a one factor multivariate time series model of metropolitan wage rates abstract the paper formulates and estimates a single factor multivariate time series model the model is a dynamic generalization of the multiple indicator or factor analysis model it is shown to be a special case of the general state space model and can be estimated by maximum likelihood methods using the kalman filter algorithm the model is used to obtain estimates of the unobserved metropolitan wage rate for los angeles based on observations of sectoral wages within the standard metropolitan statistical area hypothesis tests model diagnostics and out of sample forecasts are used to evaluate the model

comparison results and estimates on the gradient without strict convexity in this paper we establish a comparison result for solutions to the problem mbox minimize int omega f nabla u x dx quad hbox on u u u 0 in w 1 1 0 omega

dirichlet problem for demi coercive functionals on considere des fonctionnelles integrales du type f u f du ou f r n 0 est une fonction convexe ayant la propriete suivante il existe a 0 b 0 r n tel que f z a z b z r n

lipschitz regularity for minima without strict convexity of the lagrangian abstract we give in a non smooth setting some conditions under which some of the minimizers of f u x d x g x u x d x among the functions in w 1 1 that lie between two lipschitz functions are lipschitz we weaken the usual strict convexity assumption in showing that if just the faces of the epigraph of a convex function f r n r are bounded and the boundary datum u 0 satisfies a generalization of the bounded slope condition introduced by a cellina then the minima of f u x d x on u 0 w 0 1 1 whenever they exist are lipschitz a relaxation result follows

on minima of a functional of the gradient necessary conditions in this paper we propose a new method for texture segmentation based on the use of texture feature detectors derived from a decorrelation procedure of a modified version of a pseudo wigner distribution pwd the decorrelation procedure is accomplished by a cascade recursive least squared crls principal component pc neural network the goal is to obtain a more eacient analysis of images by combining the advantages of using a high resolution joint representation given by the pwd with an eaective adaptive principal component analysis pca through the use of feedforward neural networks 1999 elsevier science b v all rights reserved

dual time frequency domain system identification in this paper we obtain the maximum likelihood estimate of the parameters of discrete time linear models by using a dual time frequency domain approach we propose a formulation that considers a reduced rank linear transformation of the available data such a transformation may correspond to different options selection of time domain data transformation to the frequency domain or selection of frequency domain data obtained from time domain samples we use the proposed approach to identify multivariate systems represented in state space form by using the expectation maximisation algorithm we illustrate the benefits of the approach via numerical examples

a true time series and its indicators an alternative approach abstract de leeuw and mckelvey proposed a method for using two imperfect indicators to predict the values of an unobserved series in this article we suggest an alternative method that uses the multiple indicator approach to model the true time series and its indicators we examine the identification status of the model estimate the parameters by maximum likelihood and use the kalman filter to obtain predictions of the unobserved series the method is applied to the u s gross private saving rate using flow of funds and national income and product accounts data as indicators

weighted maximum likelihood for dynamic factor analysis and forecasting with mixed frequency data for the purpose of forecasting key macroeconomic or financial variables from a panel of time series variables we adopt the dynamic factor model and propose a weighted likelihood based method for parameter estimation the loglikelihood function is split into two parts that are weighted differently the first part is associated with the key variables while the second part is associated with the related variables which may contribute to the forecasting of key variables we derive asymptotic properties including consistency and asymptotic normality of the weighted maximum likelihood estimator we show that this estimator outperforms the standard likelihood based estimator in approximating the true unknown distribution of the data as well as in out of sample forecasting accuracy we verify the new estimation method in a monte carlo study and investigate the role of different weights in different settings in the context of forecasting gross domestic product growth this key variable is typically observed at a low quarterly frequency while the supporting variables are observed at a high monthly frequency we adopt a low frequency representation of the mixed frequency dynamic factor model and discuss the computational efficiencies of this approach in our empirical study for the u s economy we present improvements in nowcasting and forecasting accuracy when the weighted likelihood based estimation procedure is adopted

shape derivatives for minima of integral functionals for omega varying among open bounded sets in mathbb r n r n we consider shape functionals j omega j defined as the infimum over a sobolev space of an integral energy of the kind int omega f nabla u g u f u g u under dirichlet or neumann conditions on partial omega under fairly weak assumptions on the integrands f f and g g we prove that when a given domain omega is deformed into a one parameter family of domains omega varepsilon through an initial velocity field v in w 1 infty mathbb r n mathbb r n v w 1 r n r n the corresponding shape derivative of j j at omega in the direction of v v exists under some further regularity assumptions we show that the shape derivative can be represented as a boundary integral depending linearly on the normal component of v v on partial omega our approach to obtain the shape derivative is new and it is based on the joint use of convex analysis and gamma convergence techniques it allows to deduce as a companion result optimality conditions in the form of conservation laws

continuity properties of solutions to some degenerate elliptic equations abstract we consider a nonlinear possibly degenerate elliptic operator l v div a v b x v where the field a and the function b are unnecessarily strictly monotonic and a satisfies a very mild ellipticity assumption for a given boundary datum we prove the existence of the maximum and the minimum of the solutions and formulate a haar rado type result namely a continuity property for these solutions that may follow from the continuity of in the homogeneous case we formulate some generalizations of the bounded slope condition and use them to obtain the lipschitz or local lipschitz regularity of solutions to l u 0 we prove the global holder regularity of the solutions in the case where is lipschitz

improving gdp measurement a measurement error perspective we provide a new measure of historical u s gdp growth obtained by applying optimal signal extraction techniques to the noisy expenditure side and income side gdp estimates the quarter by quarter values of our new measure often differ noticeably from those of the traditional measures its dynamic properties differ as well indicating that the persistence of aggregate output dynamics is stronger than previously thought

adaptive suboptimal filtering of bilinear systems the optimal filter minimum mean square error of discrete bilinear stochastic systems with output feedback is studied here the sequential filter of bilinear systems is derived for suboptimal adaptive estimation of the unknown a priori state and observation noise statistics simultaneously with the bilinear system state the unbiased estimations of state noise variance q and observation noise variance r are obtained under some usual conditions for on line operation this paper gives the recursive form of this adaptive suboptimal filter asf computer simulations show that asf approximates the minimum mean square error mse filter very well and asf provides improved state estimates at little computing expense

on the bounded slope condition and the validity of the euler lagrange equation under the bounded slope condition on the boundary values of a minimization problem for a functional of the gradient of u we show that a continuous minimizer w is in fact lipschitzian an application of this result to prove the validity of the euler lagrange equation for w is presented

the classical problem of the calculus of variations in the autonomous case relaxation and lipschitzianity of solutions we consider the problem of minimizing b a l x t x t dt x a a x b b under the assumption that the lagrangian l is continuous and satisfies a growth assumption that does not imply superlinear growth we provide a result on the relaxation of the functional and show that a solution to the minimum problem is lipschitzian

on the euler lagrange equation for functionals of the calculus of variations without upper growth conditions for a class of functionals of the calculus of variations we prove that each minimum of the functional satisfies the associated euler lagrange equation the integrand is assumed to be convex but no upper growth condition is imposed

absolutely continuous representatives on curves for sobolev functions we consider a class of lipschitz vector fields s r n whose values lie in a suitable cone and we show that the trajectories of the system x s x admit a parametrization that is invertible and lipschitz with its inverse as a consequence every v in w 1 1 admits a representative that is absolutely continuous on almost every trajectory of x s x i fs is an arbritrary lipschitz field the

maximum likelihood estimation of the dynamic shock error model abstract in this paper an efficient estimation technique in the time domain for the dynamic shock error model is developed this approach utilizes a state space representation of the model and the kalman filtering technique to obtain the maximum likelihood estimates the resulting estimates are shown to be consistent and asymptotically normal with the inverse of the information matrix as their precision measure a consistent estimate of the information matrix is suggested to obtain the standard errors of the estimates

two dimensional nonlinear boundary value problems for elliptic equations on considere la regularite limite des solutions du probleme aux valeurs limites non lineaire f x u du d 2 u 0 dans g x u du 0 sur pour des domaines a 2 dimensions f est uniformement elliptique et g depend de du on demontre des estimations de continuite pour des derivees premieres et secondes de u sous des hypotheses faibles pour la regularite de f g et

local lipschitz continuity of solutions to a problem in the calculus of variations this article studies the problem of minimizing f du g x u over the functions u w1 1 that assume given boundary values on the function f and the domain are assumed convex in considering the same problem with g 0 and in the spirit of the classical hilbert haar theory clarke has introduced a new type of hypothesis on the boundary function the lower or upper bounded slope condition this condition which is less restrictive than the classical bounded slope condition of hartman nirenberg and stampacchia is satisfied if is the restriction to of a convex or concave function we show that for a class of problems in which g x u is locally lipschitz but not necessarily convex in u the lower bounded slope condition implies the local lipschitz regularity of solutions

on ideals of compact operators satisfying them r s inequality abstract letr s 0 1 we prove that a banach spacexsatisfies them r s inequality i e formula where is the canonical projection ofx ontox wheneverr s 2 1 and there exists a norm one projectionpon l x with ker p k x satisfying formula we characterize the last property of k x in l x by a strong version of the metric compact approximation property ofx our results extend some well known results onm ideals

arens regularity of banach algebras and the geometry of banach spaces we show that a banach algebra a such that a has the property v of a pelczynski is arens regular a strong uniqueness property of the extension of the product on a unital c algebra a to a is proved the algebraic structure of the bidual of a c algebra can be obtained through the local reflexivity principle we give examples which show that the results are sharp

consistent factor estimation in dynamic factor models with structural instability abstract this paper considers the estimation of approximate dynamic factor models when there is temporal instability in the factor loadings we characterize the type and magnitude of instabilities under which the principal components estimator of the factors is consistent and find that these instabilities can be larger than earlier theoretical calculations suggest we also discuss implications of our results for the robustness of regressions based on the estimated factors and of estimates of the number of factors in the presence of parameter instability simulations calibrated to an empirical application indicate that instability in the factor loadings has a limited impact on estimation of the factor space and diffusion index forecasting whereas estimation of the number of factors is more substantially affected

an optimal geometric condition on domains for boundary differentiability of solutions of elliptic equations abstract in this paper a geometric condition on domains will be given which guarantees the boundary differentiability of solutions of elliptic equations that is the solutions are differentiable at any boundary point we will show that this geometric condition is optimal

a boundary regularity result for minimizers of variational integrals with nonstandard growth abstract we prove global lipschitz regularity for a wide class of convex variational integrals among all functions in w 1 1 with prescribed sufficiently regular boundary values which are not assumed to satisfy any geometrical constraint as for example bounded slope condition furthermore we do not assume any restrictive assumption on the geometry of the domain and the result is valid for all sufficiently smooth domains the result is achieved with a suitable approximation of the functional together with a new construction of appropriate barrier functions

a note on the estimation of variances in state space models using the maximum a posteriori procedure this note examines an estimation procedure for the unknown parameters in a state space model proposed by tsang glover and bach the method is based on the maximum a posteriori map principle contrary to the claims of tsang et al it is shown that the algorithm performs very poorly compared to maximum likelihood some insight into the shortcomings of the map procedure is obtained by comparing it to the computation of maximum likelihood estimators by the em algorithm

on the validity of the euler lagrange equation in a nonlinear case abstract we prove the validity of the euler lagrange equation for the class of functionals of the type l u g x u d x where u g x u is a concave function our result is based on a recent paper by degiovanni and marzocchi 2009 6 where no growth assumptions on l are needed

analytic standard errors for exploratory process factor analysis exploratory process factor analysis epfa is a data driven latent variable model for multivariate time series this article presents analytic standard errors for epfa unlike standard errors for exploratory factor analysis with independent data the analytic standard errors for epfa take into account the time dependency in time series data in addition factor rotation is treated as the imposition of equality constraints on model parameters properties of the analytic standard errors are demonstrated using empirical and simulated data

unsupervised deconvolution of sparse spike trains using stochastic approximation this paper presents an unsupervised method for restoration of sparse spike trains these signals are modeled as random bernoulli gaussian processes and their unsupervised restoration requires i estimation of the hyperparameters that control the stochastic models of the input and noise signals and ii deconvolution of the pulse process classically the problem is solved iteratively using a maximum generalized likelihood approach despite questionable statistical properties the contribution of the article is threefold first we present a new core algorithm for supervised deconvolution of spike trains which exhibits enhanced numerical efficiency and reduced memory requirements second we propose an original implementation of a hyperparameter estimation procedure that is based upon a stochastic version of the expectation maximization em algorithm this procedure utilizes the same core algorithm as the supervised deconvolution method third monte carlo simulations show that the proposed unsupervised restoration method exhibits satisfactory theoretical and practical behavior and that in addition good global numerical efficiency is achieved

a variational method for second order shape derivatives we consider shape functionals obtained as minima on sobolev spaces of classical integrals having smooth and convex densities under mixed dirichlet neumann boundary conditions we propose a new approach for the computation of the second order shape derivative of such functionals yielding a general existence and representation theorem in particular we consider the p torsional rigidity functional for p geq 2

the em approach to the multiple indicators and multiple causes model via the estimation of the latent variable abstract this article considers both likelihood and bayesian estimation procedures for a model with multiple indicators and multiple causes of a single unobservable latent variable the model is complicated by its reduced form which displays a mixture of econometric and psychometric themes we avoid this complexity via the estimation of the unobservable latent variable through direct use of the original structural form this approach not only provides maximum likelihood estimates that are equivalent to those derived from the reduced form but it also permits a feasible bayesian approach which would be technically complex to execute otherwise

on simultaneous signal estimation and parameter identification using a generalized likelihood approach a common approach to blind deconvolution of bernoulli gaussian processes consists of performing both signal restoration and hyperparameter identification through maximization of a single generalized likelihood criterion it is shown on a simple example that the resulting hyperparameter estimates may not converge toward any meaningful value therefore other more reliable approaches should be adopted whenever possible

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

alternative algorithms for the estimation of dynamic factor mimic and varying coefficient regression models this paper provides a general approach to the formulation and estimation of dynamic unobserved component models after introducing the general model two methods for estimating the unknown parameters are presented both are algorithms for maximizing the likelihood function the first is based on the method of scoring the second is the em algorithm a derivative free method each iteration of em requires a kalman filter and smoother followed by straightforward regression calculations the paper suggests using the em methods to quickly locate a neighborhood of the maximum scoring can then be used to pinpoint the maximum and calculate the information matrix

the lack of strict convexity and the validity of the comparison principle for a simple class of minimizers abstract let w x a x b be an affine function in r n r n l r n r be convex and w be a local minimizer of i v l v x d x in w 1 1 r with w x w x on in the trace sense then w satisfies the comparison principle from above i e w x w x a e on if and only if a l a does not belong to the relative interior of a n dimensional face of the epigraph of l as a consequence if f is the projection of a bounded face of the epigraph of l the local minimizer w x max x x 0 f satisfies the comparison principle from above if and only if dim f n 1 or x 0

fraisse limits in functional analysis we provide a unified approach to fraisse limits in functional analysis including the gurarij space the poulsen simplex and their noncommutative analogs we obtain in this general framework many known and new results about the gurarij space and the poulsen simplex and at the same time establish their noncommutative analogs particularly we construct noncommutative analogs of universal operators in the sense of rota

identifiability of unknown noise covariance matrices for some special cases of a linear time invariant discrete time dynamic system this paper investigates the identification of unknown noise covariance matrices q and r of an lti discrete time dynamic system two algorithms based on maximum a posteriori map and maximum likelihood ml cost functions are evaluated it is demonstrated that the cost functions exhibit local minima versus those elements of q and r which dominate the steady state output covariance matrix the following three special cases are considered 1 single input single output siso system 2 multiinput single output miso systems and 3 single input multioutput simo systems with a diagonal r for these special cases specific identifiability criteria are presented and verified by examples the improvement of the map algorithm over the ml algorithm is also demonstrated

disturbance smoother for state space models summary this paper develops a method to evaluate the smoothed estimator of the disturbance vector in a state space model together with its mean squared error matrix this disturbance smoother also leads to an efficient smoother for the state vector applications include a method to calculate auxiliary residuals for unobserved components time series models and an em algorithm for estimating covariance parameters in a state space model

almost square banach spaces abstract we single out and study a natural class of banach spaces almost square banach spaces in an almost square space we can find given a finite set x 1 x 2 x n in the unit sphere a unit vector y such that x i y is almost one these spaces have duals that are octahedral and finite convex combinations of slices of the unit ball of an almost square space have diameter 2 we provide several examples and characterizations of almost square spaces we prove that non reflexive spaces which are m ideals in their biduals are almost square we show that every separable space containing a copy of c 0 can be renormed to be almost square a local and a weak version of almost square spaces are also studied

global lipschitz continuity for minima of degenerate problems we consider the problem of minimizing the lagrangian int f nabla u f u among functions on omega subset mathbb r n with given boundary datum varphi we prove lipschitz regularity up to the boundary for solutions of this problem provided omega is convex and varphi satisfies the bounded slope condition the convex function f is required to satisfy a qualified form of uniform convexity only outside a ball and no growth assumptions are made

on the lavrentiev phenomenon for multiple integral scalar variational problems abstract we prove the non occurrence of lavrentiev gaps between lipschitz and sobolev functions for functionals of the form i u f u u u when r n r is lipschitz and belongs to a wide class of open bounded sets in r n containing lipschitz domains the lagrangian f is assumed to be either convex in both variables or a sum of functions f s a s g b s with g convex and s a s g 0 b s satisfying a non oscillatory condition at infinity we thus derive the non occurrence of the lavrentiev phenomenon for unnecessarily convex functionals of the gradient no growth conditions are assumed

dynamic structural systems under indirect observation identifiability and estimation aspects from a system theoretic perspective in this partly expository paper the parameter identifiability and estimation of a general dynamic structural model under indirect observation will be considered from a system theoretic perspective the general dynamic model covers dynamic factor analytic models dynamic mimic models and joreskog s linear structural model as special cases its reduced form is under a slightly different specification known in system theory and econometrics as the stochastic stationary version of the state space model by using concepts and methods from system theory such as the observability and controllability concept the steady state kalman filter and a general nonlinear ml estimation procedure known as prediction error estimation the general dynamic model will be identified it will be shown that joreskog s lisrel procedure is a special case of the prediction error estimation procedure