fourier transform of self affine measures abstract suppose f is a self affine set on r d d 2 which is not a singleton associated to affine contractions f j a j b j a j gl d r b j r d j a for some finite a we prove that if the group generated by the matrices a j j a forms a proximal and totally irreducible subgroup of gl d r then any self affine measure p j f j p j 1 0 p j 1 j a on f is a rajchman measure the fourier transform 0 as as an application this shows that self affine sets with proximal and totally irreducible linear parts are sets of rectangular multiplicity for multiple trigonometric series moreover if the zariski closure of is connected real split lie group in the zariski topology then has a power decay at infinity hence is l p improving for all 1 p and f has positive fourier dimension in dimension d 2 3 the irreducibility of and non compactness of the image of in pgl d r is enough for power decay of the proof is based on quantitative renewal theorems for random walks on the sphere s d 1

recursive identification of wiener hammerstein systems identification of the wiener hammerstein system consisting of a linear subsystem in a cascade with a static nonlinearity f cdot followed by another linear subsystem with internal noises is considered on the basis of input and noisy output the impulse responses of the two linear subsystems are estimated by stochastic approximation sa algorithms and the nonlinear function is also estimated by sa algorithms but with kernel functions the system input is taken to be a sequence of independent and identically distributed iid gaussian random variables u k in mathcal n 0 vartheta 2 with vartheta 0 for convergence of the proposed algorithms the properties of martingale difference sequences mds and alpha mixings play an important role the estimates for coefficients of the linear subsystems as well as for values of the nonlinear function are proved to converge to the true values with probability one three numerical examples with nonlinearities possessing different properties are give

ma estimation in polynomial time the parameter estimation of moving average ma signals from second order statistics was deemed for a long time to be a difficult nonlinear problem for which no computationally convenient and reliable solution was possible we show how the problem of ma parameter estimation from sample covariances can be formulated as a semidefinite program that can be solved in a time that is a polynomial function of the ma order two methods are proposed that rely on two specific over parametrizations of the ma covariance sequence whose use makes the minimization of a covariance fitting criterion a convex problem the ma estimation algorithms proposed here are computationally fast statistically accurate and reliable none of the previously available algorithms for ma estimation methods based on higher order statistics included shares all these desirable properties our methods can also be used to obtain the optimal least squares approximant of an invalid estimated ma spectrum that takes on negative values at some frequencies which was another long standing problem in the signal processing literature awaiting a satisfactory solution

rate of convergence of recursive estimators it is proved that the sequence of recursive estimators generated by ljung s scheme combined with a suitable restarting mechanism converges under certain conditions with rate o m n 1 2 where the rate is measured by the l q norm of the estimation error for any 1 leq q infty

iterative bregman projections for regularized transportation problems this article details a general numerical framework to approximate so lutions to linear programs related to optimal transport the general idea is to introduce an entropic regularization of the initial linear program this regularized problem corresponds to a kullback leibler bregman di vergence projection of a vector representing some initial joint distribu tion on the polytope of constraints we show that for many problems related to optimal transport the set of linear constraints can be split in an intersection of a few simple constraints for which the projections can be computed in closed form this allows us to make use of iterative bregman projections when there are only equality constraints or more generally bregman dykstra iterations when inequality constraints are in volved we illustrate the usefulness of this approach to several variational problems related to optimal transport barycenters for the optimal trans port metric tomographic reconstruction multi marginal optimal trans port and in particular its application to brenier s relaxed solutions of in compressible euler equations partial un balanced optimal transport and optimal transport with capacity constraints

on the order of the minimal output representation of stochastic linear systems the relationship between the internal structure of a stochastic linear system in state space form and the order of its output representation is investigated conditions for minimal and for maximal values of the output representation s order are derived

maximum likelihood estimates via duality for log convex models when cell probabilities are subject to convex constraints the purpose of this article is to derive and illustrate a method for fitting models involving both convex and log convex constraints on the probability vector s of a product multinomial distribution we give a two step algorithm to obtain maximum likelihood estimates of the probability vector s and show that it is guaranteed to converge to the true solution some examples are discussed which illustrate the procedure

recursive solutions of estimating equations and adaptive spectral factorization a recursive spectral factorization algorithm was developed by v solo ibid vol 34 no 10 pp 1047 1051 oct 1989 to be used with recursive instrumental variables for consistent estimation of the parameters of an armax system but the convergence of the spectral factorization algorithm is questionable herein a modified adaptive spectral factorization algorithm is shown to converge and a general method for constructing convergent recursive solutions of nonlinear equations that are used to define parameter estimates is also presented

on equality of hausdorff and affinity dimensions via self affine measures on positive subsystems under mild conditions we show that the affinity dimension of a planar self affine set is equal to the supremum of the lyapunov dimensions of self affine measures supported on self affine proper subsets of the original set these self affine subsets may be chosen so as to have stronger separation properties and in such a way that the linear parts of their affinities are positive matrices combining this result with some recent breakthroughs in the study of self affine measures and their associated furstenberg measures we obtain new criteria under which the hausdorff dimension of a self affine set equals its affinity dimension for example applying recent results of barany hochman solomyak and rapaport we provide many new explicit examples of self affine sets whose hausdorff dimension equals its affinity dimension and for which the linear parts do not satisfy any positivity or domination assumptions

a stopping rule for stochastic approximation a stochastic approximation algorithm is a recursive procedure to find the solution to an unknown nonlinear equation via noisy measurements in this paper we present a stopping rule for a stochastic approximation we show that there is a high probability that the distance between the exact solution and the candidate solution is less than a specified tolerance level when the stochastic approximation stops according to our stopping rule furthermore the number of recursions required by the stopping rule is a polynomial function of the problem size

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

belief propagation dykstra s algorithm and iterated information projections belief propagation is shown to be an instance of a hybrid between two projection algorithms in the convex programming literature dykstra s algorithm with cyclic bregman projections and an alternating bregman projections algorithm via this connection new results concerning the convergence and performance of belief propagation can be proven by exploiting the corresponding literature about the two projections algorithms it hybridizes in this regard it is identified that the lack of guaranteed convergence for belief propagation results from the asymmetry of its bregman divergence by proving that when the associated hybrid projection algorithm generalization is used with a symmetric bregman divergence it always converges additionally by characterizing factorizations that are close to acyclic in a manner independent of their girth a new collection of distributions for which belief propagation is guaranteed to perform well is identified using the new projection algorithm framework

on a procedure for testing the order of time series theoretical justification of a procedure for estimating the orders of autoregressive moving average arma processes solely from the observations is presented

hausdorff dimension of planar self affine sets and measures let x bigcup varphi i x be a strongly separated self affine set in mathbb r 2 or one satisfying the strong open set condition under mild non conformality and irreducibility assumptions on the matrix parts of the varphi i we prove that dim x is equal to the affinity dimension and similarly for self affine measures and the lyapunov dimension the proof is via analysis of the dimension of the orthogonal projections of the measures and relies on additive combinatorics methods

general results on the convergence of stochastic algorithms a deterministic approach is proposed for proving the convergence of stochastic algorithms of the most general form under necessary conditions on the input noise and reasonable conditions on the nonnecessarily continuous mean field emphasis is placed on the case where more than one stationary point exists we also use this approach to prove the convergence of a stochastic algorithm with markovian dynamics

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

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

order identification of arma models based on instrumental variable estimators the author proposes a simple model selection procedure based on iv estimators which can be viewed as an extension of p stoica s method 1981 the model selection procedure is based on a simple statistic with a known limiting distribution it closely parallels the overfitting strategy applied to models estimated by nonlinear least squares

local dimensions of measures on infinitely generated self affine sets abstract we show the existence of the local dimension of an invariant probability measure on an infinitely generated self affine set for almost all translations this implies that an ergodic probability measure is exactly dimensional furthermore the local dimension equals the minimum of the local lyapunov dimension and the dimension of the space

dimension and product structure of hyperbolic measures we prove that every hyperbolic measure invariant under a c 1 fi difieomorphism of a smooth riemannian manifold possesses asymptotically almost local product structure i e its density can be approximated by the product of the densities on stable and unstable manifolds up to small exponentials this has not been known even for measures supported on locally maximal hyperbolic sets using this property of hyperbolic measures we prove the long standing eckmann ruelle conjecture in dimension theory of smooth dynamical systems the pointwise dimension of every hyperbolic measure invariant under a c 1 fi difieomorphism exists almost everywhere this implies the crucial fact that virtually all the characteristics of dimension type of the measure including the hausdorfi dimension box dimension and information dimension coincide this provides the rigorous mathematical justiflcation of the concept of fractal dimension for hyperbolic measures

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

an iterative procedure for obtaining i projections onto the intersection of convex sets abstract a frequently occuring problem is to find that probability distribution pd lying within a convex set which minimizes the i divergence between it and given pd r this document proposes an iterative procedure which requires only that the set be convex and not necessarily linear which under general conditions will converge to the desired i projection

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

some characterizations of domination we show that a cocycle has a dominated splitting if and only if there is a uniform exponential gap between singular values of its iterates then we consider sets in rm gl d mathbb r with the property that any cocycle with values in has a dominated splitting we characterize these sets in terms of existence of invariant multicones thus extending a two dimensional result by avila bochi and yoccoz we give an example showing how these multicones can fail to have convexity properties

norm product belief propagation primal dual message passing for approximate inference inference problems in graphical models can be represented as a constrained optimization of a free energy function in this paper we treat both forms of probabilistic inference estimating marginal probabilities of the joint distribution and finding the most probable assignment through a unified message passing algorithm architecture in particular we generalize the belief propagation bp algorithms of sum product and max product and tree reweighted trw sum and max product algorithms trbp and introduce a new set of convergent algorithms based on convex free energy and linear programming lp relaxation as a zero temperature of a convex free energy the main idea of this work arises from taking a general perspective on the existing bp and trbp algorithms while observing that they all are reductions from the basic optimization formula of f ihi where the function f is an extended valued strictly convex but nonsmooth and the functions hi are extended valued functions not necessarily convex we use tools from convex duality to present the primal dual ascent algorithm which is an extension of the bregman successive projection scheme and is designed to handle optimization of the general type f ihi we then map the fractional free energy variational principle for approximate inference onto the optimization formula above and introduce the norm product message passing algorithm special cases of the norm product include sum product and max product bp algorithms trbp and nmplp algorithms when the fractional free energy is set to be convex convex free energy the norm product is globally convergent for the estimation of marginal probabilities and for approximating the lp relaxation we also introduce another branch of the norm product which arises as the zero temperature of the convex free energy which we refer to as the convex max product the convex max product is convergent unlike max product and aims at solving the lp relaxation

ledrappier young formula and exact dimensionality of self affine measures in this paper we solve the long standing open problem on exact dimensionality of self affine measures on the plane we show that every self affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system in higher dimensions under certain assumptions we prove that self affine and quasi self affine measures are exact dimensional in both cases the measures satisfy the ledrappier young formula

the metric entropy of diffeomorphisms part ii relations between entropy exponents and dimension on considere f m m m m un c 2 diffeomorphisme f d une variete de riemann compacte m preservant une mesure de probabilite de borel m soit hm f l entropie metrique de f et 1 x r x x les exposants de lyapunov distincts en x on etablit une formule qui relie h m f et les r x x

identifiability and persistent excitation in full matrix fraction parameter estimation this paper analyzes the identifiability of the full matrix fraction description of multivariable systems and provides a lower bound on the persistence of excitation of the input output pair in terms of the persistence of excitation of the input

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

identification of eiv models by compensated pem this paper deals with identification of discrete time errors in variables models where the input and output data are both perturbed by different additive noises the goal is to study the effects of

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 multi time scale generalization of recursive identification algorithm for armax systems recently chen 2010 presented a new approach to recursive identification for armax systems which is a three stage recursive scheme and assumes independent and identically distributed input signals here we observe that unless the time scale of the algorithm at one stage is reasonably faster than those at the previous stages convergence to the true value may not take place to remedy this issue this note proposes a multi time scale modification of the algorithm in 5 such that convergence is achieved in addition the new scheme handles a wider class of input signals so that the input can be designed for some purpose the advantage of the multi time scale algorithm is verified with numerical examples

discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics many physical systems are described by nonlinear differential equations that are too complicated to solve in full a natural way to proceed is to divide the variables into those that are of direct interest and those that are not formulate solvable approximate equations for the variables of greater interest and use data and statistical methods to account for the impact of the other variables in the present paper we consider time dependent problems and introduce a fully discrete solution method which simplifies both the analysis of the data and the numerical algorithms the resulting time series are identified by a narmax nonlinear autoregression moving average with exogenous input representation familiar from engineering practice the connections with the mori zwanzig formalism of statistical physics are discussed as well as an application to the lorenz 96 system

the metric entropy of diffeomorphisms part i characterization of measures satisfying pesin s entropy formula soit m une variete de riemann compacte soit f m m un diffeomorphisme et soit m une mesure de probabilite de borel f invariante sur m on identifie les mesures pour lesquelles l inegalite de margulis et ruelle qui relie l entropie aux exposants de lyapunov atteint l egalite on demontre une formule valable pour toutes les mesures invariantes

a new technique for arma system identification and rational approximation the fundamental problem of identifying a linear time invariant system from measured samples of its output response to a known input is addressed utilizing a new and simple deterministic theory founded on well established passive network concepts the analysis together with documented numerical results demonstrates that the proposed method achieves two goals stable rational minimum phase transfer functions can be identified with a priori knowledge of either numerator or denominator degrees and stable rational minimum phase pade like approximations appear to be generated automatically in the nonrational case to substantiate these claims a detailed theoretical exposition of the basic ideas an extensive discussion of numerical results and a summary of related results are given

generalized yule walker equations and testing the orders of multivariate time series consistency condi ions are given for the estimates of ar parameters of multivariate arma models obtained by using generalized yule walker equations the related problem of selecting the model orders by testing the rank of the output covariance matrix is also discussed

new method of order estimation for arma armax processes let the observation y k be generated by the multivariate arma process a z y k c z w k with unknown coefficients theta a theta c and orders p r where w k is a sequence of independent and identically distributed i i d random vectors with zero mean and unknown covariance matrix r w 0 a new method for estimating the orders p r is introduced in contrast to most of the existing results the new method is not based on optimizing a certain criterion and the order estimates given in the paper are rather easy to update computationally in comparison with the criterion optimization based methods when new data arrive the method is then extended to determining the orders of armax processes under reasonable conditions the estimates are proved to converge to the true orders with probability one as time tends to infinity

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

frequency domain identification of wiener models this paper proposes a frequency domain algorithm for wiener model identifications based on exploring the fundamental frequency and harmonics generated by the unknown nonlinearity the convergence of the algorithm is established in the presence of white noise no a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric

hankel matrices for system identification abstract the coefficients of a linear system even if it is a part of a block oriented nonlinear system normally satisfy some linear algebraic equations via hankel matrices composed of impulse responses or correlation functions in order to determine or to estimate the coefficients of a linear system it is important to require the associated hankel matrix be of row full rank the paper first discusses the equivalent conditions for identifiability of the system then it is shown that the row full rank of the hankel matrix composed of impulse responses is equivalent to identifiability of the system finally for the row full rank of the hankel matrix composed of correlation functions the necessary and sufficient conditions are presented which appear slightly stronger than the identifiability condition in comparison with existing results here the minimum phase condition is no longer required for the case where the dimension of the system input and output is the same though the paper does not make such a dimensional restriction

hausdorff dimension for randomly perturbed self affine attractors in this paper we shall consider a self affine iterated function system in mathbb r d d 2 where we allow a small random translation at each application of the contractions we compute the dimension of a typical attractor of the resulting random iterated function system complementing a famous deterministic result of falconer which necessarily requires restrictions on the norms of the contraction however our result has the advantage that we do not need to impose any additional assumptions on the norms this is of benefit in practical applications where such perturbations would correspond to the effect of random noise we also give analogous results for the dimension of ergodic measures in terms of their lyapunov dimension finally we apply our method to a problem originating in the theory of fractal image compression

a high order yule walker method for estimation of the ar parameters of an arma model abstract the high order yule walker hoyw method is often used to estimate the frequencies of sinusoidal signals from noisy measurements a modification of the hoyw method is proposed for estimating the parameters of the autoregressive part of general arma processes the prime application of the hoyw method introduced in this paper is the estimation of the parameters of autoregressions from noisy measurements the performance of the proposed technique is illustrated by some numerical examples

computational acceleration of projection algorithms for the linear best approximation problem abstract this is an experimental computational account of projection algorithms for the linear best approximation problem we focus on the sequential and simultaneous versions of dykstra s algorithm and the halpern lions wittmann bauschke algorithm for the best approximation problem from a point to the intersection of closed convex sets in the euclidean space these algorithms employ different iterative approaches to reach the same goal but no mathematical connection has yet been found between their algorithmic schemes we compare these algorithms on linear best approximation test problems that we generate so that the solution will be known a priori and enable us to assess the relative computational merits of these algorithms for the simultaneous versions we present a new component averaging variant that substantially accelerates their initial behavior for sparse systems

order independence and factor convergence in iterative scaling abstract we prove two results concerning iterative scaling which have been claimed but not proved by other authors in the field iterative scaling is a procedure which begins with a probability measure q on a finite set x and a finite set of partition constraints on x it produces a sequence of iterates p0 q p1 pt in which each pt t 62 0 is an adjustment scaling of pt 1 to fit a single set of prescribed partition constraints under fairly general hypotheses the iterates pt converge to the unique probability p which simultaneously satisfies the given constraints and is exponentially equivalent to the starting measure q or equivalently which minimizes the i divergence d p q over all probabilities p on x which satisfy the constraints the first main result theorem 3 1 states that the convergence of iterative scaling to the unique limit is independent of the order in which the adjustments for the prescribed partition constraints are made provided each adjustment is made infinitely many times the second main result theorem 4 2 is that under certain commonly satisfied conditions each factor of the exponential form being built up within the algorithm one factor for each partition constraint converges separately a third group of results sections 5 6 provides an account of the relationship between the probability measures which satisfy all of the constraints and those which are exponentially equivalent to q

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

an iterative procedure for general probability measures to obtain i projections onto intersections of convex sets the iterative proportional fitting procedure ipfp was introduced formally by deming and stephan in 1940 for bivariate densities this procedure has been investigated by kullback and ruschendorf it is well known that the ipfp is a sequence of successive i projections onto sets of probability measures with fixed marginals however when finding the i projection onto the intersection of arbitrary closed convex sets e g marginal stochastic orders a sequence of successive i projections onto these sets may not lead to the actual solution addressing this situation we present a new iterative i projection algorithm under reasonable assumptions and using tools from fenchel duality convergence of this algorithm to the true solution is shown the cases of infinite dimensional ipfp and marginal stochastic orders are worked out in this context

new approach to recursive identification for armax systems for the multivariate armax system a z yk b z uk 1 c z wk recursive algorithms are proposed for estimating coefficients of a z b z and c z and the covariance matrix rw of wk assuming that the orders of a z b z and c z are known and the control uk can be arbitrarily chosen the new method consists in on line solving the algebraic equations associated with armax on the basis of observed data the algorithms are easily computable and the almost sure convergence of the algorithms is proved under reasonable conditions

duality of i projections and maximum likelihood estimation for log linear models under cone constraints abstract important order restrictions and general log linear models for multinomial experiments can often be expressed by requiring that the vector composed of the logs of the probabilities fall within a closed convex cone here we exhibit a duality relationship by way of a fenchel duality theorem between these types of problems and projections in i divergence geometry we show that many cone constrained maximum likelihood estimation problems are exactly equivalent to an i projection onto a translation of the negative polar cone this duality relationship permits the concise characterization of cone restricted maximum likelihood estimates and the use of iterative algorithms proposed by csiszar 1975 and dykstra 1985b which are analogous to the iterative proportional fitting procedure computational aspects of maximum likelihood estimates are discussed and a relationship with least squares projections onto isotonic cones is presented we discuss examples in detail to exhibit the usefulness and power

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

least squares identification for armax models without the positive real condition recursive identification problems of linear stochastic feedback control systems described by armax models are studied without imposing the strictly positive real condition on the noise model an increasing lag least squares is used in the first step to estimate the noise process while the parameter estimate is formed in the second step by an extended least squares in the algorithm there is an increase in computational cost in comparison to traditional algorithms however the results of this note do not need any a priori information or conditions on the noise model except that of stability and they are applicable to the identification of general feedback control systems

arma order estimation via matrix perturbation theory using matrix perturbation theory we obtain the statistical distribution of the smallest eigenvalue of the hankel matrix built upon the estimated covariances under the hypothesis that the corresponding exact hankel matrix possesses one single zero eigenvalue this allows us to develop and justify a new order determination scheme whose performance appears similar to those based on likelihood maximization but with a much lower computational complexity

smoothness of projections bernoulli convolutions and the dimension of exceptions erd s 1939 1940 studied the distribution of the random series p 0 n and showed that is singular for infinitely many 1 2 1 and absolutely continuous for a e in a small interval 1 1 solomyak 1995 proved a conjecture made by garsia 1962 that is absolutely continuous for a e 1 2 1 in order to sharpen this result we have developed a general method that can be used to estimate the hausdorff dimension of exceptional parameters in several contexts in particular we prove for any 0 1 2 the set of 0 1 such that is singular has hausdorff dimension strictly less than 1 for any borel set a rd with hausdorff dimension dim a d 1 2 there are points x a such that the pinned distance set x y y a has positive lebesgue measure moreover the set of x where this fails has hausdorff dimension at most d 1 dim a let k denote the middle cantor set for 1 2 and let k r be any compact set peres and solomyak 1998 showed that for a e 0 1 2 such that dim k dimk 1 the sum k k has positive length we show that the set of exceptional in this statement has hausdorff dimension at most 2 dim k dimk 0 for any borel set e rd with dim e 2 almost all orthogonal projections of e onto lines through the origin have nonempty interior and the exceptional set of lines where this fails has dimension at most d 1 dim e if is a borel probability measure on rd with correlation dimension greater than m 2 then for a prevalent set of c1 maps f rd rm in the sense described by hunt sauer and yorke 1992 the image of under f has a density with at least fractional derivatives in l2 rm

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

hausdorff dimension of the limit sets of some planar geometric constructions abstract we determine the hausdorff and box dimension of the limit sets for some class of planar non moran like geometric constructions generalizing the bedford mcmullen general sierpinski carpets the class includes affine constructions generated by an arbitrary partition of the unit square by a finite number of horizontal and vertical lines as well as some non affine examples e g the flexed sierpinski gasket

recursive identification of mimo wiener systems stochastic approximation sa algorithms are proposed to identify a multi input and multi output mimo wiener system in which the system input is taken to be a sequence of independent and identically distributed i i d gaussian random vectors uk n 0 i the algorithm for identifying the nonlinear part is designed with multi variable kernel functions under suitable conditions we show that the estimates of the coefficients of the linear subsystem and of the values of the nonlinear function converge to the respective true values with probability one

consensus based decentralized real time identification of large scale systems in this paper an approach is proposed to decentralized multi agent identification of large scale systems represented by linear discrete time stochastic mimo models it is assumed that each agent a has access only to a subset of noisy input output variables b communicates local data processing results to its neighborhood the proposed algorithm consists of two stages the first stage is a consensus based stochastic approximation algorithm for estimating input output correlation functions while at the second stage each agent utilizes a stochastic approximation algorithm with expanding truncations derived from the modified yule walker equations in order to generate all the system parameter estimates it is proved that under nonrestrictive assumptions concerning the system properties and the multi agent network topology the estimates of the correlation functions converge almost surely to their true values and those of the system parameters to a solution of the modified yule walker equations assuming intermittent observations and communication outages conditions are also given for the strong consistency of the parameter estimates simulation results provide an illustration of the algorithm properties

nonparametric regression with errors in variables the effect of errors in variables in nonparametric regression estimation is examined to account for errors in covariates deconvolution is involved in the construction of a new class of kernel estimators it is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution in fact there are two types of rates of convergence according to whether the error is ordinary smooth or super smooth it is also shown that these results hold uniformly over a class of joint distributions of the response and the covariate which is rich enough for many practical applications furthermore to achieve optimality we show that the convergence rates of all possible estimators have a lower bound possessed by the kernel estimators

message passing for graph structured linear programs proximal methods and rounding schemes the problem of computing a maximum a posteriori map configuration is a central computational challenge associated with markov random fields there has been some focus on tree based linear programming lp relaxations for the map problem this paper develops a family of super linearly convergent algorithms for solving these lps based on proximal minimization schemes using bregman divergences as with standard message passing on graphs the algorithms are distributed and exploit the underlying graphical structure and so scale well to large problems our algorithms have a double loop character with the outer loop corresponding to the proximal sequence and an inner loop of cyclic bregman projections used to compute each proximal update we establish convergence guarantees for our algorithms and illustrate their performance via some simulations we also develop two classes of rounding schemes deterministic and randomized for obtaining integral configurations from the lp solutions our deterministic rounding schemes use a re parameterization property of our algorithms so that when the lp solution is integral the map solution can be obtained even before the lp solver converges to the optimum we also propose graph structured randomized rounding schemes applicable to iterative lp solving algorithms in general we analyze the performance of and report simulations comparing these rounding schemes

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

recursive estimators with markovian jumps recursive stochastic algorithms have various applications in the literature it is assumed that the true value lies in a connected domain but in many cases it is known that the true value is contained in the union of a finite number of pairwise disjoint sets instead of a connected domain in these situations the existing algorithms may be not applicable to cope with this problem this paper proposes recursive stochastic algorithms with event triggered markovian jumps and presents sufficient conditions for almost sure convergence of the proposed algorithms as an example of applications this paper significantly improves an existing adaptive algorithm with the proposed method for consistent estimation of non minimum phase zeros

recursive identification of errors in variables wiener systems this paper considers the recursive identification of errors in variables eiv wiener systems composed of a linear dynamic system followed by a static nonlinearity both the system input and output are observed with additive noises being arma processes with unknown coefficients by a stochastic approximation incorporated with the deconvolution kernel functions the recursive algorithms are proposed for estimating the coefficients of the linear subsystem and for the values of the nonlinear function all the estimates are proved to converge to the true values with probability one a simulation example is given to verify the theoretical analysis

dimension theory of iterated function systems let si l i 1 be an iterated function system ifs on d with attractor k let denote the one sided full shift over the alphabet 1 l we define the projection entropy function h on the space of invariant measures on e associated with the coding map k and develop some basic ergodic properties about it this concept turns out to be crucial in the study of dimensional properties of invariant measures on k we show that for any conformal ifs respectively the direct product of finitely many conformal ifss without any separation condition the projection of an ergodic measure under is always exactly dimensional and its hausdorff dimension can be represented as the ratio of its projection entropy to its lyapunov exponent respectively the linear combination of projection entropies associated with several coding maps furthermore for any conformal ifs and certain affine ifss we prove a variational principle between the hausdorff dimension of the attractors and that of projections of ergodic measures 2008 wiley periodicals inc

on statistical properties of a test for model structure selection using the extended instrumental variable approach a procedure for structural estimation using the extended instrumental variable technique is presented the statistical distribution of the test quantity is obtained in the white noise case a criterion is defined by introducing a penalty term on the decreasing rate with the number of parameters of the proposed test quantity the consistency of the estimate is proven monte carlo simulations are included

structure of equilibrium states on self affine sets and strict monotonicity of affinity dimension a fundamental problem in the dimension theory of self affine sets is the construction of high dimensional measures which yield sharp lower bounds for the hausdorff dimension of the set a natural strategy for the construction of such high dimensional measures is to investigate measures of maximal lyapunov dimension these measures can be alternatively interpreted as equilibrium states of the singular value function introduced by falconer whilst the existence of these equilibrium states has been well known for some years their structure has remained elusive particularly in dimensions higher than two in this article we give a complete description of the equilibrium states of the singular value function in the three dimensional case showing in particular that all such equilibrium states must be fully supported in higher dimensions we also give a new sufficient condition for the uniqueness of these equilibrium states as a corollary giving a solution to a folklore open question in dimension three we prove that for a typical self affine set in r 3 removing one of the affine maps which defines the set results in a strict reduction of the hausdorff dimension