a new kernel based approach for linear system identification this paper describes a new kernel based approach for linear system identification of stable systems we model the impulse response as the realization of a gaussian process whose statistics differently from previously adopted priors include information not only on smoothness but also on bibo stability the associated autocovariance defines what we call a stable spline kernel the corresponding minimum variance estimate belongs to a reproducing kernel hilbert space which is spectrally characterized compared to parametric identification techniques the impulse response of the system is searched for within an infinite dimensional space dense in the space of continuous functions overparametrization is avoided by tuning few hyperparameters via marginal likelihood maximization the proposed approach may prove particularly useful in the context of robust identification in order to obtain reduced order models by exploiting a two step procedure that projects the nonparametric estimate onto the space of nominal models the continuous time derivation immediately extends to the discrete time case on several continuous and discrete time benchmarks taken from the literature the proposed approach compares very favorably with the existing parametric and nonparametric techniques

maximum likelihood estimators and worst case optimal algorithms for system identification abstract for system identification problems with stochastic noise maximum likelihood estimators are frequently used if noise is deterministic worst case optimal algorithms should be considered in this paper we study the following problem under what circumstances are maximum likelihood estimators optimal in the worst case

overall concordance correlation coefficient for evaluating agreement among multiple observers accurate and precise measurement is an important component of any proper study design as elaborated by lin 1989 biometrics 45 255 268 the concordance correlation coefficient ccc is more appropriate than other indices for measuring agreement when the variable of interest is continuous however this agreement index is defined in the context of comparing two fixed observers in order to use multiple observers in a study involving large numbers of subjects there is a need to assess agreement among these multiple observers in this article we present an overall ccc occc in terms of the interobserver variability for assessing agreement among multiple fixed observers the occc turns out to be equivalent to the generalized ccc king and chinchilli 2001 statistics in medicine 20 2131 2147 lin 1989 lin 2000 biometrics 56 324 325 when the squared distance function is used we evaluated the occc through generalized estimating equations barnhart and williamson 2001 biometrics 57 931 940 and u statistics king and chinchilli 2001 for inference this article offers the following important points first it addresses the precision and accuracy indices as components of the occc second it clarifies that the occc is the weighted average of all pairwise cccs third it is intuitively defined in terms of interobserver variability fourth the inference approaches of gee and the u statistics are compared via simulations for small samples fifth we illustrate the use of the occc by two medical examples with the gee u statistics and bootstrap approaches

optimal sampling schedule for parameter estimation of linear models with unknown but bounded measurement errors the problem of optimal sampling design for parameter estimation when data are generated by linear models is addressed the measurements are assumed to be corrupted by an unknown but bounded additive noise the sampling design assumes that the number of samples is unconstrained and no replication is allowed two main results are shown 1 for particular classes of linear models the optimal number of measurements is equal to the number of parameters as in the statistical context 2 the uncertainty intervals of the parameter estimates are bounded from above by quantities that can be computer a priori knowing only the model and the error structure

control oriented system identification a worst case deterministic approach in h sub infinity the authors formulate and solve two related control oriented system identification problems for stable linear shift invariant distributed parameter plants in each of these problems the assumed a priori information is minimal consisting only of a lower bound on the relative stability of the plant an upper bound on a certain gain associated with the plant and an upper bound on the noise level the first of these problems involves identification of a point sample of the plant frequency response from a noisy finite output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest this problem leads naturally to the second problem which involves identification of the plant transfer function in h sub infinity from a finite number of noisy point samples of the plant frequency response concrete plans for identification algorithms are provided for each of these two problems

identification of probabilistic system uncertainty regions by explicit evaluation of bias and variance errors a procedure is developed for identification of probabilistic system uncertainty regions for a linear time invariant system with unknown dynamics on the basis of time sequences of input and output data the classical framework is handled in which the system output is contaminated by a realization of a stationary stochastic process given minor and verifiable prior information on the system and the noise process frequency response pulse response and step response confidence regions are constructed by explicitly evaluating the bias and variance errors of a linear regression estimate in the model parametrizations use is made of general forms of basis functions conservatism of the uncertainty regions is limited by focusing on direct computational solutions rather than on closed form expressions using an instrumental variable method for identification the procedure is suitable also for input output data obtained from closed loop experiments

poset block equivalence of integral matrices given square matrices b and b with a poset indexed block structure for which an ij block is zero unless i j when are there invertible matrices u and v with this required zero block structure such that ubv b we give complete invariants for the existence of such an equivalence for matrices over a principal ideal domain r as one application when r is a field we classify such matrices up to similarity by matrices respecting the block structure we also give complete invariants for equivalence under the additional requirement that the diagonal blocks of u and v have determinant 1 the invariants involve an associated diagram the k web of r module homomorphisms the study is motivated by applications to symbolic dynamics and c algebras

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

structure selection for bounded parameter models consistency conditions and selection criterion strong consistency conditions for structure selection in bounded parameter models are studied a certain robust selection criterion based on the volume of the exact parameter bounding polytope is proposed for linear regression models the effectiveness of the polytope volume criterion is demonstrated on a model nonlinear in its variables but linear in its parameters its strong consistency is proved for a large class of noise distributions the usual assumptions on the noise namely independence constant variance or martingale difference properties need not be made but asymptotic independence is assumed

experiment design in a bounded error context comparison with d optimality abstract the problem of optimal experiment design for linear regression models is addressed the measurement errors are supposed to be bounded with no other hypothesis on their distribution contrary to the classical statistical approach an experiment is considered here as optimal if it minimizes the volume of the set of all parameters that are consistent with the data the model structure and the noise bounds this new design policy is compared to the classical d optimal design used in a statistical context when the number of measurements is equal to the number of parameters to be estimated the new optimality criterion although relying on quite different hypotheses on the noise distribution is shown to lead to the same optimal policy as a d optimality criterion this is no longer true when more measurements are to be made depending on the shape of the admissible experimental domain it is sometimes possible to design optimal experiments without any calculations an algorithmic procedure is suggested to be used when this is not so

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

robust identification and galois sequences abstract worst case l1 identification is studied for bibo stable linear shift invariant systems it is shown that the chebyshev identification method when used with galois input designs satisfies a certain robust convergence property and provides l1 model error bounds in worst case identification of bibo stable systems with a uniformly bounded noise set up the robust identification methodology developed is compatible with the modelling requirements of modern robust control design

a generalized orthonormal basis for linear dynamical systems in many areas of signal system and control theory orthogonal functions play an important role in issues of analysis and design in this paper it is shown that there exist orthogonal functions that in a natural way are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l sub 2sup n to this end use is made of balanced realizations of inner transfer functions the orthogonal functions can be considered as generalizations of for example the pulse functions laguerre functions and kautz functions and give rise to an alternative series expansion of rational transfer functions it is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion i e to obtain a good approximation by retaining only a finite number of expansion coefficients consequences for identification of expansion coefficients are analyzed and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients

identification and application of bounded parameter models abstract the place of parameter bounding algorithms in identification methodology is discussed such algorithms provide a radical alternative to the computation of parameter point estimates and covariances instead of p d f or mean and covariance for the noise and prior parameter estimates they require bounds in an essentially deterministic model formulation the paper is a preliminary review of some standard tasks namely experiment design testing for outliers toleranced prediction and worst case control design in the context of parameter bounding identification computational requirements of these tasks are examined and the limitations of existing parameter bounding algorithms are noted

necessary and sufficient conditions for robust identification of uncertain lti systems abstract robust identification of uncertain systems arises whenever a chosen family of models does not completely describe reality in these situations the issue of unmodeled dynamics gains significance in addition to random measurement noise to deal with such mixed stochastic deterministic settings we introduce a novel notion for robust consistency which requires that the expectation with respect to noise of the worst case with respect to unmodeled dynamics identification error asymptotically approach zero it turns out that this notion leads to transparent necessary and sufficient conditions we show that robust consistency holds if and only if there is an instrument input pair capable of annihilating the residual error as well as stochastic noise an extension of this result to the well known bounded but unknown noise model shows that if we were to remove a set of lebesgue measure zero the error bound asymptotically approaches zero

consistent parameter bounding identification for linearly parametrized model sets abstract in standard parameter bounding identification a time domain bound on the noise signal is used to construct parameter bounds one of the properties of this standard approach is that there is no consistency if a conservative noise bound has been chosen it is shown that alternative bounds on the noise signal give rise to consistent parameter bounding identification methods i e asymptotically in the number of data samples the feasible parameter set converges to the true parameter vector the first alternative noise bound that is introduced is a bound on the cross covariance between the noise and some instrumental input signal the noise bound is represented by a small number of linear inequalities which can be used in parameter bounding by linear programming it is shown that there is consistency under fairly general conditions even when a conservative bound has been chosen additionally a procedure is presented to estimate the cross covariance bound from data similar consistency results are shown for two other types of noise bounds a bound on the discrete fourier transform of the noise in combination with sinusoidal excitation and a time domain bound on the noise after measurement averaging with periodic excitation

a non parametric approach to estimate the total deviation index for non normal data concordance indices are used to assess the degree of agreement between different methods that measure the same characteristic in this context the total deviation index tdi is an unscaled concordance measure that quantifies to which extent the readings from the same subject obtained by different methods may differ with a certain probability common approaches to estimate the tdi assume data are normally distributed and linearity between response and effects subjects methods and random error here we introduce a new non parametric methodology for estimation and inference of the tdi that can deal with any kind of quantitative data the present study introduces this non parametric approach and compares it with the already established methods in two real case examples that represent situations of non normal data more specifically skewed data and count data the performance of the already established methodologies and our approach in these contexts is assessed by means of a simulation study copyright 2015 john wiley sons ltd

strong shift equivalence and positive doubly stochastic matrices abstract we give sufficient conditions for a positive stochastic matrix to be similar and strong shift equivalent over r to a positive doubly stochastic matrix through matrices of the same size we also prove that every positive stochastic matrix is strong shift equivalent over r to a positive doubly stochastic matrix consequently the set of nonzero spectra of primitive stochastic matrices over r with positive trace and the set of nonzero spectra of positive doubly stochastic matrices over r are identical we exhibit a class of 2 2 matrices pairwise strong shift equivalent over r through 2 2 matrices for which there is no uniform upper bound on the minimum lag of a strong shift equivalence through matrices of bounded size in contrast we show for any n n primitive matrix of positive trace that the set of positive n n matrices similar to it contains only finitely many sse r classes

optimal algorithms theory for robust estimation and prediction this paper deals with the theory of optimal algorithms for problems which cannot be solved exactly the theory developed allows for the derivation of new and interesting results in parameter estimation and in time series prediction in situations where no reliable statistical hypothesis can be made on the functions and modeling errors involved but only a bound on them is known in particular the derivation of computationally simple optimal algorithms for these two problems is investigated the practical effectiveness of the algorithms obtained is illustrated by several numerical examples

brief on robustness in system identification this paper studies robustness issues in system identification specifically a general framework for robust convergence analysis is given for identification of stable linear time invariant systems this is used to derive a rather complete set of results on robust convergence under average l p norms orlicz norms and cross correlation type noise semi norms the new theory is used to discuss and to study robustness issues in identification of linear time invariant models when the true plant is not exactly linear robustness issues in system identification against unmodelled nonlinear dynamics are important as real plants exhibit typically at best nearly linear dynamics the results show clearly that the effects of unmodelled dynamics are typically more serious than those of random noise

a generalized concordance correlation coefficient for continuous and categorical data this paper discusses a generalized version of the concordance correlation coefficient for agreement data the concordance correlation coefficient evaluates the accuracy and precision between two measures and is based on the expected value of the squared function of distance we have generalized this coefficient by applying alternative functions of distance to produce more robust versions of the concordance correlation coefficient in this paper we extend the application of this class of estimators to categorical data as well and demonstrate similarities to the kappa and weighted kappa statistics we also introduce a stratified concordance correlation coefficient which adjusts for explanatory factors and an extended concordance correlation coefficient which measures agreement among more than two responses with these extensions the generalized concordance correlation coefficient provides a unifying approach to assessing agreement among two or more measures that are either continuous or categorical in scale

global attitude and gyro bias estimation based on set valued observers a b s t r a c t the problem of attitude and rate gyro bias estimation is addressed by resorting to measurements acquired from rate gyros and vector observations a set valued observer svo is proposed that has no singulari ties and that for any initial conditions provides a bounding set with guarantees of containing the actual unknown rotation matrix the sensor readings are assumed to be corrupted by bounded measurement noise and constant gyro bias conditions for the boundedness of the estimated sets are established and implementation details are discussed the feasibility of the technique is demonstrated in simulation

analytical methods for parameter space delimination and application to shallow lake phytoplankton dynamics modeling the first step in parameter estimation is to reduce the dimensionality of the problem by deriving estimates from independent experimentation and from the literature in addition insensitive parameters are either removed or fixed in the remaining lower dimensional problem parameter space delimitation is possible by analytical means three conjunctive methods are derived period average analysis extremum analysis and quasisteady state analysis the basic idea is to find conditions for the parameters that must be fulfilled in order to comply with average and extreme values in the observations the approach is applied to the modeling of the phytoplankton dynamics of lake balaton the analytical techniques prove to supply valuable insight into parameter interrelationships and model adequacy and can serve as satisfactory substitutes for formal parameter estimation techniques in the early stages of model development

persistent identification of systems with unmodeled dynamics and exogenous disturbances in this paper a novel framework of system identification is introduced to capture the hybrid features of systems subject to both deterministic unmodeled dynamics and stochastic observation disturbances using the concepts of persistent identification control oriented system modeling and stochastic analysis we investigate the central issues of irreducible identification errors and time complexity in such identification problems upper and lower bounds on errors and speed of persistent identification are obtained the error bounds are expressed as functions of observation lengths sizes of unmodeled dynamics and probability distributions of disturbances asymptotic normality and complexity lower bounds are investigated when periodic inputs and ls estimation are applied generic features of asymptotic normality are further explored to extend the asymptotic lower bounds to a wider range of signals and identification mappings

computation of nonconservative stability perturbation bounds for systems with nonlinearly correlated uncertainties consideration is given to the problem of robust stability analysis of linear dynamic systems with uncertain physical parameters entering as polynomials in the state equation matrices a method is proposed giving necessary and sufficient conditions for computing the uncertain system stability margin in parameter space which provides a measure of maximal parameter perturbations preserving stability of the perturbed system around a known stable nominal system a globally convergent optimization algorithm that enables solutions to the problem to be obtained is presented using the polynomial structure of the problem the algorithm generates a convergent sequence of interval estimates of the global extremum these intervals provide a measure of the accuracy of the approximating solution achieved at each step of the iterative procedure some numerical examples are reported showing attractive features of the algorithm from the point of view of computational burden and convergence behavior

equivariant flow equivalence for shifts of finite type by matrix equivalence over group rings let g denote a nite group in this paper by a g shift of nite type g sft we will mean a shift of nite type sft together with a continuous g action which commutes with the shift where in addition the action is free and the sft is irreducible and is non trivial contains more than one orbit we will classify these systems up to g 5ow equivalence this equivalence relation can be described in terms of g sfts skew products or suspension 5ows x 2 for example two g sfts are g 5ow equivalent if and only if there exists an orientation preserving homeomorphism between their mapping tori which commutes with the induced g actions a g sft can be presented by a nite square matrix a over z g the positive cone of the integral group ring zg w parry personal communication 2001 let ia 1 denote the nn matrix whose upper left corner is ia and which otherwise equals the in nite identity matrix let e zg be the group of nn matrices generated by basic elementary matrices those which di er from i in at most one entry which must be o diagonal over zg let w a denote the weight class of a de nition 4 1 the conjugacy class in g of the group of weights of loops based at a xed vertex we show that the weight class is an invariant of g 5ow equivalence when w a w b g we will show that g sfts presented by matrices a and b are g 5ow equivalent if and only if there are matrices u and v in e zg such that u ia 1v ib 1 theorem 6 1 the complete classi cation up to g 5ow equivalence which allows the possibility w a g has a more complicated statement theorem 6 4 in the case that g is trivial our classi cation reduces to the familiar classi cation of franks 14 by cokernel group and determinant when g is non trivial the classi cation up to e zg is much more dibcult and interesting and remains an open problem we consider these algebraic issues inxx 8 and 9 in x 8 we give the modest requisite k theory terminology and background and for the case g z 2 we give a constructive partial result theorem 8 1 and some very concrete illustrative examples examples 8 6 and 8 7 which indicate how the zg equivalence problem becomes more dibcult when g is non trivial that is zg6 z in x 9 we consider e zg equivalence of injective matrices in this case gl zg equivalence amounts to isomorphism of cokernel modules and the re nement toe zg equivalence is classi ed by k 1 zg h for an associated subgroup h ofs k 1 zg as one consequence if g is abelian and det ia is not a zerodiviso r in zg then det ia determines the g 5ow equivalence class up

a frequency domain estimator for use in adaptive control systems abstract this paper presents a frequency domain estimator that can identify both a parametrized nominal model of a plant as well as a frequency domain bounding function on the modeling error associated with this nominal model this estimator which we call a robust estimator can be used in conjunction with a robust control law redesign algorithm to form a robust adaptive controller

frequency domain identification with generalized orthonormal basis functions a method is considered for the identification of linear parametric models based on a least squares identification criterion that is formulated in the frequency domain to this end use is made of the empirical transfer function estimate etfe identified from time domain data as a parametric model structure use is made of a finite expansion sequence in terms of recently introduced generalized basis functions being generalizations of the classical pulse and laguerre and kautz types of bases an asymptotic analysis of the estimated models is provided and conditions for consistency are formulated explicit and transparent bias and variance expressions are established the latter ones also valid in a situation of undermodeling

robust estimation and filtering in the presence of bounded noise optimal algorithms for robust estimation and filtering are constructed the noise is considered a deterministic variable belonging to a set described by a norm previous results obtained for complete one to one and approximate information by m milanese and r tempo ibid vol 30 p 730 8 1985 are extended to partial and approximate information this information is considered useful in dealing with dynamic systems not completely identifiable and or with two different sources of noise such as process and measurement noise for different norms characterizing the noise optimal algorithms in a min max sense are shown in particular for hilbert norms a linear optimal algorithm is the well known minimum variance estimator for l sub infinity norm an optimal algorithm computable by linear programming is presented state estimation is formalized in the context of the general theory for stable systems an approximate state estimation is obtained by neglecting higher order powers an upper bound determining the approximation introduced is derived a numerical example illustrates the application of the theory

optimal inner bounds of feasible parameter set in linear estimation with bounded noise some problems arising in parameter estimation theory with unknown but bounded measurement errors are discussed in this theory a key role is played by the feasible parameter set i e the set of all parameter values consistent with the system model and the error bounds if a linear relationship between parameters and measurements is assumed this set is a polytope an exact representation of this polytope may be too complex for practical use and approximate descriptions in terms of simple shaped sets contained in the feasible parameter set inner bounds have shown to be useful in several applications balls in l sub infinity norms boxes l sub 2 norms ellipsoids and l sub 1 norms diamonds are used as bounding sets results are given on the computation of maximal balls when their shape is either known or partially free a numerical example is given in which the results of a computation of inner boxes of fixed shape and fixed orientation are given and compared

an approach to identification for robust control given measured data generated by a discrete time linear system we propose a model consisting of a linear time invariant system affected by norm bounded perturbation under mild assumptions the plants belonging to the resulting uncertain family form a convex set the approach depends on two key parameters an a priori given bound of the perturbation and the input used to generate the data it turns out that the size of the uncertain family can be reduced by intersecting the model families obtained by making use of different inputs the model validation problem in this identification scheme is analyzed for a given energy level the invalidation problem yields the family of those models which can never be invalidated for any possible input of fixed energy and any possible perturbation this leads to the intersection of all uncertain families a consequence of the invalidation problem is that for finite length measurements not all models can be invalidated using fixed energy inputs

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

nonlinear least absolute values and minimax model fitting abstract up to now the least absolute values l 1 and minimax l criteria have seldom been used in model fitting even if they are preferable for theoretical reasons their non differentiability causes numerical and analytical difficulties fortunately a recent reformulation of l 1 and l as equivalent constrained differentiable problems enables one to numerically solve them using standard nonlinear programming software this paper exploits this reformulation for analytical purposes in particular limits are derived concerning the ability of l 1 and l to resolve highly similar nonlinearly parametric terms from error corrupted observations examples are exponentials of nearly equal decay in compartmental models and almost coinciding peaks in spectroscopy

a concordance correlation coefficient to evaluate reproducibility a new reproducibility index is developed and studied this index is the correlation between the two readings that fall on the 45 degree line through the origin it is simple to use and possesses desirable properties the statistical properties of this estimate can be satisfactorily evaluated using an inverse hyperbolic tangent transformation a monte carlo experiment with 5 000 runs was performed to confirm the estimate s validity an application using actual data is given

optimality of central and projection algorithms for bounded uncertainty this paper investigates optimality properties of central and projection algorithms for linear problems in the field of system identification in a context in which uncertainty is described in a deterministic rather than statistical way particular attention is devoted to least squares algorithms when the measurement noise is assumed to be unknown but bounded in a hilbert norm a major contribution of this paper consists in proving that least squares algorithms enjoy strong optimality properties on the contrary it is pointed out that these properties do not hold for other frequently used projection algorithms such as least absolute values or minimax algorithms corresponding to a description of the measurement error in h or l norm respectively

estimation theory for nonlinear models and set membership uncertainty this chapter studies the problem of estimating a given function of a vector of unknowns called the problem element by using measurements depending non linearly on the problem element and affected by unknown but bounded noise assuming that both the solution sought and the measurements depend polynomially on the unknown problem element a method is given to compute the axis aligned box of minimal volume containing the feasible solution set i e the set of all unknowns consistent with the actual measurements and the given bound on the noise the center of this box is a point estimate of the solution which enjoys useful optimality properties the sides of the box represent the intervals of possible variation of the estimates important problems like parameter estimation of exponential models time series prediction with arma models and parameter estimates of discrete time state space models can be formalized and solved by using the developed theory

overall indices for assessing agreement among multiple raters the need to assess agreement exists in various clinical studies where quantifying inter rater reliability is of great importance use of unscaled agreement indices such as total deviation index and coverage probability cp is recommended for two main reasons i they are intuitive in a sense that interpretations are tied to the original measurement unit ii practitioners can readily determine whether the agreement is satisfactory by directly comparing the value of the index to a prespecified tolerable cp or absolute difference however the unscaled indices were only defined in the context of comparing two raters or multiple raters that assume homogeneity of variances across raters in this paper we introduce a set of overall indices based on the root mean square of pairwise differences that are unscaled and can be used to evaluate agreement among multiple raters that often exhibit heterogeneous measurement processes in practice furthermore we propose another overall agreement index based on the root mean square of pairwise differences that is scaled and extends the concept of the recently proposed relative area under cp curve in the presence of multiple raters we present the definitions of overall indices and propose inference procedures in which bootstrap methods are used for the estimation of standard errors we assess the performance of the proposed approach and demonstrate its superiority over the existing methods when raters exhibit heterogeneous measurement processes using simulation studies finally we demonstrate the application of our methods using a renal study

recursive computation of inner bounds for the parameters of linear models minimum volume ellipsoidal outer bounds on the parameters of linear regression type models with bounded model output error can be computed by an established algorithm a complementary algorithm to compute maximum volume ellipsoidal inner bounds is derived it is little more complicated than the existing outer bounding algorithm in conjunction with that algorithm it allows parameter values to be classified as acceptable dubious or unacceptable it is also found to be effective in determining output error bounds by trial and error during development of parameter bounding models

identification in the presence of classes of unmodeled dynamics and noise identification involves obtaining a model from an a priori chosen model class es using finite corrupted data the corruption may be due to several reasons ranging from noise to unmodeled dynamics since the real system may not belong to the model class two popular approaches probabilistic and set membership identification deal with this problem by imposing temporal constraints on the noise sample paths we differentiate between the two sources of error by imposing different types of constraints on the corruption if the source of corruption is noise we model it by imposing temporal constraints on the possible realizations of noise on the other hand if it results from unmodeled dynamics informational constraints are imposed contrary to probabilistic identification where the parameters of the identified model converge to the true parameters in the presence of noise current results in set membership identification do not have this convergence property our approach leads to bridging this gap between probabilistic and set membership identification when the source of corruption is noise for the case when both unmodeled dynamics and noise are present we derive consistency results for the case when the unmodeled dynamics can be described either by a linear time invariant system or by a static nonlinearity

estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors linear families of models and estimators the problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available of suitable but only a bound on them is known in the present paper only linear parametrizations and estimators are considered very simple and computationally feasible algorithms are derived for evaluating two different types of uncertainty intervals estimates uncertainty intervals parameter uncertainty intervals the relationships between the eui s and the pui s are established and the solution to the problem of the minimum uncertainty intervals estimator is given the latter can be obtained by means of a simple linear programming algorithm

structure identification of parameter bounding models by use of noise structure bounds the selection of a model for a given set of records is discussed for the case when the output error is required to be always within some specified bounds a new selection criterion is proposed the model should be the simplest giving sufficiently unstructured output errors the lack of structure is specified by requiring the candidate model to be capable of giving sufficiently small sample autocorrelations of the model output errors over a range of lags computational algorithms to apply the criterion are presented and illustrated by tests on ar processes

asymptotically convergent modified recursive least squares with data dependent updating and forgetting factor for systems with bounded noise continual updating of estimates required by most recursive estimation schemes often involves redundant usage of information and may result in system instabilities in the presence of bounded output disturbances an algorithm which eliminates these difficulties is investigated based on a set theoretic assumption the algorithm yields modified least squares estimates with a forgetting factor it updates the estimates selectively depending on whether the observed data contain sufficient information the information evaluation required at each step involves very simple computations in addition the parameter estimates are shown to converge asymptotically at an exponential rate to a region around the true parameter

identification input design for consistent parameter estimation of linear systems with binary valued output observations input design is of essential importance in system identification for providing sufficient probing capabilities to guarantee convergence of parameter estimates to their true values this paper presents conditions on input signals that characterize their probing richness for strongly consistent parameter estimation of linear systems with binary valued output observations necessary and sufficient conditions on periodic signals are derived for sufficient richness these conditions are further studied under different system configurations including open loop and feedback systems and different scenarios of noises including actuator noise input measurement noise and output measurement noise in addition to system parameter estimation essential properties of identifiability and input conditions are also derived when sensor thresholds or noise distribution functions are unknown the findings of this paper provide a foundation to study identification of systems that either use binary valued or quantized sensors or involve communication channels which mandate quantization of signals

brief unfalsified model parametrization based on frequency domain noise information in this paper the results concerning unfalsified model parametrization are extended to the case where identification noises are magnitude bounded in the frequency domain it is shown that while every unfalsified model can still be represented by a linear fractional transformation of a block diagonal norm bounded transfer function matrix the dimensions of the involved matrix valued transfer functions are of the order of the identification experiment data length moreover the verification of the parametrization condition only requires computing the maximal singular values of two constant matrices these results are established on the basis of a relation between a lower triangular toeplitz matrix and the discrete fourier transformation of its first column elements however an analysis shows that the parametrization condition can be satisfied only when the noise level is very low this implies that the proposed least squares minimization based algorithms are not very appropriate in model set identification

statistical methods in assessing agreement models issues and tools measurements of agreement are needed to assess the acceptability of a new or generic process methodology and formulation in areas of laboratory performance instrument or assay validation method comparisons statistical process control goodness of fit and individual bioequivalence in all of these areas one needs measurements that capture a large proportion of data that are within a meaningful boundary from target values target values can be considered random measured with error or fixed known depending on the situation various meaningful measures to cope with such diverse and complex situations have become available only in the last decade these measures often assume that the target values are random this article reviews the literature and presents methodologies in terms of coverage probability in addition analytical expressions are introduced for all of the aforementioned measurements when the target values are fixed and when the error structure is homogenous or heterogeneous proport

closed loop persistent identification of linear systems with unmodeled dynamics and stochastic disturbances the essential issues of time complexity and probing signal selection are studied for persistent identification of linear time invariant systems in a closed loop setting by establishing both upper and lower bounds on identification accuracy as functions of the length of observation size of unmodeled dynamics and stochastic disturbances we demonstrate the inherent impact of unmodeled dynamics on identification accuracy reduction of time complexity by stochastic averaging on disturbances and probing capability of full rank periodic signals for closed loop persistent identification these findings indicate that the mixed formulation in which deterministic uncertainty of system dynamics is blended with random disturbances is beneficial to reduction of identification complexity

total deviation index for measuring individual agreement with applications in laboratory performance and bioequivalence in areas of inter laboratory quality control method comparisons assay validation and individual bioequivalence etc the agreement between observations and target reference values is of interest the mean of the squared difference between observations and target values msd is a good measure of the total deviation a new user friendly statistic the total deviation index tdi1 p is introduced that translates the msd into an index that can be directly compared to a predetermined criterion the tdi1 p describes a boundary such that a majority 100 1 p per cent of the observations are within the boundary measurement unit and or per cent from their target values statistical inference using the sample counter part estimate is presented a monte carlo experiment with 5000 runs was performed to confirm the estimate s validity applications in laboratory performance and validation as well as individual bioequivalence are presented copyright 2000 john wiley sons ltd