on the choice of parameterization for identification the effect on an identification procedure of the choice of system parameterization is considered first a formal framework is presented in which to assess this effect and some previous results are reviewed in this framework then the class of methods that minimize an input output objective function are studied sufficient conditions on identifiable parameterizations of linear models are stated which render the associated model estimators equally accurate in asymptotic statistical terms these are shown to apply to parameterizations with maximal number of free parameters

new developments for matrix fraction descriptions this article aims at giving a new answer for the challenging problem of the parametrisation of multi input multi output matrix fraction descriptions in order to reach this goal new parametrisations of matrix fraction descriptions called fully parametrised left matrix fraction descriptions f lmfd are first introduced their structural properties as well as their suitability for multi input multi output model description are more precisely analysed as any over parametrised model description the f lmfd cannot describe a transfer function uniquely the structure of the space of equivalent f lmfd is then investigated through the determination of its basis the study carried out in this article is the prelude to a computational improvement of the identification of matrix fraction descriptions with gradient based optimisation methods

the dynamics of some discrete population models in this paper we are interested in providing sufficient conditions guaranteeing the fact that all positive solutions of the discrete delay difference equation a ii 1 aa f a e converge as n 00 in e a is a constant real number with 0 0 sufficiently small thus formally equation e comes from x t h x t h yx t d x t r for small h if we set z f x ht then the preceding equation for t n and r h m becomes yh 1 1 h y n hd y n m which is of the form e where a 1 yh and f u hd u u 2 0 clearly h 0 is small if and only if a e 0 1 1069 h

global attractivity in nonlinear difference equations of higher order with a forcing term consider the following nonlinear difference equation of order k 1 with a forcing term 0 1 x n 1 a n x n b n f x n k r n n 0 1 where an is a positive sequence in 0 1 bn is a positive sequence rn is a real sequence k is a nonnegative integer and f is a continuous function with 0 we establish a sufficient condition for every solution of eq 0 1 to converge to zero as n several new global attractivity results are obtained for some special cases of eq 0 1 which have been studied widely in the literature our results can be applied to some difference equations derived from mathematical biology

an adaptive orthogonal search algorithm for model subset selection and non linear system identification a new adaptive orthogonal search aos algorithm is proposed for model subset selection and non linear system identification model structure detection is a key step in any system identification problem this consists of selecting significant model terms from a redundant dictionary of candidate model terms and determining the model complexity model length or model size the final objective is to produce a parsimonious model that can well capture the inherent dynamics of the underlying system in the new aos algorithm a modified generalized cross validation criterion called the adjustable prediction error sum of squares apress is introduced and incorporated into a forward orthogonal search procedure the main advantage of the new aos algorithm is that the mechanism is simple and the implementation is direct and easy and more importantly it can produce efficient model subsets for most non linear identification problems

model structure selection for multivariable systems by cross validation methods using cross validation ideas two procedures are proposed for making a choice between different model structures used for approximate modelling of multivariable systems the procedures are derived under fairly general conditions the true system does not need to be contained in the model set model structures do not need to be nested and different criteria may be used for model estimation and validation the proposed structure selection rules are shown to be invariant to parameter scaling under certain conditions essentially requiring that the system belongs to the model set and that the maximum likelihood method is used for parameter estimation they are shown to be asymptotically equivalent to the generalized akaike structure selection criteria

structure and order estimation of multivariable stochastic processes an easy to implement numerically efficient algorithm which estimates the kronecker invariants is presented a procedure allowing estimation of the structure of a state space representation for a multivariable stationary stochastic process from measured output data is presented it is assumed that the observed vector time series is a realization of a process with rational spectrum or the output of a stable time invariant linear system driven by white noise an algorithm is proposed which selects a maximal set of linearly independent rows of the hankel matrix built upon the estimated covariance sequence and thus yields estimates of the kronecker invariants when applied to simulated examples it systematically yielded the good structure without any ambiguity i e with a surprising robustness with respect to the choice of the probability of false alarm the numerical efficiency of the procedure is remarkable and no exhaustive search over the set of all possible kronecker indexes has to be performed

map model order selection rule for 2 d sinusoids in white noise we consider the problem of jointly estimating the number as well as the parameters of two dimensional 2 d sinusoidal signals observed in the presence of an additive white gaussian noise field existing solutions to this problem are based on model order selection rules and are derived for the parallel one dimensional 1 d problem these criteria are then adapted to the 2 d problem using heuristic arguments employing asymptotic considerations we derive a maximum a posteriori map model order selection criterion for jointly estimating the parameters of the 2 d sinusoids and their number the proposed model order selection rule is strongly consistent as an example the model order selection criterion is applied as a component in an algorithm for parametric estimation and synthesis of textured images

classical test theory as a first order item response theory application to true score prediction from a possibly nonparallel test we give an account of classical test theory ctt in terms of the more fundamental ideas of item response theory irt this approach views classical test theory as a very general version of irt and the commonly used irt models as detailed elaborations of ctt for special purposes we then use this approach to ctt to derive some general results regarding the prediction of the true score of a test from an observed score on that test as well from an observed score on a different test this leads us to a new view of linking tests that were not developed to be linked to each other in addition we propose true score prediction analogues of the dorans and holland measures of the population sensitivity of test linking functions we illustrate the accuracy of the first order theory using simulated data from the rasch model and illustrate the effect of population differences using a set of real data

model structure selection by cross validation two criteria for choosing between different model structures are proposed their derivation is within a natural cross validatory assessment context and is fairly assumption free in particular the two criteria can be used for discriminating between non nested model structures and more importantly the true system is not required to belong to the considered set of models should the true system belong to the model set the two proposed criteria will asymptotically reduce to some well known structure selection criteria this is believed to be a desirable feature of our proposals on the other hand it provides a nice cross validation interpretation of some well known model structure selection rules also the cross validation interpretation helps one to choose which criteria to use in a given application the paper also has a second purpose somewhat decoupled from that mentioned above it contains an extensive survey of the literature that is useful in its own right

the determination of optimum structures for the state space representation of multivariate stochastic processes when identifying a model for a multivariate stationary stochastic process an important problem is that of determining the structure of the state variable model several overlapping parameterizations can usually be fitted to a given process and the question arises as to which structure leads to the most accurate parameter estimates the accuracy of parameter estimates is often measured by the determinant of the fisher information matrix we show that all admissible structures will give asymptotically the same value to this criterion for finite data some structures may still be better than others and two heuristic structure estimation methods are analyzed some simulation results are also presented

efficient mixed spectrum estimation with applications to target feature extraction we present a decoupled parameter estimation dpe algorithm for estimating sinusoidal parameters from both 1 d and 2 d data sequences corrupted by autoregressive ar noise in the first step of the dpe algorithm we use a relaxation relax algorithm that requires simple fast fourier transforms ffts to obtain the estimates of the sinusoidal parameters we describe how the relax algorithm may be used to extract radar target features from both 1 d and 2 d data sequences in the second step of the dpe algorithm a linear least squares approach is used to estimate the ar noise parameters the dpe algorithm is both conceptually and computationally simple the algorithm not only provides excellent estimation performance under the model assumptions in which case the estimates obtained with the dpe algorithm are asymptotically statistically efficient but is also robust to mismodeling errors

asymptotic properties of the positive equilibrium of a discrete survival model this paper is concerned with the discrete wazewska and lasota model x n 1 x email protected n pe n x n k where email protected 0 1 n email protected 0 and email protected 0 1 2 we show that every positive solution of is persistent and then we provide sufficient conditions for oscillation of all solutions about x finally we give sufficient conditions for x to be stable or attractive

periodic solution and almost periodic solution of impulsive lasota wazewska model with multiple time varying delays this paper deals with the impulsive lasota wazewska model with multiple time varying delays our results show that the system is uniformly persistent under some appropriate conditions the sufficient condition for global exponential stability of the system is given applying mawhin s continuation theorem of coincidence degree we prove that the periodic system has at least one strictly positive periodic solution by employing hull theory of impulsive almost periodic system the existence and uniqueness of strictly positive almost periodic solution of the almost periodic system is obtained two examples are provided to illustrate our results

on diffeomorphisms between classes of linear systems abstract in this paper we show that the following classes of linear dynamical systems are diffeomorphic to each other fixed order asymptotically stable strictly bounded real strictly positive real stable and minimum phase and invertible these results are then used to prove the diffeomorphisms between the state bundles associated with these classes of systems and between their associated principal fibre bundles we shall conclude this paper by discussing how these results can be used to deduce geometric properties of other classes of linear systems and to construct overlapping parametrizations

on tikhonov regularization bias and variance in nonlinear system identification abstract regularization is a general method for solving ill posed and ill conditioned problems traditionally ill conditioning in system identification problems is approached using regularization methods such as ridge regression and principal component regression in this work it is argued that the tikhonov regularization method is a powerful alternative for regularization of nonlinear system identification problems by introducing smoothness of the model as a prior its properties is discussed in terms of an analysis of bias and variance and illustrated by a semirealistic simulation example

on line structure selection for multivariable state space models an algorithm is described for the selection of model structure for identifying state space models of black box character the algorithm receives as input a given system in a given parametrization it is then tested whether this parametrization is suitable well conditioned for identification purposes if not a better one is selected and the transformation of the system to the new representation is performed this algorithm can be used as a block both in an iterative off line identification procedure and for recursive on line identification it can be called whenever there is some indication that the model structure is ill conditioned it is discussed how the model structure selection algorithm can be interfaced with an off line identification procedure a complete procedure is described and tested on real and simulated data

paper selecting the best linear transfer function model statistics currently used to determine the best model order based on the covariance of the parameter estimates or the instrumental product moment matrix are critically examined particularly for their applicability to situations where input and output units differ or where there is a large or small steady state gain a normalization process is advocated which extends the usefulness and reliability of the statistics in these situations a procedure for comparing determinant statistics for models of different orders is described which simplifies current methods the improved procedures and statistics are compared using simulated data and an instrumental variable estimation method confirming their worth

instrumental product moment model order testing extensions and application the model order testing of linear dynamical models from input output data is considered using instrumental product moment ipm methods in particular the basic technique is extended to cover more general situations and an application to aircraft engine testing is presented

identification of non linear system structure and parameters using regime decomposition abstract an off line algorithm for empirical modeling and identification of non linear dynamic systems is presented the minimal input to the algorithm is a sequence of empirical data and the model order using this information the algorithm searches for an optimal model structure and parameters within a rich non linear model set the model representation is based on the interpolation of a number of simple local models where each local model has a limited range of validity but the local models yield a complete global model when interpolated the method is illustrated using simulated data

identification of non linear systems using empirical data and prior knowledge an optimization approach abstract the choice of a parametric model structure in empirical and semi empirical non linear modeling is usually viewed as an important and critical step however it is known that by augmenting the least squares identification criterion with a term that imposes a penalty on the non smoothness of the model an optimal non parametric model can be found explicitly the optimal non parametric model will depend on the particular form of the penalty which can be looked upon as a priori knowledge or the desired properties of the model in this paper these results are extended in several directions i we show how useful types of prior knowledge other than smoothness can be included as a term in the criterion or as a constraint and how this influences the optimal model ii dynamic models and a general prediction error penalty are considered iii we present a practical numerical procedure for the identification of a close to optimal semi parametric model the numerical approach is motivated by the difficulty of deriving the optimal non parametric model if there are complicated constraints or penalty terms in the criterion and finally iv we discuss determination of the appropriate model complexity through selecting weights on the different penalties on the basis of empirical data since the optimal non parametric model is identified using an augmented optimization criterion and all prior knowledge and desired model properties may be specified through the augmented optimization criterion it is the choice of this criterion that is critical in this approach this elevates the empirical and semi empirical modeling problems to a more transparent and engineering friendly level than is achieved by directly specifying a parametric model structure hence our results shed some more light on modern non linear empirical modeling approaches like radial basis functions splines and neural networks in addition to providing a fundamental insight into the role of different kinds of prior knowledge this high level formulation is also attractive from a practical point of view as it lies closer to engineering thinking and less guesswork is required the flexibility and power of this approach are illustrated with a semi realistic simulation example

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

subspace based multivariable system identification from frequency response data two noniterative subspace based algorithms which identify linear time invariant mimo multi input multioutput systems from frequency response data are presented the algorithms are related to the recent time domain subspace identification techniques the first algorithm uses equidistantly in frequency spaced data and is strongly consistent under weak noise assumptions the second algorithm uses arbitrary frequency spacing and is strongly consistent under more restrictive noise assumptions promising results are obtained when the algorithms are applied to real frequency data originating from a large flexible structure

dimensionally recursive order determination of linear discrete system it is well known that the determinant ratio of the product moment matrix of observed input output data gives a quick way of testing the order of a linear discrete system and that the ipm instrumental product moment matrix is useful for eliminating the effect of the noise this paper describes the dimensionally recursive algorithm for the determinant ratio associated with a new ipm matrix this ipm matrix is constructed by using the lagged inputs themselves as the instrumental variables so that it would have a nesting structure the algorithm is derived by taking advantage of its nesting structure a particular quantity yielded naturally during the algorithm is shown to be a useful order test statistic and a more robust order statistic is developed by using the parameter estimate given during the algorithm by monte carlo simulations the test procedures based on these statistics are confirmed to be valid in spite of the simple construction of the ipm matrix even in the case where the noise is seriall

indirect adaptive pole placement control of mimo stochastic systems self tuning results in this paper we consider indirect adaptive pole placement control appc of linear multivariable stochastic systems instead of the canonical representation often used in the literature we propose using a non minimal but otherwise uniquely identifiable pseudo canonical parameterization that is more suitable for multivariable armax model identification to identify the plant we use the weighted extended least squares wels algorithm a least squares method with slowly decreasing weights which was introduced in bercu 1995 the pole placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable we prove that with a reasonable amount of prior information the resulting appc scheme is globally stabilizing and asymptotically self tuning regardless of the degree of persistency of external excitation these results represent the most complete study of stochastic multivariable appc systems to this date

the range error test in the structural identification of linear multivariable systems among the approaches that have been proposed in recent years for the identification of discrete time linear multivariable systems very efficient procedures are based on the introduction of a set of input output canonical models and on the separate determination of the process structure structural identification and parameters parametric identification this paper introduces a new simple test which allows us to perform the structural identification without the drawbacks usually associated with singularity tests the proposed test gives an a priori prediction of the model performance in order to avoid trial and error procedures in the determination of a suitable structure for the process to be identified

a higher order correlation method for model order and parameter estimation abstract the identification of linear systems with unknown orders is considered the observed input and output signals are corrupted by the gaussian random coloured noise or other non gaussian random coloured noise with zero third order statistics it is also assumed that a priori statistical information of these two kinds of noise input and output is unknown the input signal to the identified system is a zero mean stationary non gaussian random sequence by applying a proposed estimation algorithm the system orders and parameters can be estimated accurately finally two simulation results are presented to illustrate the proposed algorithm

invariants and canonical forms for systems structural and parametric identification the basic definitions regarding invariant functions and canonical forms for an equivalence relation on a generic set are first recalled with reference to observable state space models and to the equivalence relation induced by a change of basis it is then shown how the image of a complete set of independent invariants for the considered equivalence relation can be used to parametrize a subset of canonical forms in the given set then the set of polynomial input output models of the type p z y t q z u t and the equivalence relation induced by the premultiplication of p and q by a unimodular matrix are considered and canonical forms parametrized by a complete set of independent invariants introduced since the two sets of canonical forms share common sets of complete independent invariants very simple algebraical links between state space and input output canonical forms can be deduced the previous results are used to design efficient algorithms solving the problem of the canonical structural and parametric realization and identification of generic input output sequences generated by a linear discrete time invariant multivariable system the results obtained in the identification of a real process are then reported

the attack of the psychometricians this paper analyzes the theoretical pragmatic and substantive factors that have hampered the integration between psychology and psychometrics theoretical factors include the operationalist mode of thinking which is common throughout psychology the dominance of classical test theory and the use of construct validity as a catch all category for a range of challenging psychometric problems pragmatic factors include the lack of interest in mathematically precise thinking in psychology inadequate representation of psychometric modeling in major statistics programs and insufficient mathematical training in the psychological curriculum substantive factors relate to the absence of psychological theories that are sufficiently strong to motivate the structure of psychometric models following the identification of these problems a number of promising recent developments are discussed and suggestions are made to further the integration of psychology and psychometrics

an efficient linear method for arma spectral estimation a three step method for obtaining asymptotically maximum likelihood arma spectral estimates using only linear transformations of the data is presented the computational efficiency of the algorithm is comparable to that of yule walker algorithms but the three step method gives asymptotically statistically efficient estimates the implementation of the algorithm is discussed in detail and numerical examples are presented to illustrate its performance

multifold predictive validation in armax time series models this article presents a new procedure for multifold predictive validation in time series the procedure is based on the so called filtered residuals in sample prediction errors evaluated in such a way that they are similar to out of sample ones the filtered residuals are obtained from parameters estimated by eliminating from the estimation process the estimated innovations at the points to be predicted thus instead of using the deletion of observations to validate the predictions as in classical cross validation the procedure is based on deletion of the estimated innovations it is proved that the filtered residuals are uncorrelated up to terms of small order with the in sample innovations a property shared with the out of sample residuals the parameters needed for computing the filtered residuals can be obtained by estimating a model with innovational outliers at the points to be predicted the proposed multifold predictive validation is asymptotically equivalent to an efficient model selecti

asymptotic distribution of the order selected by aic in multivariate autoregressive model fitting first statistical properties of partial autocorrelation matrices of multivariate autoregressive processes are briefly reviewed then using the result we derive the asymptotic distribution of the order selected by akaike s information criterion contrary to our intuition the asymptotic probability of selecting the correct order tends to 1 as the number of the variates becomes large

permanence oscillation and attractivity of the discrete hematopoiesis model with variable coefficients abstract in this paper we consider the nonlinear delay difference equation with periodic coefficients p n 1 p n n p n n 1 p n m and demonstrate that solutions are permanent the existence of a positive periodic solution is proven and sufficient conditions for the attractivity of this solution are obtained oscillation and nonoscillation about the positive periodic solution is considered

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

on the sampling theory roundations of item response theory models item response theory it models are now in common use for the analysis of dichotomous item responses this paper examines the sampling theory foundations for statistical inference in these models the discussion includes some history on the stochastic subject versus the random sampling interpretations of the probability in irt models the relationship between three versions of maximum likelihood estimation for irt models estimating versus estimating predictors irt models and loglinear models the identifiability of irt models and the role of robustness and bayesian statistics from the sampling theory perspective

application of statistical information criteria for optimal fuzzy model construction theoretical studies have shown that fuzzy models are capable of approximating any continuous function on a compact domain to any degree of accuracy however constructing a good fuzzy model requires finding a good tradeoff between fitting the training data and keeping the model simple a simpler model is not only easily understood but also less likely to overfit the training data even though heuristic approaches to explore such a tradeoff for fuzzy modeling have been developed few principled approaches exist in the literature due to the lack of a well defined optimality criterion in this paper we propose several information theoretic optimality criteria for fuzzy models construction by extending three statistical information criteria 1 the akaike information criterion aic 1974 2 the bhansali downham information criterion bdic 1977 and 3 the information criterion of schwarz 1978 and rissanen 1978 sric we then describe a principled approach to explore the fitness complexity tradeoff using these optimality criteria together with a fuzzy model reduction technique based on the singular value decomposition svd the role of these optimality criteria in fuzzy modeling is discussed and their practical applicability is illustrated using a nonlinear system modeling example

scattering from very large randomly rough surfaces using a markov random field equivalent current a markov random field mrf model is employed to learn the statistical properties of an equivalent current situated above a rough surface where this equivalent current represents near field electromagnetic scattered fields the mrf parameters are learned by considering numerical scattering from a relatively small rough surface which can be solved efficiently via existing numerical methods the mrf parameters may then be used to synthesize multiple realizations of the equivalent current associated with scattering from a much larger rough surface these equivalent currents may be used to efficiently calculate the far field scattered field statistics for large surfaces the advantages of this approach are manifested in the fact that once the mrf parameters are learned a forward model is no longer needed to generate random realizations of the equivalent currents and the mrf model can be employed to generate equivalent surfaces of size beyond the capability of existing numerical models to improve the accuracy of the mrf model a narrowband filter is used to preprocess the computed current distributions prior to mrf model training one dimensional rough surfaces are considered here to demonstrate the idea and the method of ordered multiple interactions momi is employed to perform the numerical forward modeling promising mrf generated results are demonstrated with comparison to direct momi solutions

the global attractivity of difference equations of nonincreasing nonlinearities with applications abstract the global attractivity of the unique positive equilibrium of the equation x n 1 g x n k 1 x n k 2 x n k m n 0 1 2 is investigated where g is a nonincreasing continuous function in each of its arguments and the k are positive integers we are able to use our results to extract some important global attractivity criteria of the positive equilibria of the discrete clark model x n 1 x n f x n k and the rational recursive sequence x n 1 a bx n a x n 1 as well

parameter and structure identification of linear multivariable systems abstract in this paper a parameter and structure identification scheme which can be used for both continuous and discrete time systems is presented this scheme has an on line nature and it incorporates standard techniques such as state variable filters and adaptation laws developed through stability analysis the canonical form being used is based on the output injection which is constructed to assign all the poles of the system to an arbitrary chosen real number it is therefore named the canonical form

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

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

recursive estimation of mixed autoregressive moving average order summary the order p q of an autoregressive moving average sequence y t may be estimated by minimizing a criterion log 2 p q log t t with respect to p and q where 2 is the maximum likelihood estimate of the variance of the innovations t it is suggested that instead a2 be estimated from a series of regressions of y t on y t 1 y t 2 y t p 5 t 1 t q where the t are obtained by fitting a long autoregression to the data it is shown how the sequence of regressions may for p q be economically recursively calculated by embedding them in a sequence of bivariate autoregressions asymptotic properties of the procedure are established under very general conditions

extinction persistence and global stability in models of population growth abstract first we systematize earlier results on the global stability of discrete model a n 1 a n f a n m of population growth second we invent the effect of delay m when f is unimodal new deep and strong results are discussed in section 4 although theorems 3 5 section 3 are still freshly new this paper may be considered as a discrete version of our earlier work on the model x t x t f x t d v giang y lenbury nonlinear delay differential equations involving population growth math comput modelling 40 2004 583 590 we are mainly using limit set of persistent solution which is discussed in more general by p walters an introduction to ergodic theory springer verlag berlin 1982

multilevel model prediction multilevel models are proven tools in social research for modeling complex hierarchical systems in multilevel modeling statistical inference is based largely on quantification of random variables this paper distinguishes among three types of random variables in multilevel modeling model disturbances random coefficients and future response outcomes and provides a unified procedure for predicting them these predictors are best linear unbiased and are commonly known via the acronym blup they are optimal in the sense of minimizing mean square error and are bayesian under a diffuse prior