs are corrupted by white noise an instrumental variable method where instrumental variables are composed of combinations of input signals is proposed to give consistent estimates of system parameters for open loop operation and it is also thoroughly evaluated by monte carlo simulation analysis

robust parametric transfer function estimation using complex logarithmic frequency response data the statistical properties of a logarithmic least squares frequency domain estimator are analyzed in an error in variables framework it is shown that contrary to most frequency domain estimators the logarithmic least squares estimator remains practically consistent when the variances of the frequency domain data are not a priori known if available the variance at each spectral line of the logarithmic frequency response data can be used to weight the logarithmic least squares estimator resulting in parameter estimates with a smaller variability an estimate of these variances can be derived from the residual errors at the excited spectral lines besides its robustness to lack of prior noise information it is demonstrated that the logarithmic estimator behaves remarkably well in the presence of outliers

a new look at time series of counts summary this paper proposes a simple new model for stationary time series of integer counts previous work has focused on thinning methods and classical time series autoregressive moving average difference equations in contrast our methods use a renewal process to generate a correlated sequence of bernoulli trials by superpositioning independent copies of such processes stationary series with binomial poisson geometric or any other discrete marginal distribution can be readily constructed the model class proposed is parsimonious non markov and readily generates series with either short or long memory autocovariances the model can be fitted with linear prediction techniques for stationary series as an example a stationary series with binomial marginal distributions is fitted to the number of rainy days in 210 consecutive weeks at key west florida

comparison of some instrumental variable methods consistency and accuracy aspects a general analysis of various instrumental variable methods is given the investigation includes methods for open loop operation as well as methods designed for closed loop operation the instrumental variables are formed as different combinations of inputs delayed inputs delayed outputs filtered inputs and external setpoint variations necessary conditions as well as sufficient conditions for consistency are explicitly derived and discussed the paper also includes some simple counter examples to general consistency for some common instrumental variable methods also asymptotic accuracy properties are reviewed it is e g studied how the use of filters will influence the covariance matrix of the parameter estimates

on the uniqueness of prediction error models for systems with noisy input output data abstract this paper addresses the uniqueness problem of the prediction error pe identification for a class of linear systems with noisy input and output data necessary and sufficient conditions are derived for the corresponding pe loss function to have asymptotically a unique global minimum the results indicate that a pe algorithm may give very bad parameter estimates for systems not satisfying these conditions such a possibility is illustrated by a numerical example while the pe method is used as a vehicle for illustration the derived conditions for global uniqueness or identifiability apply to any consistent estimation method based on second order data

transfer function synthesis using frequency response data various linear least squares methods for transfer function synthesis from frequency response data are presented in a unified format solutions are derived from householder transformations and recursive least squares an alternative formulation derived from a time domain error criterion is also shown to be of the linear least squares type the comparative performance of the various methods is illustrated by several examples

identification of continuous time systems using arbitrary signals abstract this paper presents a parametric frequencydomain identification algorithm for linear time invariant continuous time systems excited by arbitrary signals unlike the current available methods this approach allows accurate modeling in the complete frequency band from dc to nyquist

frequency domain identification of linear systems using arbitrary excitations and a nonparametric noise model presents a generalized frequency domain identification method to identify single input single output siso systems combining two previously published extensions in one method arbitrary but persistent excitations are allowed and a nonparametric noise model is extracted from the same data that are used to identify the system the method is directly applicable to identification in feedback if an external persistently exciting reference signal is available

consistent identification of stochastic linear systems with noisy input output data abstract a novel criterion is introduced for parametric errors in variables identification of stochastic linear systems excited by non gaussian inputs the new criterion is at least theoretically insensitive to a class of input output disturbances because it implicitly involves higher than second order cumulant statistics in addition it is shown to be equivalent to the conventional mean squared error mse as if the latter was computed in the ideal case of noise free input output data the sampled version of the criterion converges to the novel mse and guarantees strongly consistent parameter estimators the asymptotic behavior of the resulting parameter estimators is analyzed and guidelines for minimum variance experiments are discussed briefly informative enough input signals and persistent of excitation conditions are specified computatonally attractive recursive least squares variants are also developed for on line implementation of arma modeling and their potential is illustrated by applying them to time delay estimation in low snr environment the performance of the proposed algorithms and comparisons with conventional methods are corroborated using simulated data

identification of linear dynamic systems using piecewise constant excitations use misuse and alternatives abstract time domain identification of linear dynamic systems using discrete time models relies heavily on the use of piecewise constant excitation signals zoh assumption if this assumption is not met severe errors can be generated and the results can be useless in this article we study the implications of the zoh assumption and an alternative is formulated this leads to frequency domain identification methods based on the band limited assumption that the signals obey the shannon sampling theory the theory and practical aspects of both approaches are compared finally it will be shown that periodic excitations or perturbation signals can offer significant advantages in both approaches

identification of multivariable stochastic linear systems via polyspectral analysis given noisy input output time domain data the paper considers the problem of identification of unknown parameters of multivariable linear errors invariables models attention is focused on frequency domain approaches where the integrated polyspectrum bispectrum or trispectrum of the input and the integrated cross polyspectrum respectively of the given time domain input output data are exploited two new classes of parametric frequency domain approaches are proposed and analyzed an integrated polyspectrum based persistence of excitation condition on system input is defined both classes of the parameter estimators are shown to be strongly consistent in any measurement noise sequences with vanishing bispectra when integrated bispectrum based approaches are used the proposed parameter estimators are shown to be strongly consistent in gaussian measurement noise when integrated trispectrum based approaches are used the input to the system need not be a linear process but must have nonvanishing bispectrum or trispectrum

brief performance evaluation of methods for identifying continuous time autoregressive processes identification of continuous time autoregressive processes from discrete time data by replacing the differentiation operator by an approximation is considered a linear regression model can then be formulated the least squares method and the instrumental variables method must be used with some care to get parameter estimates of good quality the bias is studied explicitly in the paper together with the asymptotic distribution and expressions are presented for the covariance matrix of the estimated parameters it turns out that there are small differences in the dominating bias term for the different methods whereas the statistical properties are comparable overall the performance is similar to that of a prediction error method for short sampling intervals

binary time series modeling with application to adhesion frequency experiments repeated adhesion frequency assay is the only published method for measuring the kinetic rates of cell adhesion cell adhesion plays an important role in many physiological and pathological processes traditional analysis of adhesion frequency experiments assumes that the adhesion test cycles are independent bernoulli trials this assumption often can be violated in practice motivated by the analysis of repeated adhesion tests a binary time series model incorporating random effects is developed a goodness of fit statistic is introduced to assess the adequacy of distribution assumptions on the dependent binary data with random effects the asymptotic distribution of the goodness of fit statistic is derived and its finite sample performance is examined through a simulation study application of the proposed methodology to real data from a t cell experiment reveals some interesting information including the dependency between repeated adhesion tests

removing and adding edges for the traveling salesman problem we present a framework for approximating the metric tsp based on a novel use of matchings traditionally matchings have been used to add edges to make a given graph eulerian whereas our approach also allows for the removal of certain edges leading to a decreased cost for the tsp on graphic metrics graph tsp we show that the approach gives a 1 461 approximation algorithm with respect to the held karp lower bound for graph tsp restricted either to half integral solutions to the held karp relaxation or to a class of graphs that contains subcubic and claw free graphs we show that the integrality gap of the held karp relaxation matches the conjectured ratio 4 3 the framework also allows for generalizations in a natural way and leads to analogous results for the s t path traveling salesman problem on graphic metrics where the start and end vertices are prespecified

generalized arma models with martingale difference errors the analysis of non gaussian time series has been studied extensively and has many applications many successful models can be viewed as special cases or variations of the generalized autoregressive moving average garma models of benjamin et al 2003 where a link function similar to that used in generalized linear models is introduced and the conditional mean under the link function assumes an arma structure under such a model the transformed time series under the same link function assumes an arma form as well unfortunately unless the link function is an identity function the error sequence defined in the transformed arma model is usually not a martingale difference sequence in this paper we extend the garma model in such a way that the resulting arma model in the transformed space has a martingale difference sequence as its error sequence the benefit of such an extension are four folds it has easily verifiable conditions for stationarity and ergodicity its gaussian pseudo likelihood estimator is consistent standard time series model building tools are ready to use and its mle s asymptotic distribution can be established we also proposes two new classes of non gaussian time series models under the new framework the performance of the proposed models is demonstrated with simulated and real examples

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 negative binomial model for time series of counts we study generalized linear models for time series of counts where serial dependence is introduced through a dependent latent process in the link function conditional on the covariates and the latent process the observation is modelled by a negative binomial distribution to estimate the regression coefficients we maximize the pseudolikelihood that is based on a generalized linear model with the latent process suppressed we show the consistency and asymptotic normality of the generalized linear model estimator when the latent process is a stationary strongly mixing process we extend the asymptotic results to generalized linear models for time series where the observation variable conditional on covariates and a latent process is assumed to have a distribution from a one parameter exponential family thus we unify in a common framework the results for poisson log linear regression models of davis et al 2000 negative binomial logit regression models and other similarly specified generalized linear models language en

brief paper recursive identification for multivariate errors in variables systems the recursive algorithm is given for estimating matrix coefficients of the multivariate errors in variables eiv systems it is shown that under mild conditions the estimate given by the algorithm converges to a limit belonging to the solution set of the yule walker equation satisfied by the true coefficients of the system the sufficient conditions guaranteeing the uniqueness of the solution to the yule walker equation are given in this case the estimate provided by the recursive algorithm is strongly consistent

restoration of differently blurred versions of an image with measurement errors in the psf s restoration of an object from t observations is considered each image is distorted by a different deterministic blur and additive noise the point spread function psf for each observation is unknown however a noisy measurement of it is available taking the errors in measurements of the psfs into consideration the maximum likelihood and wiener filters are derived it is shown that these filters give better results when the regression filter and the conventional wiener filter i e the one which ignores the presence of the noise in the psfs the consistency and the ill conditioning characteristics of the filters are discussed regularized forms for these filers are obtained

brief paper study of conditional ml estimators in time and frequency domain system identification this paper shows that the full covariance matrix can be replaced by its main diagonal in maximum likelihood estimation mle of linear dynamic systems in the time or frequency domain without affecting the asymptotic properties this is a very important result for frequency domain identification since it allows to use nonparametric noise models it also provides a theoretical justification for the common practice in time domain identification to neglect the initial condition effects of the noise model

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

regression models for nonstationary categorical time series asymptotic estimation theory for the analysis of nonstationary categorical time series a parsimonious and flexible class of models is proposed these models are generalizations of regression models for stochastically independent categorical observations consistency asymptotic normality and efficiency of the maximum likelihood estimator are shown under weak and easily verifiable requirements some models for binary time series are discussed in detail to demonstrate asymptotic properties a theorem is given addressing maximum likelihood estimation for general stochastic processes then it is shown that the assumptions of this theorem are consequences of the requirements for categorical time series for this proof some lemmas are used which may be of interest in similar cases

linear dynamic errors in variables models some structure theory abstract this paper gives a survey of some recent results on problems of identifiability or more general of the relation between the observations and certain system characteristics for linear dynamic errors in variables models for a large part of the paper the noise components are assumed to be mutually uncorrelated after the general problem statement a rather complete analysis of the single input single output case is given also the case of three variables and the case where the number of inputs is equal to the number of outputs are discussed in detail finally the use of higher order cummulant spectra for identifiability is investigated

modeling of continuous time systems using a discrete time representation abstract the problem of the representation of continuous time systems by difference equations is studied a solution is proposed using a sample integration technique the convolution integrals are approximated by digital filters resulting in an arbitrary high accuracy in a wide frequency band

parametric identification of transfer functions in the frequency domain a survey this paper gives a survey of frequency domain identification methods for rational transfer functions in the laplace s or z domain the interrelations between the different approaches are highlighted through a study of the equivalent cost functions the properties of the various estimators are discussed and illustrated by several examples

transfer function synthesis using frequency response data an improved method for transfer function synthesis from measured frequency response data is presented the improvement is due to a new scheme of matrix adaptation that eliminates measurement dependent inaccuracies step by step arbitrary coefficients can be set to any preassigned values so that account can be taken of previous knowledge of the investigated system an extension to integrating systems is developed the efficiency of the proposed method is demonstrated for an example taken from the literature

paper identification of scalar errors in variables models with dynamics the paper considers the task of identifying a causal linear dynamic system excited by stationary gaussian zero mean noise of unknown spectrum and given measurements of the system input and output contaminated by independent additive stationary noise signals of unknown spectra while the solution is normally not unique finite dimensional parameterizations of the solution set are given in some cases involving just one parameter even though the various spectra may not be rational

identification of linear relations from noisy data geometrical aspects abstract the problem of determining linear models from data corrupted by noise has been revisited by several authors in recent years with reference to the frisch scheme this work presents some geometrical aspects regarding the sets of solutions obtained in the identification procedure an analysis is made on how these sets vary as the amount of noise on the data varies the existence of particular solutions for data linked by a number of linear relations greater than one is also shown

a generalized gaussian process model for computer experiments with binary time series non gaussian observations such as binary responses are common in some computer experiments motivated by the analysis of a class of cell adhesion experiments we introduce a generalized gaussian pr

cardinal interpolation a bayesian probability density for an interpolating function is developed and its desirable properties and practical potential are demonstrated this density has an often needed but previously unachieved property here called cardinal interpolation which ensures extrapolation to the density of the least squares linear model in particular the mean of the cardinal interpolation density is a smooth function that intersects given x y points and which extrapolates to their least squares line and the variance of this density is a smooth function that is zero at the point x values that increases with distance from the nearest point x value and that extrapolates to the well known quadratic variance function for the least squares line the new cardinal interpolation density is developed for gaussian radial basis interpolators using fully bayesian methods that optimize interpolator smoothness this optimization determines the basis function widths and yields an interpolating density that is non gaussian except for large magnitude x and which is therefore not the outcome of a gaussian process further new development shows that the salient property of extrapolation to the density of the least squares linear model can be achieved for more general approximating not just interpolating functions

stochastic system identification with noisy input using cumulant statistics addresses the problem of estimating the parameters of stochastic linear systems when the measurements of the system input as well as the system output are noise contaminated it is assumed that the input is non gaussian and the noises are gaussian the square root of the magnitude of the fourth cumulant of a generalized error signal is proposed as a performance criterion for parameter estimation an optimization algorithm is presented strong consistency of the proposed parameter estimators is proved under certain sufficient conditions both single input single output and multiple input multiple output cases are investigated finally simulation results are presented to illustrate the proposed approach

modal parameter estimation from input output fourier data using frequency domain maximum likelihood identification abstract a multi variable frequency domain maximum likelihood estimator is proposed to identify the modal parameters together with confidence intervals directly from the input output fourier data the use of periodic excitation signals enables the use of a so called non parametric errors in variables noise model for an accurate description of the measurement set up the combination with a maximum likelihood identification approach yields a solver that is extremely robust to errors in the data such as noise and leakage and hence results in accurate models since the maximum likelihood approach involves an optimization problem a least squares estimator is proposed as well with the availability of a stabilization diagram both algorithms have been optimized for modal analysis applications by a significant reduction of the computation time and memory requirements in the case when random noise excitation is required the proposed method allows a parametric compensation for effects of leakage

brief identification of static errors in variables models the rank reducibility problem the problem of identifying linear static relations from noisy data is investigated under the assumptions of the frisch scheme the work presents an attempt to simplify the search for solutions of the related rank reducibility problem the proposed approach is based on a relaxation of the original problem by means of algebraic manipulations of the non linear equations which characterize the solution set it is shown that this method can be advantageously used when particular conditions regarding the number of variables and the number of linear relations are satisfied

a regression model for time series of counts summary this paper discusses a model for regression analysis with a time series of counts correlation is assumed to arise from an unobservable process added to the linear predictor in a log linear model an estimating equation approach used for parameter estimation leads to an iterative weighted and filtered least squares algorithm asymptotic properties for the regression coefficients are presented we illustrate the technique with an analysis of trends in u s polio incidence since 1970