from time series to linear system part i finite dimensional linear time invariant systems abstract in the first part of this paper the definition of a dynamical system as simply consisting of a family of time series will be developed in this context the notions of linearity time invariance and finite dimensionality will be introduced it will be shown that a given family of time series may be represented by a system of ar equations riw t l rl 1w t l 1 r0w t 0 or equivalently by a finite dimensional linear time invariant system x t 1 ax t bu t y t cx t du t w u y if and only if this family is linear shift invariant and complete or as is equivalent closed in the topology of pointwise convergence this yields a very high level and elegant set of axioms which characterize these familiar objects it is emphasized however that no a priori choice is made as to which components of w are inputs and which are outputs such a separation always exists in any specific linear time invariant model starting from these definitions the structural indices of such systems are introduced and it is shown how an ar representation of a system having a given behaviour can be constructed these results will be used in a modelling context in part ii of the paper

mimo system identification state space and subspace approximations versus transfer function and instrumental variables the identification of multi input multi output mimo linear systems has previously received a new impetus with the introduction of the state space ss approach based on subspace approximations this approach has immediately gained popularity owing to the fact that it avoids the use of canonical forms requires the determination of only one structural parameter and has been empirically shown to yield mimo models with good accuracy in many cases however the ss approach suffers from several drawbacks there is no well established rule tied to this approach for determining the structural parameter and perhaps more important the ss parameter estimates depend on the data in a rather complicated way which renders almost futile any attempt to analyze and optimize the performance of the estimator in this paper we consider a transfer function tf approach based on instrumental variables iv as an alternative to the ss approach we use the simplest canonical tf parameterization in which the denominator is equal to a scalar polynomial times the identity matrix the analysis and optimization of the statistical accuracy of the tf approach is straightforward additionally a simple test tailored to this approach is devised for estimating the single structural parameter needed a simulation study in which we compare the performances of the ss and the tf approaches shows that the latter can provide more accurate models than the former at a lower computational cost

a bias correction method for identification of linear dynamic errors in variables models this paper considers the problem of identifying linear systems where the input is observed in white noise but the output is observed in colored noise which also includes process disturbances an efficient method is developed which can perform unbiased parameter estimation without utilizing a prefilter the developed method is characterized by attractive features direct use of the observed data without prefiltering no need to evaluate autocorrelation functions for the input noise no need to identify a high order augmented system and provision of a direct unbiased estimate of the system parameters without parameter extraction computer simulations are presented to illustrate its superior performance including its significantly reduced computational complexity

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

errors in variables identification using maximum likelihood estimation in the frequency domain this paper deals with the identification of errors in variables eiv models corrupted by additive and uncorrelated white gaussian noises when the noise free input is an arbitrary signal not required to be periodic in particular a frequency domain maximum likelihood ml estimator is proposed and analyzed in some detail as some other eiv estimators this method assumes that the ratio of the noise variances is known the estimation problem is formulated in the frequency domain it is shown that the parameter estimates are consistent an explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is derived the possibility to effectively use lowpass filtered data by using only part of the frequency domain is discussed analyzed and illustrated

on the choice of outlet boundary conditions for patient specific analysis of aortic flow using computational fluid dynamics boundary conditions bcs are an essential part in computational fluid dynamics cfd simulations of blood flow in large arteries although several studies have investigated the influence of bcs on predicted flow patterns and hemodynamic wall parameters in various arterial models there is a lack of comprehensive assessment of outlet bcs for patient specific analysis of aortic flow in this study five different sets of outlet bcs were tested and compared using a subject specific model of a normal aorta phase contrast magnetic resonance imaging pc mri was performed on the same subject and velocity profiles extracted from the in vivo measurements were used as the inlet boundary condition computational results obtained with different outlet bcs were assessed in terms of their agreement with the pc mri velocity data and key hemodynamic parameters such as pressure and flow waveforms and wall shear stress related indices our results showed that the best overall performance was achieved by using a well tuned three element windkessel model at all model outlets which not only gave a good agreement with in vivo flow data but also produced physiological pressure waveforms and values on the other hand opening outlet bcs with zero pressure at multiple outlets failed to reproduce any physiologically relevant flow and pressure features

covariance matching for continuous time errors in variables problems a covariance matching approach for continuous time errors in variables problems is considered the noise free input signal is not explicitly modeled and is only assumed to be a stationary process it is described how three different systems of equations in the model parameters are obtained and how the parameters are estimated based on these systems of equations the approach is illustrated by some numerical studies

from time series to linear system part iii approximate modelling abstract in the third part of this paper the problem of finding a linear time invariant complete system which models an observed time series will be continued however in this part it will be assumed that the model is required to explain the observations only approximately this raises the question of what is meant by an approximate model and how one should judge a model against data which in a strict sense falsify the model the initial sections of this paper introduce the methodology either the maximal admissible complexity is fixed and the best fitting model in the model class is sought or the maximally tolerated misfit is fixed and the least complex model in the model class is sought this is illustrated by means of finite dimensional models where natural complexity and misfit functions suggest themselves subsequently what is meant by the complexity of a linear time invariant complete system is discussed a concrete complexity function is proposed which is defined in terms of the richness of the behaviour on finite time intervals and is in one to one correspondence with the number of inputs the number of states and the observability indices of the underlying minimal i s o system the next definition is that of the misfit between an observed time series and a system a concrete misfit function is proposed which takes into consideration the lag structure of the system and in how far the observations fail to corroborate the ar equations which define the system s behaviour how the misfit may be computed by means of the correlation function of the data is then shown these concepts are subsequently used in order to set up two algorithms for approximate modelling of an observed q dimensional time series the first algorithm fixes the maximal complexity in a sense this comes down to fixing the number and the lags of the required ar equations the second algorithm fixes the tolerated misfit it is adaptive in nature in the sense that the number and the structure of the resulting ar equations will depend on the observations these ideas and algorithms are illustrated by means of two simulated examples

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

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

note on the applicability of the james stein estimator in regional hydrologic studies the applicability of the james stein estimator in regional hydrologic studies which entail the estimation of an n dimensional location parameter is discussed regional studies are frequently characterized by relatively short generally correlated samples drawn from nonsymmetric and bounded i e nonnormal populations by means of computer simulation studies the james stein estimator subject to the lindley modification and adoption of the positive part rule suggested by efron and morris and conditioned on the assumption of independence was shown to be robust in the case of the hydrologically plausible distribution considered here namely weibull distributions with coefficient of skewness ranging from 0 to 10 however in contrast to traditional methods of regionalization the effect of cross correlation is a diminishment of the relative risk advantage of the james stein estimator even in the best case of normal variables this is discussed and illustrated

comment on identification in the linear errors in variables model on considere un modele etudie par kapteyn et wansbeek 1983 et on presente des conditions necessaires et suffisantes d identification

on the accuracy of a covariance matching method for continuous time errors in variables identification on the accuracy of a covariance matching method for continuous time errors in variables identification

a parametric model for studying the aorta hemodynamics by means of the computational fluid dynamics abstract perturbed aorta hemodynamics as for the carotid and the coronary artery has been identified as potential predicting factor for cardiovascular diseases in this study we propose a parametric study based on the computational fluid dynamics with the aim of providing information regarding aortic disease in particular the blood flow inside a parametrized aortic arch is computed as a function of morphological changes of baseline aorta geometry flow patterns wall shear stress time average wall shear stress and oscillatory shear index were calculated during the cardiac cycle the influence of geometrical changes on the hemodynamics and on these variables was evaluated the results suggest that the distance between inflow and aortic arch and the angle between aortic arch and descending trunk are the most influencing parameters regarding the wss related indices while the effect of the inlet diameter seems limited in particular an increase of the aforementioned distance produces a reduction of the spatial distribution of the higher values of the time average wall shear stress and of the oscillatory shear index independently on the other two parameters while an increase of the angle produce an opposite effect moreover as expected the analysis of the wall shear stress descriptors suggests that the inlet diameter influences only the flow intensity as conclusion the proposed parametric study can be used to evaluate the aorta hemodynamics and could be also applied in the future for analyzing pathological cases and virtual situations such as pre and or post operative cardiovascular surgical states that present enhanced changes in the aorta morphology yet promoting important variations on the considered indexes

identification of the dynamic shock error model with autocorrelated errors abstract the paper gives necessary and sufficient conditions for the local identifiability of dynamic regression models with autocorrelated errors in the variables the conditions are simple counting rules combining the order parameters of a model and directly generalize the results of maravall and aigner a new method of identification is presented allowing a compact derivation of the results

a bayesian surrogate for regional skew in flood frequency analysis the problem of how to best utilize site and regional flood data to infer the shape parameter of a flood distribution is considered one approach to this problem is given in bulletin 17b of the u s water resources council 1981 for the log pearson distribution here a lesser known distribution is considered namely the power normal which fits flood data as well as the log pearson and has a shape parameter denoted by derived from a box cox power transformation the problem of regionalizing is considered from an empirical bayes perspective where site and regional flood data are used to infer the distortive effects of spatial correlation and heterogeneity of site sampling variance of are explicitly studied with spatial correlation being found to be of secondary importance the end product of this analysis is the posterior distribution of the power normal parameters expressing in probabilistic terms what is known about the parameters given site flood data and regional information on this distribution can be used to provide the designer with several types of information the posterior distribution of the t year flood is derived the effect of nonlinearity in on inference is illustrated because uncertainty in is explicitly allowed for the understatement in confidence limits due to fixing analogous to fixing log skew is avoided finally it is shown how to obtain the marginal flood distribution which can be used to select a design flood with specified exceedance probability

relation between diameter and flow in major branches of the arch of the aorta in the analysis of arterial branching the classical cube law has provided a working model for the relation between the diameter of a blood vessel and the flow which the vessel carries on a long term basis the law has shown good agreement with biological data but questions remain regarding its applicability to all levels of the arterial tree the present study tests the hypothesis that the cube law may not be valid in the first few generations of the arterial tree where vessel capacitance and gross anatomy may play important roles biological data have shown some support for this hypothesis in the past but the heterogeneity characteristic of past data has not allowed a conclusive test so far we present new data which have been obtained from the same location on the arterial tree and in sufficient number to make this test possible for the first time also while past tests have been based primarily on correlation of the measured data with an assumed power law we show here that this can be misleading the present data allow a simpler test which does not involve correlation and which leads to more direct conclusions for the vessels surveyed the results show unequivocally that the relation between diameter and flow is governed by a square law rather than the classical cube law coupled with past findings this suggests that the square law may apply at the first few levels of the arterial tree while the cube law continues from there to perhaps the precapillary levels

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

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

outflow boundary conditions for three dimensional finite element modeling of blood flow and pressure in arteries flow and pressure waves emanate from the heart and travel through the major arteries where they are damped dispersed and reflected due to changes in vessel caliber tissue properties and branch points as a consequence solutions to the governing equations of blood flow in the large arteries are highly dependent on the outflow boundary conditions imposed to represent the vascular bed downstream of the modeled domain the most common outflow boundary conditions for three dimensional simulations of blood flow are prescribed constant pressure or traction and prescribed velocity profiles however in many simulations the flow distribution and pressure field in the modeled domain are unknown and cannot be prescribed at the outflow boundaries an alternative approach is to couple the solution at the outflow boundaries of the modeled domain with lumped parameter or one dimensional models of the downstream domain we previously described a new approach to prescribe outflow boundary conditions for simulations of blood flow based on the dirichlet to neumann and variational multiscale methods this approach termed the coupled multidomain method was successfully applied to solve the non linear one dimensional equations of blood flow with a variety of models of the downstream domain this paper describes the extension of this method to three dimensional finite element modeling of blood flow and pressure in the major arteries outflow boundary conditions are derived for any downstream domain where an explicit relationship of pressure as a function of flow rate or velocities can be obtained at the coupling interface we developed this method in the context of a stabilized semi discrete finite element method flow rate and pressure distributions are shown for different boundary conditions to illustrate the dramatic influence of alternative boundary conditions on these quantities

regional flood quantile estimation for a weibull model estimation of annual flood quantiles at a given site based on a regional weibull model with independence in space and time is considered a common shape parameter over sites motivated by an index flood assumption was assumed an exact simple formula for the cramer rao lower bound for the variance of unbiased estimators of the quantile is obtained and the gain of regional flood frequency analysis over single site analysis can be quantified via this formula the estimation techniques of the method of moments the method of probability weighted moments and the method of maximum likelihood are compared

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

estimation of quantized linear errors in variables models we present an estimation algorithm for dynamic shock error models dsem given 1 bit quantized noisy measurements of the input and output the algorithm is called the binary series estimation algorithm bsea bsea is computationally inexpensive since it involves counting the number of occurrences of particular patterns of zeros and ones in the input and output sequences it yields consistent parameter estimates that are asymptotically normal

a generalised instrumental variable estimator for multivariable errors in variables identification problems a new and very general estimation method the generalised instrumental variable estimator give has been introduced to deal with the errors in variables identification the give contains several well known estimation methods as special cases that can be obtained by various user choices in give these methods include the bias eliminating least squares method a number of different versions of the frisch scheme and the extended compensated least squares method this article shows how previous analysis for single input single output systems can be extended in a non trivial way to also cope with multi input multi output systems various computational aspects of give are presented and it is shown how the parameter estimates can be computed in an efficient way the asymptotic distribution of the parameter estimates is also derived and analysed

identifiability in multivariate dynamic linear errors in variables models abstract this article considers multivariate causal transfer function systems with latent stationary inputs and outputs their observation is assumed to be disturbed by errors in variables ev the main identification results for such models so far consist of structure theory derived are descriptions of classes of ev transfer function systems compatible with given covariance structures of the observed variables under various causality constraints the case of unique determination is treated only for one dimensional models the article derives a great variety of conditions under which a multivariate ev transfer function system is uniquely determined by the second order moments of the observed variables for this purpose it considers a general model class of nonparametric systems and subclasses of systems with some parameterized components having fixed order parameters if parametric the transfer function is a rational matrix parametric inputs or errors follow vector autoregressive moving average arma

the identification of multivariate linear dynamic errors in variables models abstract the paper establishes necessary and sufficient conditions for the local identifiability of multivariate linear time series models with measurement errors the models have a linear relation with rational transfer matrix function and variables specified by unrestricted vector arma processes of fixed orders or more general variables the identifiability conditions finally are simple counting rules combining the order parameters of a model the paper derives the results bydisplaying in detail a new identification method which is based on the factorization and the expansion into partial fractions of rational matrices

simulation bayes and bootstrap in statistical hydrology statistical simulation in hydrology is discussed from a bayesian perspective the inherent difficulties in both parametric simulation based on a parent distribution and classical nonparametric simulation based on the bootstrap are discussed as an alternative to these procedures a nonparametric bayesian simulation methodology polya resampling is introduced it consists of simulating from a nonparametric predictive distribution obtained from the analysis of a reference sample and it is asymptotically equivalent to the bootstrap the method is generalized to take into account a prior hypothesis on the parametric distribution of a variable a hybrid simulation model is then obtained that includes parametric and nonparametric simulation as particular cases an extensive application is presented in a related paper fortin et al 1997 where polya resampling is used to compare statistical models for flood frequency analysis in this paper an example is used to demonstrate how polya resampling can help assess the influence of a distribution hypothesis on simulation results

on line estimation of dynamic shock error models based on the kullback leibler information measure develops two sequential or on line estimation schemes in the time domain for dynamic shock error models which are special cases of errors in variables models the author s approach utilizes a state space representation of the model kalman filtering techniques and on line algorithms the first on line algorithm is based on the expectation maximization algorithm and uses a recursive gauss newton scheme to maximize the kullback leibler information measure the second on line algorithm the author proposes is a gradient based scheme and uses stochastic approximations to maximize the log likelihood in comparison to the off line maximum likelihood estimation scheme used in ghosh 1989 the author s on line algorithms have significantly reduced computational costs and negligible memory requirements simulations illustrate the satisfactory performance of the algorithms in estimating errors in variables systems with parameters that vary slowly with time or undergo infrequent jump changes

l 2 optimal identification of mimo errors in variables models from the v gap geometrical interpretation an l 2 optimal identification method is extended to cope with mimo errors in variables eiv model estimation based on a geometrical interpretation for the v gap metric the l 2 optimal approximate models are composed of system and noise models and characterised by a normalised right graph symbol nrgs and its complementary inner factor cif respectively this metric can be evaluated as the supreme of sine values of the maximal principal angles between nrgs frequency responses of two concerned models in order to make full use of the angular cosine formula for complex vectors to reduce computational loads a cif of the nrgs of the perturbed model is introduced and thus the system parameter optimisation can be efficiently solved by sequential quadratic programming methods with the estimated system model the associated noise model can be built by right multiplication of an inner matrix finally a simulation example demonstrates the effectiveness of the proposed identification method

brief paper unifying some higher order statistic based methods for errors in variables model identification in this paper the problem of identifying linear discrete time systems from noisy input and output data is addressed several existing methods based on higher order statistics are presented it is shown that they stem from the same set of equations and can thus be united from the viewpoint of extended instrumental variable methods a numerical example is presented which confirms the theoretical results some possible extensions of the methods are then given

two component extreme value distribution for flood frequency analysis theoretical considerations supported by statistical analysis of 39 annual flood series afs of italian basins suggest that the two component extreme value tcev distribution can be assumed as a parent flood distribution i e one closely representative of the real flood experience this distribution belongs to the family of distributions of the annual maximum of a compound poisson process which is a solid theoretical basis for afs analysis however the two parameter distribution of this family obtained on the assumption of identically distributed floods does not account for the high variability of both observed skewness and largest order statistics so that a significant number of observed floods qualify as outliers under this distribution the more general tcev distribution assumes individual floods to arise from a mixture of two exponential components its four parameters can be estimated by the maximum likelihood method a regionalized tcev distribution with parameters representative of a set of 39 italian afs s was shown to closely reproduce the observed distribution of skewness and that of the largest order statistic

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

evaluation of 4d flow mri based non invasive pressure assessment in aortic coarctations abstract severity of aortic coarctation coa is currently assessed by estimating trans coarctation pressure drops through cardiac catheterization or echocardiography in principle more detailed information could be obtained non invasively based on space and time resolved magnetic resonance imaging 4d flow data yet the limitations of this imaging technique require testing the accuracy of 4d flow derived hemodynamic quantities against other methodologies with the objective of assessing the feasibility and accuracy of this non invasive method to support the clinical diagnosis of coa we developed an algorithm 4df feppe to obtain relative pressure distributions from 4d flow data by solving the poisson pressure equation 4df feppe was tested against results from a patient specific fluid structure interaction fsi simulation whose patient specific boundary conditions were prescribed based on 4d flow data since numerical simulations provide noise free pressure fields on fine spatial and temporal scales our analysis allowed to assess the uncertainties related to 4d flow noise and limited resolution 4df feppe and fsi results were compared on a series of cross sections along the aorta bland altman analysis revealed very good agreement between the two methodologies in terms of instantaneous data at peak systole end diastole and time averaged values biases means of differences were 0 4 mmhg 1 1 mmhg and 0 6 mmhg respectively limits of agreement 2 sd were 0 978 mmhg 1 06 mmhg and 1 97 mmhg respectively peak to peak and maximum trans coarctation pressure drops obtained with 4df feppe differed from fsi results by 0 75 mmhg and 1 34 mmhg respectively the present study considers important validation aspects of non invasive pressure difference estimation based on 4d flow mri showing the potential of this technology to be more broadly applied to the clinical practice

identification of simultaneous equation models with measurement errors based on time series structure abstract the paper establishes simple conditions leading to the global identifiability of multivariate armax errors in variables models in the form of a simultaneous equation system with errors in the exogenous variables the identification is based on the conventional rank condition and on time series structure inherent to the model the conditions particularly identify models with non autocorrelated exogenous variables in the absence of over identifying zero restrictions the model allows autocorrelated and cross correlated errors

the influence of boundary conditions on wall shear stress distribution in patients specific coronary trees patient specific geometrical data on human coronary arteries can be reliably obtained multislice computer tomography msct imaging msct cannot provide hemodynamic variables and the outflow through the side branches must be estimated the impact of two different models to determine flow through the side branches on the wall shear stress wss distribution in patient specific geometries is evaluated murray s law predicts that the flow ratio through the side branches scales with the ratio of the diameter of the side branches to the third power the empirical model is based on flow measurements performed by doriot et al 2000 in angiographically normal coronary arteries the fit based on these measurements showed that the flow ratio through the side branches can best be described with a power of 2 27 the experimental data imply that murray s law underestimates the flow through the side branches we applied the two models to study the wss distribution in 6 coronary artery trees under steady flow conditions the average wss between the side branches differed significantly for the two models the average wss was 8 higher for murray s law and the relative difference ranged from 5 to 27 these differences scale with the difference in flow rate near the bifurcations the differences in wss were more pronounced the size of the low wss regions was significantly larger when applying the empirical model 13 ranging from 12 to 68 predicting outflow based on murray s law underestimates the flow through the side branches especially near side branches the regions where atherosclerotic plaques preferentially develop the differences are significant and application of murray s law underestimates the size of the low wss region

flood frequency analysis with historical and paleoflood information an investigation is made of flood quantile estimators which can employ historical and paleoflood information in flood frequency analyses two categories of historical information are considered censored data where the magnitudes of historical flood peaks are known and binomial data where only threshold exceedance information is available a monte carlo study employing the two parameter lognormal distribution shows that maximum likelihood estimators mles can extract the equivalent of an additional 10 30 years of gage record from a 50 year period of historical observation the mle routines are shown to be substantially better than an adjusted moment estimator similar to the one recommended in bulletin 17b of the united states water resources council hydrology committee 1982 the mle methods performed well even when floods were drawn from other than the assumed lognormal distribution

robust flood frequency models the concept of a robust model is briefly explored in the context of flood frequency analysis two necessary properties of a robust model are advanced namely resistance and efficiency strategies for seeking more robust models are discussed because of its versatility the five parameter wakeby distribution can credibly be considered a parent flood distribution four regionalized wakeby parents are employed in simulation studies to search for robust models these parents were shown by houghton to be representative of u s flood experience in the sense that certain raw flood data characteristics could be reproduced a limited range of sampling experiments were undertaken the results suggest that of the site specific estimators considered the two parameter log normal maximum likelihood estimator is most resistant with gumbel estimators employing either maximum likelihood or probability weighted moments displaying comparable resistance several estimators which utilize regional flood information were compared included were empirical bayes estimators which are structurally similar to james stein rules and regionalized estimators based on the flood index method these estimators exhibited substantial improvements in aggregate risk performance over their site specific counterparts particularly for short record lengths regionalized estimators appear to be preferable for short record lengths while estimators which combine both site and regional flood information are preferable for longer record lengths when such estimation procedures are considered other distributional models such as log pearson type iii and wakeby become practical alternatives to the two parameter log normal model

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

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

the set of observationally equivalent errors in variables models abstract linear dynamic errors in variables or factor models with uncorrelated noise components are considered we give a description of the set of all noise spectra which are oberservationally equivalent with respect to the second moments of observations

a structure theory for linear dynamic errors in variables models we deal with problems connected with the identification of linear dynamic systems in situations when inputs and outputs may be contaminated by noise the case of uncorrelated noise components and the bounded noise case is considered if also the inputs may be contaminated by noise a number of additional complications in identification arise in particular the underlying system is not uniquely determined from the population second moments of the observations a description of classes of observationally equivalent systems is given continuity properties of mappings relating classes of observationally equivalent systems to the spectral densities of the observations are derived and the classes of spectral densities corresponding to a given maximum number of outputs are studied

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

principal information theoretic approaches 2000 principal information theoretic approaches journal of the american statistical association vol 95 no 452 pp 1349 1353

worst case identification of errors in variables models in closed loop a worst case identification method in frequency domain is proposed to cope with the identification of errors in variables models eivms in closed loop with a priori bound for the disturbing noises of an eivm in closed loop a frequency domain normalized coprime factor model ncfm with perturbation is derived and thus the identification of the eivm becomes that of the ncfm by employing the v gap metric as an optimization criterion the worst case error for an identified nominal ncfm is easily quantified and the parameter optimization can be effectively solved by linear matrix inequalities lmis during the parameter optimization the derivative of the nominal ncfm is constrained to some degree to reduce the effect of overfitting phenomenon different from other eivm identification methods we use v gap metric to characterize the disturbing noises and quantify the worst case error for the nominal ncfm as a result the identification result is not a deterministic model but a model set moreover this model set can be perfectly combined with the robust controller design finally a numerical simulation is presented to verify the proposed method

the performance of the two component extreme value distribution in regional flood frequency analysis the performance of the regional two component extreme value tcev estimation procedure in estimating both dimensionless regional frequency curves showing the t year flood as a multiple of the mean annual flood and site curves incorporating local and regional information was assessed using computer simulation experiments it was found that the tcev procedure produces estimates of both dimensionless regional curves and scaled site quantiles that are relatively unbiased but very variable when data are drawn from tcev or wakeby parents although estimates are very biased when data follow a gev distribution the tcev procedure is robust in the sense that its worst efforts are less bad than those of the alternatives considered but performance declines significantly as sample sizes reduce

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

suppression of bursting abstract we investigate the possibility of using a single small amplitude control input and feedback to stabilize equilibrium sets in a class of highly nonlinear o 2 symmetric dynamical systems possessing structurally stable heteroclinic cycles the leading order behavior near the equilibria is bilinear and homogeneous in the state variables while nonlinearities representing the symmetry breaking effect of the controller are crucial after a series of simplifying transformations we use ideas from optimal control theory to construct a stabilizing controller this study is motivated by the desire to stabilize the burst sweep cycle in low dimensional models of a turbulent boundary layer in the last two sections we apply the techniques to the 10 dimensional system of aubry et al 1988 kw bilinear systems dynamical systems heteroclinic cycles normal forms optimal control symmetry

robust flood frequency analysis performance of ema with multiple grubbs beck outlier tests flood frequency analysis generally involves the use of simple parametric probability distributions to smooth and extrapolate the information provided by short flood records to estimate extreme flood flow quantiles parametric probability distributions can have difficulty simultaneously fitting both the largest and smallest floods a danger is that the smallest observations in a record can distort the exceedance probabilities assigned to the large floods of interest the identification and treatment of such potentially influential low floods pilfs frees a fitting algorithm to describe the distribution of the larger observations this can allow parametric flood frequency analysis to be both efficient and also robust to deviations from the proposed probability model s lower tail historically pilf identification involved subjective judgement we propose a new multiple grubbs beck outlier test mgbt for objective pilf identification mgbt pilf identification rates akin to type i errors are reported for the lognormal ln distribution and the log pearson type iii lp3 distribution with a variety of skew coefficients mgbt pilf identification generally matched subjective identification from a recent california flood frequency study monte carlo results show that censoring of pilfs identified by the mgbt algorithm improves the extreme quantile estimator efficiency of the expected moments algorithm ema for negatively skewed lp3 distributions and has little effect for zero or positive skews simultaneously it protects against deviations from the lp3 in the lower tail as illustrated by distorted ln examples thus mgbt generally makes flood frequency analysis based on the lp3 distribution with ema both more accurate and more robust

identification of invariants of over parameterized models finite sample results this paper shows that a certain class of estimates of invariants of over parameterized models are with probability one independent of the particular over parameterization chosen the result is nonasymptotic and the estimators considered minimize a cost function that is invariant with respect to the same parameter transformation as the overparameterized model

brief paper box jenkins identification revisited part iii part i of this series of three papers handles the identification of single input single output box jenkins models on arbitrary frequency grids in an open and closed loop setting part ii discusses the computational aspects and illustrates the theory on simulations and a real life problem this paper extends the results of parts i and ii to multiple input multiple output systems contrary to the classical time domain approach the presented technique does not require symbolic calculus for multiple output polynomial box jenkins models

box jenkins identification revisited part i theory in classical time domain box jenkins identification discrete time plant and noise models are estimated using sampled input output signals the frequency content of the input output samples covers uniformly the whole unit circle in a natural way even in case of prefiltering recently the classical time domain box jenkins framework has been extended to frequency domain data captured in open loop the proposed frequency domain maximum likelihood ml solution can handle i discrete time models using data that only covers a part of the unit circle and ii continuous time models part i of this series of two papers i generalizes the frequency domain ml solution to the closed loop case and ii proves the properties of the ml estimator under non standard conditions contrary to the classical time domain case it is shown that the controller should be either known or estimated the proposed ml estimators are applicable to frequency domain data as well as time domain data

comparisons of two moments based estimators that utilize historical and paleoflood data for the log pearson type iii distribution 1 the expected moments algorithm ema cohn et al 1997 and the bulletin 17b interagency committee on water data 1982 historical weighting procedure b17h for the log pearson type iii distribution are compared by monte carlo computer simulation for cases in which historical and or paleoflood data are available the relative performance of the estimators was explored for three cases fixed threshold exceedances a fixed number of large floods and floods generated from a different parent distribution ema can effectively incorporate four types of historical and paleoflood data floods where the discharge is explicitly known unknown discharges below a single threshold floods with unknown discharge that exceed some level and floods with discharges described in a range the b17h estimator can utilize only the first two types of historical information including historical paleoflood data in the simulation experiments significantly improved the quantile estimates in terms of mean square error and bias relative to using gage data alone ema performed significantly better than b17h in nearly all cases considered b17h performed as well as ema for estimating x100 in some limited fixed threshold exceedance cases ema performed comparatively much better in other fixed threshold situations for the single large flood case and in cases when estimating extreme floods equal to or greater than x500 b17h did not fully utilize historical information when the historical period exceeded 200 years robustness studies using gev simulated data confirmed that ema performed better than b17h overall ema is preferred to b17h when historical and paleoflood data are available for flood frequency analysis

identification of multivariable dynamic errors in variables system with arbitrary inputs the present work deals with the identification of multivariable linear dynamic system from noisy input output observations where the input signal is arbitrary and the input output noises are mutually correlated a frequency domain identification framework is developed in which the consistent estimator of the multivariable plant model parameters and of the input output noise covariance matrix is defined as the solution of a set of normal equations and sufficient conditions for the uniqueness of the parameter estimate are established based on the rank property of the matrix of the normal equation the uncertainty bound of the parameter estimates is constructed and compared with the cramer rao lower bound the proposed methodology is validated on a simulated multivariable dynamic system

the rank of reduced dispersion matrices psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements psychometricians concentrate on cases in which low rank can be attained preferably rank one the spearman case econometricians cocentrate on cases in which the rank cannot be reduced below the number of variables minus one the frisch case in this paper we give an extensive historial discussion of both fields we prove the two key results in a more satisfactory and uniform way we point out various small errors and misunderstandings and we present a methodological comparison of factor analysis and regression on the basis of our results

linear models based on noisy data and the frisch scheme we address the problem of identifying linear relations among variables based on noisy measurements this is a central question in the search for structure in large data sets often a key assumption is that measurement errors in each variable are independent this basic formulation has its roots in the work of charles spearman in 1904 and of ragnar frisch in the 1930s various topics such as errors in variables factor analysis and instrumental variables all refer to alternative viewpoints on this problem and on ways to account for the anticipated way that noise enters the data in the present paper we begin by describing certain fundamental contributions by the founders of the field and provide alternative modern proofs to certain key results we then go on to consider a modern viewpoint and novel numerical techniques to the problem the central theme is expressed by the frisch kalman dictum which calls for identifying a noise contribution that allows a maximal number of simultaneous linear relations a

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

errors in variables identification of dynamic systems excited by arbitrary non white input abstract this work deals with the identification of dynamic systems from noisy input output observations where the noise free input is not parameterized the basic assumptions made are 1 the dynamic system can be modeled by a discrete or continuous time rational transfer function model 2 the temporal input output disturbances are mutually independent identically distributed noises and 3 the input power spectrum is non white not necessarily rational and is modeled nonparametrically the system identifiability is guaranteed by exploiting the non white spectrum property of the noise free input a frequency domain identification strategy is developed to estimate consistently the plant model parameters and the input output noise variances the uncertainty bound of the estimates is calculated and compared to the cramer rao lower bound the efficiency of the proposed algorithm is illustrated on numerical examples

a unified framework for eiv identification methods when the measurement noises are mutually correlated in this paper the previously introduced generalized instrumental variable estimator give is extended to the case of errors in variables models where the additive input and output noises are mutually correlated white processes it is shown how many estimators proposed in the literature can be described as various special cases of a generalized instrumental variable framework it is also investigated how to analyze the common situation where some of the equations that define the estimator are to hold exactly and others to hold approximately in a least squares sense providing a detailed study of the accuracy analysis

global identification of the dynamic shock error model abstract the paper gives necessary and sufficient conditions for the global identifiability of dynamic regression models with errors in the variables the conditions are simple counting rules combining the order parameters of a model they are counterparts of conditions previously established for local identifiability in a series of papers