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

the steiglitz mcbride identification algorithm revisited convergence analysis and accuracy aspects the convergence and accuracy properties of the steiglitz and mcbride identification method are examined the analysis is valid for a sufficiently large number of data it is shown that the method can converge to the true parameter vector only when the additive output noise is white in that case the method is proved to be locally convergent to the true parameters the global convergence properties are also investigated it is pointed out that the method is not always globally convergent some sufficient conditions guaranteeing global convergence are given assuming convergence takes place the estimates are shown to be asymptotically gaussian distributed an explicit expression is given for their asymptotic covariance matrix

on restricted perturbations in inverse images and a description of normalizer algebras in c algebras abstract let e and f be banach spaces and t a bounded linear map from e into f using a certain perturbation function t we find a useful sufficient criterion that t maps the closed unit ball onto a closed set applying this to the quotient map from a c algebra a onto its quotient banach space a l r by the sum l r of closed left and right ideals l and r of a we obtain that the closed unit ball of a maps onto the closed unit ball of a l r this gives an independent description of the images of the right normalizer algebra n r d and the normalizer algebra n d n l d n r d of a hereditary c subalgebra d of a by the quotient map from a onto a cl ad cl da we use this to prove a necessary and sufficient criterion for a c algebra b to be a c quotient algebra of a c subalgebra of a c algebra a the latter criterion will be applied in the situation where a equals the car algebra in some forthcoming papers cf section 6 for more details

on consistent estimation of the characteristic coefficient and the poles of multivariate linear systems the estimation of the characteristic coefficients and the poles of linear systems is considered it is shown that estimates obtained from the sample correlation function of possibly nonstationary multivariable observations are consistent

optimal instrumental variable estimation and approximate implementations the accuracy properties of instrumental variables iv methods are investigated extensions such as prefiltering of data and use of additional instruments are included in the analysis the parameter estimates are shown to be asymptotically gaussian distributed an explicit expression is given for the covariance matrix of their distribution the covariance matrix is then taken as a multivariable measure of accuracy it is shown how it can be optimized by an appropriate selection of instruments and prefilter the so obtained optimal instrumental variable estimates cannot be used directly since the true system and the statistical properties of the disturbance must be known in order to compute the optimal instruments and prefilters a multistep procedure consisting of three or four simple steps is then proposed as a way to overcome this difficulty this procedure includes modeling of the disturbance as an arma process using a statistically efficient method such as a prediction error method the statistical properties of the estimates obtained with the multistep procedure are also analyzed those estimates are shown to be asymptotically gaussian distributed as well the covariance matrix of the estimation errors is compared to that corresponding to a prediction error method for some model structures these two approaches give the same asymptotic accuracy the conclusion is that the multistep procedure which is quite easy to implement and also has nice uniqueness properties can be viewed as an interesting alternative to prediction error methods

two new conjugate gradient methods based on modified secant equations following the approach proposed by dai and liao we introduce two nonlinear conjugate gradient methods for unconstrained optimization problems one of our proposed methods is based on a modified version of the secant equation proposed by zhang deng and chen and zhang and xu and the other is based on the modified bfgs update proposed by yuan an interesting feature of our methods is their account of both the gradient and function values under proper conditions we show that one of the proposed methods is globally convergent for general functions and that the other is globally convergent for uniformly convex functions to enhance the performance of the line search procedure we also propose a new approach for computing the initial steplength to be used for initiating the procedure we provide a comparison of implementations of our methods with the efficient conjugate gradient methods proposed by dai and liao and hestenes and stiefel numerical test results show the efficiency of our proposed methods

the overdetermined recursive instrumental variable method a recursive instrumental variable algorithm is derived for the overdetermined case in which the number of instruments is greater than the number of estimated parameters in some applications the algorithm provides improved parameter estimation accuracy compared to the standard recursive instrumental variable method the performance of the algorithm is illustrated by simulation results

a new method for ar order determination of an arma process using a combination of the minimum description length mdl criterion and overdetermined instrumental variable method a computationally efficient method for ar order determination of an arma process is proposed it is shown that the well known singular value decomposition svd method for ar order determination is a special case of the proposed method numerical simulations are presented to show the effectiveness of this method

a generalized least absolute deviation method for parameter estimation of autoregressive signals this paper proposes a generalized least absolute deviation glad method for parameter estimation of autoregressive ar signals under non gaussian noise environments the proposed glad method can improve the accuracy of the estimation of the conventional least absolute deviation lad method by minimizing a new cost function with parameter variables and noise error variables compared with second and high order statistical methods the proposed glad method can obtain robustly an optimal ar parameter estimation without requiring the measurement noise to be gaussian moreover the proposed glad method can be implemented by a cooperative neural network nn which is shown to converge globally to the optimal ar parameter estimation within a finite time simulation results show that the proposed glad method can obtain more accurate estimates than several well known estimation methods in the presence of different noise distributions

instrumental variable methods for arma spectral estimation the modified yule walker technique of arma spectral estimation is shown to be a special case of the instrumental variable method of system identification several recursive instrumental variable algorithms are proposed for adaptive spectral estimation including a new algorithm for the overdetermined case an efficient lattice algorithm is presented for solving the modified yule walker equations given the sample correlation coefficients the performance of some of the algorithms is illustrated by simulation results

paper pseudo canonical forms identifiable parametrizations and simple parameter estimation for linear multivariable systems parameter estimation in this paper the estimation of parameters for the pseudo canonical input output models introduced in correa g o and glover k automatica 20 429 442 1984 is considered modifications of three equation error type estimators linear least squares compensated and instrumental variable estimator are derived which incorporate the constraint on parameter values associated with these models the consistency of the proposed estimators is analysed finally results are presented on the construction of parametrization independent instrumental variables

large sample estimation of the ar parameters of an arma model the purpose of this note is to show that the optimal instrumental variable estimate of the ar parameters of an arma model recently proposed in 1 can also be interpreted as a large sample approximation of a maximum likelihood estimate

min max optimal instrumental variable estimation method for multivariate linear time series systems a min max optimal instrumental variable iv estimation method for multivariate linear time series systems is presented a monte carlo study is performed to assess the merits of the min max optimal iv method using two different parametrizations of the multivariate time series system the analysis indicates that the proposed estimation method yields accurate estimation results at modest computational cost

the kirchberg wassermann operator system is unique in 1998 kirchberg and wassermann constructed a separable nuclear operator system with the property that the canonical unital homomorphism from the maximal c algebra onto the c envelope is injective we show that such an operator system is unique and completely order isomorphic to the operator system associated with the noncommutative poulsen simplex

comments on the wong and polak minimax approach to accuracy optimization of instrumental variable methods optimizing the accuracy of instrumental variable iv estimates on a minimax basis is discussed some flaws in an earlier approach of this kind are pointed out it is indicated that the minimax approach to accuracy optimization of iv estimates although conceptually attractive will in general lead to intractable problems

on the asymptotic accuracy of pseudo linear regression algorithms the accuracy properties of a general pseudo linear regression plr method are examined both off line and on line algorithms are considered assuming the parameter estimates converge they will under weak conditions be asymptotically gaussian distributed expressions for the corresponding covariance matrices are given it is shown that the asymptotic covariance matrix of the off line plr algorithm is bounded from above by the matrix corresponding to the on line plr algorithm and from below by that corresponding to the prediction error method some simple numerical illustrations of the theoretical results are also included

direct and indirect least squares methods in continuous time parameter estimation the discrete time least squares approach is extended to the estimation of parameters in continuous nonlinear models the resulting direct integral least squares dils method is both simple and numerically efficient and it usually improves the mean squared error of the estimates compared with the conventional indirect least squares ils method the biasedness of the dils estimates may become serious if the sample points are widely spaced in time and or the signal to noise ratio is low and so a continuous time symmetric bootstrap sb estimator which removes this problem is described the dils sb and ils methods form a three stage procedure combining the robustness and numerical efficiency of direct methods with the asymptotic unbiasedness of ils procedures

on consistency of subspace methods for system identification subspace methods for identification of linear time invariant dynamical systems typically consist of two main steps first a so called subspace estimate is constructed this first step usually consists of estimating the range space of the extended observability matrix secondly an estimate of system parametersis obtained based on the subspace estimate in this paper the consistency of a large class of methods for estimating the extended observability matrix is analyzed persistence of excitation conditions on the input signal are given which guarantee consistent estimates for systems with only measurement noise for systems with process noise it is shown that a persistence of excitation condition on the input is not sufficient more precisely an example for which the subspace methods fail to give a consistent estimate of the transfer function is given this failure occurs even if the input is persistently exciting of any order it is also shown that this problem can be eliminated if stronger conditions on the input signal are imposed

quotients exactness and nuclearity in the operator system category abstract we continue our study of tensor products in the operator system category we define operator system quotients and exactness in this setting and refine the notion of nuclearity by studying operator systems that preserve various pairs of tensor products one of our main goals is to relate these refinements of nuclearity to the kirchberg conjecture in particular we prove that the kirchberg conjecture is equivalent to the statement that every operator system that is min er nuclear is also el c nuclear we show that operator system quotients are not always equal to the corresponding operator space quotients and then study exactness of various operator system tensor products for the operator system quotient we prove that an operator system is exact for the min tensor product if and only if it is min el nuclear we give many characterizations of operator systems that are min er nuclear el c nuclear min el nuclear and el max nuclear these characterizations involve operator system analogues of various properties from the theory of c algebras and operator spaces including the wep and llp

optimal instrumental variable estimates of the ar parameters of an arma process the modified yule walker myw equations for estimating the ar parameters of an arma process are presented as a special case of an instrumental variable iv method the consistency and accuracy of the ar parameter estimates are studied it is shown that estimation accuracy increases monotonically with the number of myw equations for an optimal choice of the weighting matrix used in the least squares solution of these equations the asymptotic error covariance of the optimal iv method equals that of the prediction error method the results of this paper verify experimental results reported in the literature regarding the performance of the myw method and provide the necessary accuracy analysis furthermore they suggest several simple asymptotically efficient multistep algorithms for estimating the ar parameters which are presented in a companion paper

a double parameter scaled bfgs method for unconstrained optimization abstract a double parameter scaled bfgs method for unconstrained optimization is presented in this method the first two terms of the known bfgs update formula are scaled with a positive parameter while the third one is scaled with another positive parameter these parameters are selected in such a way as to improve the eigenvalues structure of the bfgs update the parameter scaling the first two terms of the bfgs update is determined by clustering the eigenvalues of the scaled bfgs matrix on the other hand the parameter scaling the third term is determined as a preconditioner to the hessian of the minimizing function combined with the minimization of the conjugacy condition from conjugate gradient methods under the inexact wolfe line search the global convergence of the double parameter scaled bfgs method is proved in very general conditions without assuming the convexity of the minimizing function using 80 unconstrained optimization test functions with a medium number of variables the preliminary numerical experiments show that this double parameter scaled bfgs method is more efficient than the standard bfgs update or than some other scaled bfgs methods

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

updating conjugate directions by the brgs formula many iterative algorithms for optimization calculations form positive definite second derivative approximations b say automatically butb is not stored explicitly because of the need to solve equations of the formbd g we consider working with matricesz whose columns satisfy the conjugacy conditionsz 1 bz 1 particular attention is given to updatingz in a way that corresponds to revisingb by the bfgs formula a procedure is proposed that seems to be much more stable than the direct use of a product formula 1 an extension to this procedure provides some automatic rescaling of the columns ofz which avoids some inefficiencies due to a poor choice of the initial second derivative approximation our work is also relevant to active set methods for linear inequality constraints to updating the cholesky factorization ofb and to explaining some properties of the bfgs algorithm

focussing matrices for coherent signal subspace processing a class of focussing matrices is proposed for use in the coherent signal subspace method csm h wang and m kaveh ibid vol assp 33 aug 1985 when the directions of arrival of wideband sources fall into more than one group of one beamwidth each this class leads to performance substantially better than those suggested in previous studies on direction of arrival estimation new insight into the structures of various focussing matrices and their effect on the performance of csm is presented the performance of csm is compared for several classes of these matrices on the simulations as well as relative sufficiency analyses

on ℒ structures of nuclear c algebras we study the local operator space structure of nuclear c algebras it is shown that a c algebra is nuclear if and only if it is an space for some and actually for every 6 the constant provides an interesting invariant for nuclear c algebras indeed if is a nuclear c algebra then we have 1 6 and if is a unital nuclear c algebra with we show that must be stably finite we also investigate the connection between the rigid 1 structure and the rigid complete order 1 structure on c algebras where the latter structure has been studied by blackadar and kirchberg in their characterization of strong nf c algebras another main result of this paper is to show that these two local structrues are actually equivalent on unital nuclear c algebras we obtain this by showing that if a unital nuclear c algebra is a rigid 1 space then it is inner quasi diagonal and thus is a strong nf algebra it is also shown that if a unital nuclear c algebra is an 1 space then it is quasi diagonal and thus is an nf algebra

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 computation of the cramer rao bound for arma parameter estimation the cramer rao lower bound crlb provides a useful tool for evaluating the performance of parameter estimation techniques several techniques for the computation of the asymptotic form of the crlb for arma models are presented it is shown that the asymptotic crlb can be expressed as an explicit function of the model parameters

parallel quasi newton methods for unconstrained optimization we discuss methods for solving the unconstrained optimization problem on parallel computers when the number of variables is sufficiently small that quasi newton methods can be used we concentrate mainly but not exclusively on problems where function evaluation is expensive first we discuss ways to parallelize both the function evaluation costs and the linear algebra calculations in the standard sequential secant method the bfgs method then we discuss new methods that are appropriate when there are enough processors to evaluate the function gradient and part but not all of the hessian at each iteration we develop new algorithms that utilize this information and analyze their convergence properties we present computational experiments showing that they are superior to parallelization either the bfgs methods or newton s method under our assumptions on the number of processors and cost of function evaluation finally we discuss ways to effectively utilize the gradient values at unsuccessful trial points that are available in our parallel methods and also in some sequential software packages

limited memory reduced hessian methods for large scale unconstrained optimization limited memory bfgs quasi newton methods approximate the hessian matrix of second derivatives by the sum of a diagonal matrix and a fixed number of rank one matrices these methods are particularly effective for large problems in which the approximate hessian cannot be stored explicitly it can be shown that the conventional bfgs method accumulates approximate curvature in a sequence of expanding subspaces this allows an approximate hessian to be represented using a smaller reduced matrix that increases in dimension at each iteration when the number of variables is large this feature may be used to define limited memory reduced hessian methods in which the dimension of the reduced hessian is limited to save storage limited memory reduced hessian methods have the benefit of requiring half the storage of conventional limited memory methods in this paper we propose a particular reduced hessian method with substantial computational advantages compared to previous reduced hessian methods numerical results from a set of unconstrained problems in the cute test collection indicate that our implementation is competitive with the limited memory codes l bfgs and l bfgs b

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

transformation of uniformly distributed particle ensembles abstract this paper introduces a new method to construct asymptotically f distributed sequences of points in the r d the algorithm is based on a transformation proposed by hlawka and muck by exploitation of the special structure the method proves to be very efficient

the revised dfp algorithm without exact line search in this paper we discuss the convergence of the dfp algorithm with revised search direction under some inexact line searches we prove that the algorithm is globally convergent for continuously differentiable functions and the rate of convergence of the algorithm is one step superlinear and n step second order for uniformly convex objective functions from the proof of this paper we obtain the superlinear and n step second order convergence of the dfp algorithm for uniformly convex objective functions

recursive identification algorithms for continuous systems using an adaptive procedure abstract recursive identification algorithms for continuous systems from sampled input and output data are discussed the continuous system is identified through an approximated discrete time estimation model with continuous system parameters an approximated discrete time model of the continuous system under study is first obtained by bilinear transformation then using the estimated denominator of the transfer function of the discrete time model to construct adaptive iir filters introduced to avoid direct approximations of differentiations from sampled data an approximated discrete time estimation model with continuous system parameters is derived the discrete time estimation model is composed of filtered sampled system input and output signals with filtered inputs and delayed filtered outputs as instrumental variables some kinds of recursive instrumental variable identification algorithms are proposed to obtain consistent estimates in the presence of noise the proposed identification algorithms ha

reduced hessian quasi newton methods for unconstrained optimization quasi newton methods are reliable and efficient on a wide range of problems but they can require many iterations if the problem is ill conditioned or if a poor initial estimate of the hessian is used in this paper we discuss methods designed to be more efficient in these situations all the methods to be considered exploit the fact that quasi newton methods accumulate approximate second derivative information in a sequence of expanding subspaces associated with each of these subspaces is a certain reduced approximate hessian that provides a complete but compact representation of the second derivative information approximated up to that point algorithms that compute an explicit reduced hessian approximation have two important advantages over conventional quasi newton methods first the amount of computation for each iteration is significantly less during the early stages this advantage is increased by forcing the iterates to linger on a manifold whose dimension can be significantly smaller than the subspace in which curvature has been accumulated second approximate curvature along directions that lie off the manifold can be reinitialized as the iterations proceed thereby reducing the influence of a poor initial estimate of the hessian these advantages are illustrated by extensive numerical results from problems in the cute test set our experiments provide strong evidence that reduced hessian quasi newton methods are more efficient and robust than conventional bfgs methods and some recently proposed extensions

updating of conjugate direction matrices using members of broyden s family many iterative algorithms for optimization calculations use a second derivative approximation b say in order to calculate the search directiond b 1 f x in order to avoid invertingb we work with matricesz whose columns satisfy the conjugacy relationsztbz i we present an update ofz that is compatible with members of the broyden family that generate positive definite second derivative approximations the algorithm requires only 3n2 o n flops for the update ofz and the calculation ofd the columns of the resultantz matrices have interesting conjugacy and orthogonality properties with respect to previous second derivative approximations and function gradients respectively the update also provides a simple proof of dixon s theorem for the bfgs method we adapt the algorithm in order to obtain a null space method for linearly constrained calculations

brief continuous time approaches to identification of continuous time systems a fundamental continuous time approach to identification of continuous time systems is considered a consequent and coherent continuous time analysis leads to parameter estimation schemes expressed in the continuous time domain for the purpose of digital realization the estimators are discretized leading to various discrete time recursive procedures and exercised numerically

asymptotic analysis of the bias of the modified yule walker estimator an explicit formula is derived for the asymptotic bias in the autoregressive estimates obtained by the modified yule walker method the sample bias obtained in monte carlo simulations is compared to the theoretical formulas for two examples

system identification using nonstationary signals the conventional method for identifying the transfer function of an unknown linear system consists of a least squares fit of its input to its output it is equivalent to identifying the frequency response of the system by calculating the empirical cross spectrum between the system s input and output divided by the empirical auto spectrum of the input process however if the additive noise at the system s output is correlated with the input process e g in case of environmental noise that affects both system s input and output the method may suffer from a severe bias effect we present a modification of the cross spectral method that exploits nonstationary features in the data in order to circumvent bias effects caused by correlated stationary noise the proposed method is particularly attractive to problems of multichannel signal enhancement and noise cancellation when the desired signal is nonstationary in nature e g speech or image

matrix convexity operator analogues of the bipolar and hahn banach theorems abstract several basic results of convexity theory are generalized to the quantized matrix convex sets of wittstock these include the bipolar theorem a gauge version of the hahn banach theorem and the existence theorem for support functionals

lattice implementation of some recursive parameter estimation algorithms linear dynamic models of plants are usually parametrized by the coefficients of difference equations lattice structures and their reflection coefficients provide an alternative parametrization that offers several advantages including numerical robustness computational efficiency and ease of hardware implementation the recursive square root normalized lattice versions of the following well known parameter estimation algorithms are presented recursive least squares recursive instrumental variable extended least squares and recursive maximum likelihood

parameter consistency and quadratically constrained errors in variables least squares identification in this article we investigate the consistency of parameter estimates obtained from least squares identification with a quadratic parameter constraint for generality we consider infinite impulse response systems with coloured input and output noise in the case of finite data we show that there always exists a possibly indefinite quadratic constraint depending on the noise realisation that results in a constrained optimisation problem that yields the true parameters of the system when a persistency condition is satisfied when the noise covariance matrix is known to within a scalar multiple we prove that solutions of the quadratically constrained least squares qcls estimator with a semidefinite constraint matrix are both unbiased and consistent in the sense that the averaged problem and limiting problem produce respectively unbiased and true with probability 1 estimators in addition we provide numerical results that illustrate these properties of the qcls estimator

analysis of a self scaling quasi newton method we study the self scaling bfgs method of oren and luenberger 1974 for solving unconstrained optimization problems for general convex functions we prove that the method is globally convergent with inexact line searches we also show that the directions generated by the self scaling bfgs method approach newton s direction asymptotically this would ensure superlinear convergence if in addition the search directions were well scaled but we show that this is not always the case we find that the method has a major drawback to achieve superlinear convergence it may be necessary to evaluate the function twice per iteration even very near the solution an example is constructed to show that the step sizes required to achieve a superlinear rate converge to 2 and 0 5 alternately

a numerically stable dual method for solving strictly convex quadratic programs an efficient and numerically stable dual algorithm for positive definite quadratic programming is described which takes advantage of the fact that the unconstrained minimum of the objective function can be used as a starting point its implementation utilizes the cholesky and qr factorizations and procedures for updating them the performance of the dual algorithm is compared against that of primal algorithms when used to solve randomly generated test problems and quadratic programs generated in the course of solving nonlinear programming problems by a successive quadratic programming code the principal motivation for the development of the algorithm these computational results indicate that the dual algorithm is superior to primal algorithms when a primal feasible point is not readily available the algorithm is also compared theoretically to the modified simplex type dual methods of lemke and van de panne and whinston and it is illustrated by a numerical example

information tradeoffs in using the sample autocorrelation function in arma parameter estimation this paper considers bounds on the statistical efficiency of estimators of the poles and zeros of an arma process based on estimates of the process autocorrelation function acf special attention is paid to autoregressive ar and ar plus white noise processes it is seen that reducing the arma process data to a given set of consecutive lags of the popular lagged product acf estimates prior to parameter estimation increases cramer rao bounds on the generalized error covariance a parametric study of the bound deterioration for some illustrative signal and noise situations reveals some empirical strategies for choosing acf estimate lags to preserve statistical information analysis is based on the relative information index rii 2 and derivations of the large sample fisher s information matrix for the raw data and for the lagged product acf estimate of an arma process are included

a criterion for selecting information preserving data reductions for use in the design of multiple parameter estimators corresp a scalar measure of the fractional amount of the total information for parameter estimation that is retained when a record of raw data is reduced to a given statistic is introduced this measure the relative information index rii is a function of fisher s information matrices for the statistic and for the raw data and it resembles an efficiency measure in that it acquires values between zero and one a criterion based on the rii is formulated for statistic selection and some applications are discussed

injectivity of operator spaces we study the structure of injective operator spaces and the existence and uniqueness of the injective envelopes of operator spaces we give an easy example of an injective operator space which is not completely isometric to any c algebra this answers a question of wittstock 23 furthermore we show that an operator space e is injective if and only if there exists an injective c algebra a and two projections p and q in a such that e is completely isometric to paq

on instrumental variable estimation of sinusoid frequencies and the parsimony principle multiple sinusoids in noise can be modeled as an arma process with the ar parameters satisfying certain symmetry relations according to the parsimony principle the constraints on the ar parameters should he taken into account to get improved estimation accuracy it is shown in this note that when estimating the ar parameters by a general instrumental variable method such a parsimony does not necessarily apply however the parsimony principle does hold when an optimal instrumental variable method is used

performance evaluation of the modified yule walker estimator the modified yule walker myw equations are often used to estimate the autoregressive parameters of time series the asymptotic estimation error variance of these parameters can be computed using a formula developed for the instrumental variable method the performance of the myw estimator is studied by evaluating this formula for different signal to noise ratios and process bandwidths as a function of the number of equations used by the estimator the cramer rao lower bound for the estimation error variance is computed for comparison the optimally weighted myw estimator is briefly discussed

bounds on the accuracy of gaussian arma parameter estimation methods based on sample covariances the asymptotic accuracy of gaussian arma parameter estimation methods based on a fixed number of sample covariances is considered several key results are briefly reviewed including i a general asymptotic expression for the error covariance of the arma parameter estimates ii the fact that this error covariance is always greater than a certain lower bound iii the fact that this lower bound is strictly greater than the cramer rao bound iv an explicit arma estimation technique that asymptotically achieves the bound the key result of this note is a proof that this lower bound approaches the cramer rao bound as the number of sample covariances tends to infinity

the noncommutative choquet boundary let s be an operator system a self adjoint linear sub space of a unital c algebra a such that 1 s and a c s is generated by s a boundary representation for s is an irreducible rep resentationof c s on a hilbert space with the property that s has a unique completely positive extension to c s the set s of all unitary equivalence classes of boundary representations is the non commutative counterpart of the choquet boundary of a function system s c x that separates points of x it is known that the closure of the choquet boundary of a function system s is the y boundary of x relative to s the corresponding noncommutative problem of whether every operator system has suf ficiently many boundary representations was formulated in 1969 but has remained unsolved despite progress on related issues in particu lar it was unknown if s 6 for generic s in this paper we show that every separable operator system has sufficiently many boundary representations our methods use separability in an essential way

recursive identification algorithms for right matrix fraction description models multivariable identification algorithms are usually designed only for left matrix fraction description lmfd models in this paper we consider recursive identification algorithms for right matrix fraction description rmfd models with diagonal denominator matrices the algorithms are of prediction error pe and model reference mr type results from simulations illustrate the performance of the algorithms

brief paper optimal instrumental variable methods for identification of multivariable linear systems the identification of multivariable linear systems using instrumental variable iv methods is discussed the emphasis is on accuracy properties the iv estimates of multi input multi output system parameters are proved to be asymptotically gaussian distributed under weak conditions an explicit expression for the covariance matrix of the parameter estimates is given it is then shown how this matrix can be optimized by appropriately choosing the iv variant the optimal accuracy so obtained is for some model structures equal to that corresponding to a prediction error method

application of the lattice filter to robust estimation of ar and arma models a method for estimating the parameters of an autoregressive moving average arma model is proposed a p q stage lattice whitening filter is used to obtained consistent estimates of the ar parameters of an arma p p model it is shown that a set of ma parameter estimates can also be obtained using this approach with little added computation the method is used for estimation of the ar parameters of an arma process in additive white noise it is shown that the lattice filter is also useful in robust estimation of the ar parameter on an arma process with additive outliers

an approximation theorem for nuclear operator systems abstract we prove that an operator system s is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps s m n and m n s such that converges to id s in the point norm topology our proof is independent of the choi effros kirchberg characterization of nuclear c algebras and yields this characterization as a corollary we give an explicit example of a nuclear operator system that is not completely order isomorphic to a unital c algebra

c algebras generated by operator systems an operator systemx such thatx is ac algebra and such that the canonical embedding ofxinx is a unital complete isometry is called ac system ifais a unitalc algebra andlis a closed left ideal ofa thena l l has a natural operator system structure relative to which it is ac system it is shown that any separablec system is of this form for some separablea and that an arbitrary inseparablec system is an inductive limit of separablec systems associated with any operator systemxis a universalc algebrac u x which containsxas a generating subsystem and is maximal among suchc algebras in the sense that any other suchc algebra is canonically a homomorphic image ofc u x ifxis additionally ac system then thec subalgebrac r x ofx generated byxis minimal amongc algebras containingxas a generating subsystem in the sense thatc r x is canonically a homomorphic image of any other suchc algebra it follows that there is a canonical homomorphism c u x c r x which extends the identity map onx whenxis ac algebra of dimension greater than 1 is never injective one of the main results of the paper is that there exists a separable nuclearc systemxcontainingm2 c for which is an isomorphism this implies that for any embedding ofxas an operator subsystem of ac algebraa thec subalgebra ofagenerated byxis isomorphic toc u x moreoverc u m2 c is notc exact andc u m2 c c u x from which it follows thatc u x and hencea are not exactc algebras thusx though a nuclear operator system cannot be embedded in a nuclearc algebra

single sample modal identification of a nonstationary stochastic process gauss markov processes excited by nonstationary noises are encountered in the modeling of vibrating systems we prove that the classical instrumental variable method as well as the ho kalman realization algorithm for identifying the pole part modal characteristics of the model are consistent when used on a single sample of the nonstationary signal

sinusoidal signals with random amplitude least squares estimators and their statistical analysis the asymptotic properties of constrained and unconstrained least squares estimates of the parameters of a random amplitude sinusoid are analyzed an explicit formula for the asymptotic covariance matrix of the estimation errors is derived for both the constrained and unconstrained estimators accuracy aspects are investigated with the following main results for a certain weighting matrix which is shown to be the same for the constrained and unconstrained methods the estimation errors achieve their lower bounds it is proven that in the optimal case the constrained method always outperforms the unconstrained method it is also proven that the accuracy of the optimal estimators improves as the number of least squares equations increases a formula for the sample length needed for the asymptotic theory to hold is derived and its dependence on the lowpass modulating sequence is stressed simulations provide illustrations of the difference between the constrained and unconstrained estimators as well as the difference between the optimal and basic estimates the influence of the number of least squares equations and the characteristics of the lowpass envelope on the estimation accuracy is also investigated

on the parsimony principle the parsimony principle is frequently used in system identification on more or less heuristical grounds recently a formal proof of this principle has been given here the assumptions used in that proof are examined to some extent it will be shown by means of some counterexamples that these assumptions cannot be relaxed unless additional restrictions are introduced a result showing how the parsimony principle should be used when estimating the parameters of regression models by the least squares method is also presented

ein operatorwertiger hahn banach satz abstract we generalize arveson s extension theorem for completely positive mappings 1 to a hahn banach principle for matricial sublinear functionals with values in an injective c algebra or an ideal in b h we characterize injective w algebras by a matricial order condition we illustrate the matricial hahn banach principle by three applications 1 let a b b be unital c algebras b a subalgebra of a and b b injective if a b is a completely bounded self adjoint b bihomomorphism then it can be expressed as the difference of two completely positive b bihomomorphism 2 let m be a w algebra containing 1 h on a hilbert space h if m is finite and hyperfinite there exists an invariant expectation mapping p of b h onto m p is an extension of the center trace 3 combes 7 proved that a lower semicontinuous scalar weight on a c algebra is the upper envelope of bounded positive functionals we generalize this result to unbounded completely positive mappings with values in an injective w algebra

comparison of total least squares and instrumental variable methods for parameter estimation of transfer function models the estimation of the parameters of a transfer function model is considered relationships between the total least squares tls and instrumental variable iv approaches are outlined both methods

modifying the bfgs update by a new column scaling technique letb be a positive definite symmetric approximation to the second derivative matrix of the objective function of a minimization calculation we study modifications of the bfgs method that apply a scaling technique to the columns of a conjugate direction matrixz satisfyingz t bz i for a simple scaling technique similar to the ones considered by powell 1987 and 1989 we show that due to a two iteration cycle linear convergence can occur when the method is applied to a quadratic function and wolfe s line search is employed although for exact line searches quadratic termination can be proved we then suggest a different scaling technique that prevents certain columns thought to contain important curvature information from being scaled for this algorithm we prove global and superlinear convergence and demonstrate the superiority of our method over the bfgs formula on a range of illconditioned optimization problems moreover we present an implementation of our algorithm that requires only 3n 2 o n multiplications per iteration

fast adaptive algorithms for ar parameters estimation using higher order statistics time varying statistics in linear filtering and linear estimation problems necessitate the use of adaptive or time varying filters in the solution with the rapid availability of vast and inexpensive computation power models which are non gaussian even nonstationary are being investigated at increasing intensity statistical tools used in such investigations usually involve higher order statistics hos the classical instrumental variable iv principle has been widely used to develop adaptive algorithms for the estimation of arma processes despite the great number of iv methods developed in the literature the cumulant based procedures for pure autoregressive ar processes are almost nonexistent except lattice versions of iv algorithms this paper deals with the derivation and the properties of fast transversal algorithms hence by establishing a relationship between classical iv methods and cumulant based ar estimation problems new fast adaptive algorithms fast transversal recursive instrumental variable ftriv and generalized least mean squares glms are proposed for the estimation of ar processes the algorithms are seen to have better performance in terms of convergence speed and misadjustment even in low snr the extra computational complexity is negligible the performance of the algorithms as well as some illustrative tracking comparisons with the existing adaptive ones in the literature are verified via simulations the conditions of convergence are investigated for the glms

a tolerant algorithm for linearly constrained optimization calculations two extreme techniques when choosing a search direction in a linearly constrained optimization calculation are to take account of all the constraints or to use an active set method that satisfies selected constraints as equations the remaining constraints being ignored we prefer an intermediate method that treats all inequality constraints with small residuals as inequalities with zero right hand sides and that disregards the other inequality conditions thus the step along the search direction is not restricted by any constraints with small residuals which can help efficiency greatly particularly when some constraints are nearly degenerate we study the implementation convergence properties and performance of an algorithm that employs this idea the implementation considerations include the choice and automatic adjustment of the tolerance that defines the small residuals the calculation of the search directions and the updating of second derivative approximations the main convergence theorem imposes no conditions on the constraints except for boundedness of the feasible region the numerical results indicate that a fortran implementation of our algorithm is much more reliable than the software that was tested by hock and schittkowski 1981 therefore the algorithm seems to be very suitable for general use and it is particularly appropriate for semi infinite programming calculations that have many linear constraints that come from discretizations of continua