asymptotic distributions of quasi maximum likelihood estimators for spatial autoregressive models this paper investigates asymptotic properties of the maximum likelihood estimator and the quasi maximum likelihood estimator for the spatial autoregressive model the rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model it is important to make the distinction with dif ferent spatial scenarios under the scenario that each unit will be influenced by only a few neighboring units the estimators may have n rate of convergence and be asymp totically normal when each unit can be influenced by many neighbors irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence

gmm with many moment conditions this paper provides a first order asymptotic theory for generalized method of moments gmm estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak examples in which these asymptotics are relevant include instrumental variable iv estimation with many possibly weak or uninformed instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments under certain regularity conditions the gmm estimators are shown to converge in probability but not necessarily to the true parameter and conditions for consistent gmm estimation are given a general framework for the gmm limit distribution theory is developed based on epiconvergence methods some illustrations are provided including consistent gmm estimation of a panel model with time varying individual effects consistent limited information maximum likelihood estimation as a continuously updated gmm estimator and consistent iv structural estimation using large numbers of weak or irrelevant instruments some simulations are reported

the optimal choice of moments in dynamic panel data models this paper derives an approximation of the mean square error mse of the gmm estimator in dynamic panel data models the approximation is based on higher order asymptotic theory under double asymptotics while first order theory under double asymptotics provides information about the bias it does not provide enough information about the variance of the estimator higher order theory enables us to obtain information about the variance from this result a procedure for choosing the number of instruments is proposed the simulations confirm that the proposed procedure improves the precision of the estimator

initial conditions and moment restrictions in dynamic panel data models estimation of the dynamic error components model is considered using two alternative linear estimators that are designed to improve the properties of the standard first differenced gmm estimator both estimators require restrictions on the initial conditions process asymptotic efficiency comparisons and monte carlo simulations for the simple ar 1 model demonstrate the dramatic improvement in performance of the proposed estimators compared to the usual first differenced gmm estimator and compared to non linear gmm the importance of these results is illustrated in an application to the estimation of a labour demand model using company panel data

a measure of the tracking capability of recursive stochastic algorithms with constant gains a criterion is given for measuring the tracking capability of recursive algorithms when applied to slowly time varying systems the optimal gain for a given disturbance is also calculated this criterion is seen to have some connection with the fisher information matrix and allows us to select a priori the best algorithm for identifying a given unknown parameter which may be subject to smooth unknown disturbances examples of applications are given in the areas of identification theory and data communication theory

on the use of an spsa based model free feedback controller in active noise control for periodic disturbances in a duct in this paper a feedback active noise control fanc system using a model free mf controller based on simultaneous perturbation stochastic approximation spsa algorithm is considered the structure of the fanc system is first described and the spsa algorithm is briefly reviewed subsequently the spsa based mf control algorithm employed in the fanc system is derived computer simulations are carried out to suggest that the spsa based mf control algorithm is effective for anc system and much more efficient than the finite difference stochastic approximation fdsa algorithm the controller based on the spsa based mf control algorithm is implemented on the texas instruments digital signal processor dsp tms320vc33 experimental results show that the proposed scheme is able to significantly reduce periodic disturbances without the need to model the secondary path at the same time the simulations and the experimental verification tests also show that the convergence rate of the spsa based mf control algorithm is acceptable and the spsa based mf control algorithm has better tracking ability under variable secondary path this observation implies that the spsa based mf controller eliminates the need of modeling of the secondary path for the fanc system

dynamic spatial panel models networks common shocks and sequential exogeneity this paper considers a class of generalized methods of moments gmm estimators for general dynamic panel models allowing for weakly exogenous covariates and cross sectional dependence due to spatial lags unspecified common shocks and time varying interactive effects we significantly expand the scope of the existing literature by allowing for endogenous time varying spatial weight matrices without imposing explicit structural assumptions on how the weights are formed an important area of application is in social interaction and network models where our specification can accommodate data dependent network formation we consider an exemplary social interaction model and show how identification of the interaction parameters is achieved through a combination of linear and quadratic moment conditions for the general setup we develop an orthogonal forward differencing transformation to aid in the estimation of factor components while maintaining orthogonality of moment conditions this is an important ingredient to a tractable asymptotic distribution of our estimators in general the asymptotic distribution of our estimators is found to be mixed normal due to random norming however the asymptotic distribution of our test statistics is still chi square

the effects of dynamic feedbacks on ls and mm estimator accuracy in panel data models the finite sample behavior is analyzed of particular least squares ls and a range of generalized method of moments mm estimators in panel data models with individual effects and both a lagged dependent variable regressor and another explanatory variable the latter may be affected by lagged feedbacks from the dependent variable too asymptotic expansions indicate how the order of magnitude of bias of mm estimators tends to increase with the number of moment conditions exploited they also provide analytic evidence on how the bias of the various estimators depends on the feedbacks and on other model characteristics such as prominence of individual effects and correlation between observed and unobserved heterogeneity simulation results corroborate the theoretical findings and reveal that in small samples of models with dynamic feedbacks none of the techniques examined dominates regarding bias and mean squared error over all parametrizations examined

universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems the purpose of this paper is to investigate neural network capability systematically the main results are 1 every tauber wiener function is qualified as an activation function in the hidden layer of a three layered neural network 2 for a continuous function in s r sup 1 to be a tauber wiener function the necessary and sufficient condition is that it is not a polynomial 3 the capability of approximating nonlinear functionals defined on some compact set of a banach space and nonlinear operators has been shown and 4 the possibility by neural computation to approximate the output as a whole not at a fixed point of a dynamical system thus identifying the system

a one measurement form of simultaneous perturbation stochastic approximation the simultaneous perturbation stochastic approximation spsa algorithm has proven very effective for difficult multivariate optimization problems where it is not possible to obtain direct gradient information as discussed to date spsa is based on a highly efficient gradient approximation requiring only two measurements of the loss function independent of the number of parameters being estimated this note presents a form of spsa that requires only one function measurement for any dimension theory is presented that identifies the class of problems for which this one measurement form will be asymptotically superior to the standard two measurement form

weighted means in stochastic approximation of minima weighted averages of kiefer wolfowitz type procedures which are driven by larger step lengths than usual can achieve the optimal rate of convergence a priori knowledge of a lower bound on the smallest eigenvalue of the hessian matrix is avoided the asymptotic mean squared error of the weighted averaging algorithm is the same as would emerge using a newton type adaptive algorithm several different gradient estimates are considered one of them leads to a vanishing asymptotic bias this gradient estimate applied with the weighted averaging algorithm usually yields a better asymptotic mean squared error than applied with the standard algorithm

alternative approximations to the distributions of instrumental variable estimators the paper considers the ols the iv and two method of moments estimators mm and mmk of the coefficients of a single equation where the explanatory variables are correlated with the disturbance term the mm and mmk estimators are generalizations of the liml and limlk estimators respectively multivariate first order approximations to the distributions are derived under normality using a parameter sequence where the number of instruments increases as the number of observations increases numerical results show these approximations are more accurate compared to large sample approximations even if the number of instruments is small the moments of the multivariate limit distributions of the mm and mmk estimators can be consistently estimated under a variety of parameter sequences including the large sample sequence the new approximate confidence regions perform well in terms of exact levels compared to traditional ones the iv estimator of the coefficient of a single explanatory endogenous variable is interpreted as a shrinkage estimator which is dominated in practical cases by the mm and mmk estimators in terms of nearness to the true value in the sense of pitman

panel data models with spatially correlated error components abstract in this paper we consider a panel data model with error components that are both spatially and time wise correlated the model blends specifications typically considered in the spatial literature with those considered in the error components literature we introduce generalizations of the generalized moments estimators suggested in kelejian and prucha 1999 a generalized moments estimator for the autoregressive parameter in a spatial model international economic review 40 509 533 for estimating the spatial autoregressive parameter and the variance components of the disturbance process we then use those estimators to define a feasible generalized least squares procedure for the regression parameters we give formal large sample results for the proposed estimators we emphasize that our estimators remain computationally feasible even in large samples

data based stability analysis of a class of nonlinear discrete time systems nowadays with modern sensor technologies the inputs outputs and states of the system can be accurately measured based on this fact analyzing the properties of the system which has unknown mathematical model directly by using the measured data has become feasible in this paper some data based methods are proposed for state stability analysis of a class of nonlinear discrete time systems we also discuss the problem of finding the domain of attraction of the equilibrium point using these data based methods

discrete time model reference adaptive control of nonlinear dynamical systems using neural networks a multilayer discrete time neural net nn controller is presented for the direct model reference adaptive control of a class of multi input multi output mim0 nonlinear dynamical systems the nonlinear dynamical system is assumed to be controllable and its state vector is available for measurement the nn controller exhibits learning while functioning features instead of learning then control so that control is immediate with no explicit learning phase needed the tracking error between the output of a nonlinear plant and an ideal linear model converges within a very short time persistence of excitation pe is not needed linearity in the parameters is not required and certainty equivalence is not used this overcomes several limitations of standard adaptive control the novel weight tuning paradigm for the nn controller is based on the well known delta rule but includes a modification to the learning rate parameter plus a correction term it guarantees tracking as well as bounded nn weights in non i

a forward method for optimal stochastic nonlinear and adaptive control a computational approach is taken to solve the optimal partially observed nonlinear stochastic control problem the approach is to systematically solve the stochastic dynamic programming equations forward in time using a nested stochastic approximation technique although computationally intensive this provides a straightforward numerical solution for this class of problems and provides an alternative to the usual curse of dimensionality associated with solving the dynamic programming equation backwards in time in particular the curse is seen to take a new form where the amount of computation depends on the amount of uncertainty in the problem and the length of the horizon as a matter of more practical interest it is shown that the cost degrades monotonically as the complexity of the algorithm is reduced this provides a strategy for suboptimal control with clear performance computation trade offs a numerical study focusing on a generic optimal stochastic adaptive control example is included to demonstrate the feasibility of the method

a control scheme for a class of discrete nonlinear stochastic systems a control scheme is presented for effective stabilization of discrete time nonlinear stochastic systems where the nonlinearity involves a zero mean independent random sequence the control is of a constant feedback type and makes use of finite time solutions of a riccati like matrix difference equation stability results are both in terms of mean square and almost sure stochastic stability moreover a matrix inequality is given to check the existence of weighting matrices which would result in a stable regulator problem

asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and t are large we consider a dynamic panel ar 1 model with fixed effects when both n and t are large under the t fixed n large asymptotic approximation the ordinary least squares ols or gaussian maximum likelihood estimator mle is known to be inconsistent due to the well known incidental parameter problem we consider an alternative asymptotic approximation where n and t grow at the same rate it is shown that although ols or the mle is asymptotically biased a relatively simple fix to ols or the mle results in an asymptotically unbiased estimator under the assumption of gaussian innovations the bias corrected mle is shown to be asymptotically efficient by a hajek type convolution theorem

stationary performance of linear stochastic systems under single step optimal control linear quadratic optimal control with finite time horizon is considered for the case of penalties on the squared inputs and outputs the relative weighting of these penalties is treated as a design parameter it is shown that for positive real systems the stationary variances of the input and the output vary monotonically with this design parameter

a polyhedral approach to the rural postman problem abstract in this paper we study the polyhedron associated with the rural postman problem rpp because the rpp is np hard we cannot expect to find a complete description of the rural postman polyhedron of a general graph but a partial knowledge of such a description frequently proves to be useful for both theoretical and computational purposes we have tried to characterize the facial structure of this unbounded full dimensional polyhedron sets of valid inequalities inducing facets have been studied as well as their use in a cutting plane algorithm the application of this algorithm to a set of rpp instances taken from the literature and two instances of larger size taken from a real world graph is described all these instances were solved to optimality

odd minimum cut sets and b matchings we show that the determination of a minimum cut set of odd cardinality in a graph with even and odd vertices can be dealt with by a minor modification of the polynomially bounded algorithm of gomory and hu for multi terminal networks we connect this problem to the problem of identifying a matching or blossom constraint that chops off a point which is not contained in the convex hull of matchings or proving that no such inequality exists both the b matching problems without and with upper bounds are considered we discuss how the results of this paper can be used in conjunction with commercial lp packages lo solve b matching problems

the time series and cross section asymptotics of dynamic panel data estimators in this paper we derive the asymptotic properties of within groups wg gmm and liml estimators for an autoregressive model with random effects when both t and n tend to infinity gmm and liml are consistent and asymptotically equivalent to the wg estimator when t n 0 the fixed t results for gmm and liml remain valid but wg although consistent has an asymptotic bias in its asymptotic distribution when t n tends to a positive constant the wg gmm and liml estimators exhibit negative asymptotic biases of order 1 t 1 n and 1 2n t respectively in addition the crude gmm estimator that neglects the autocorrelation in first differenced errors is inconsistent as t n c 0 despite being consistent for fixed t finally we discuss the properties of a random effects pseudo mle with unrestricted initial conditions when both t and n tend to infinity

fixed effects dynamic spatial panel data models and impulse response analysis abstract real data often have complicated correlations over cross section and time such correlations are of particular interests in empirical studies this paper considers using high order spatial lags and high order time lags to model complicated correlations over cross section and time we propose to use the quasi maximum likelihood qml method to estimate the model we establish the asymptotic theory of the quasi maximum likelihood estimator qmle including the consistency and limiting distribution under large n and large t setup where n denotes the number of individuals and t the number of time periods we investigate the problem of estimating impulse response functions and the associated 1 confidence intervals average direct indirect and total impacts are defined along the same spirits of lesage and pace 2009 under the dynamic spatial panel data setup the estimation and inferential theory for the three impacts are studied model selection issue is also considered monte carlo simulations confirm our theoretical results and show that the qmle after bias correction has good finite sample performance

robust neural network tracking controller using simultaneous perturbation stochastic approximation this paper considers the design of robust neural network tracking controllers for nonlinear systems the neural network is used in the closed loop system to estimate the nonlinear system function we introduce the conic sector theory to establish a robust neural control system with guaranteed boundedness for both the input output i o signals and the weights of the neural network the neural network is trained by the simultaneous perturbation stochastic approximation spsa method instead of the standard backpropagation bp algorithm the proposed neural control system guarantees closed loop stability of the estimation system and a good tracking performance the performance improvement of the proposed system over existing systems can be quantified in terms of preventing weight shifts fast convergence and robustness against system disturbance

the maximum benefit chinese postman problem and the maximum benefit traveling salesman problem abstract this paper introduces the maximum benefit chinese postman problem mbcpp and the maximum benefit traveling salesman problem mbtsp for the mbcpp a benefit is realized each time a link of a directed graph is traversed the mbcpp relaxes the constraint of the chinese postman problem that each link be traversed at least once and finds a tour of maximum total net benefit for the mbtsp a benefit is derived when a node is visited and a cost is incurred when a link is traversed the mbtsp relaxes the constraint of the traveling salesman problem that each node be visited exactly or at least once and finds a tour of maximum total net benefit both problems are formulated as linear integer programming problems a solution algorithm is given that repeatedly solves a relaxation of the formulation as a minimum cost flow problem using a branch and bound procedure computational examples are presented

neural net based direct self tuning control of nonlinear plants use of neural networks for direct self tuning control of stochastic nonlinear plants has been proposed the control is based upon inverse modelling of a pseudo plant the input to the pseudo plant is same as the plant input while its output consists of a linear combination of the plant input and output the controller is directly identified as a mean square optimal inverse estimator of the pseudo plant this approach allows the control of inverse unstable plants local convergence properties as well as results of simulation studies are presented

optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation the simultaneous perturbation stochastic approximation spsa algorithm has attracted considerable attention for challenging optimization problems where it is difficult or impossible to obtain a direct gradient of the objective say loss function the approach is based on a highly efficient simultaneous perturbation approximation to the gradient based on loss function measurements spsa is based on picking a simultaneous perturbation random vector in a monte carlo fashion as part of generating the approximation to the gradient this paper derives the optimal distribution for the monte carlo process the objective is to minimize the mean square error of the estimate the authors also consider maximization of the likelihood that the estimate be confined within a bounded symmetric region of the true parameter the optimal distribution for the components of the simultaneous perturbation vector is found to be a symmetric bernoulli in both cases the authors end the paper with a numerical study related to the area of experiment design

control of nonlinear dynamical systems using neural networks ii observability identification and control for pt i see ibid vol 4 1993 this paper considers the problems of regulation and tracking of a dynamical system when the state variables of the dynamical system are not accessible the existence of the nonlinear maps describing the identifier and controller are first established and the implications for neural network realizations are described simulation results are included to complement the theoretical discussions

another look at the instrumental variable estimation of error components models this article develops a framework for efficient iv estimators of random effects models with information in levels which can accommodate predetermined variables our formulation clarifies the relationship between the existing estimators and the role of transformations in panel data models we characterize the valid transformations for relevant models and show that optimal estimators are invariant to the transformation used to remove individual effects we present an alternative transformation for models with predetermined instruments which preserves the orthogonality among the errors finally we consider models with predetermined variables that have constant correlation with the effects and illustrate their importance with simulations

formulation and estimation of dynamic models using panel data abstract this paper presents a statistical analysis of time series regression models for longitudinal data with and without lagged dependent variables under a variety of assumptions about the initial conditions of the processes being analyzed the analysis demonstrates how the asymptotic properties of estimators of longitudinal models are critically dependent on the manner in which samples become large by expanding the number of observations per person holding the number of people fixed or by expanding the number of persons holding the number of observations per person fixed the paper demonstrates which parameters can and cannot be identified from data produced by different sampling plans

profile quasi maximum likelihood estimation of partially linear spatial autoregressive models abstract we propose profile quasi maximum likelihood estimation of spatial autoregressive models that are partially linear the rate of convergence of the spatial parameter estimator depends on some general features of the spatial weight matrix of the model the estimators of other finite dimensional parameters in the model have the regular n rate of convergence and the estimator of the nonparametric component is consistent but with different restrictions on the choice of bandwidth parameter associated with different natures of the spatial weights monte carlo simulations verify our theory and indicate that our estimators perform reasonably well in finite samples

qml estimation of spatial dynamic panel data models with endogenous time varying spatial weights matrices in spatial panel data models when a spatial weights matrix is constructed from economic or social distance spatial weights could be endogenous and also time varying this paper presents model specification and proposes qmle estimation of spatial dynamic panel data models with endogenous time varying spatial weights matrices asymptotic properties of the proposed qmle are rigorously established we extend the notion of spatial near epoch dependence to allow time dependence by using spatial time lln for near epoch dependence process and clt for martingale difference sequence we establish the consistency and asymptotic normality of qmle monte carlo experiments show that the proposed estimators have satisfactory finite sample performance

stability analysis of hybrid composite dynamical systems descriptions involving operators and differential equations we address the stability analysis of composite hybrid dynamical feedback systems of the type depicted in fig 1 consisting of a block usually the plant which is described by an operator l and of a finite dimensional block described by a system of ordinary differential equations usually the controller we establish results for the well posedness attractivity asymptotic stability uniform boundedness asymptotic stability in the large and exponential stability in the large for such systems the hypotheses of these results are phrased in terms of the i o properties of l and in terms of the lyapunov stability properties of the subsystem described by the indicated ordinary differential equations the applicability of our results is demonstrated by means of general specific examples involving c 0 semigroups partial differential equations or integral equations which determine l

solving the prize collecting rural postman problem abstract in this work we present an algorithm for solving the prize collecting rural postman problem this problem was recently defined and is a generalization of other arc routing problems like for instance the rural postman problem the main difference is that there are no required edges instead there is a profit function on the edges that must be taken into account only the first time that an edge is traversed the problem is modeled as a linear integer program where the system has an exponential number of inequalities we propose a solution algorithm where iteratively we solve relaxed models with a small number of inequalities that provide upper bounds and we propose exact separation procedures for generating violated cuts when possible we also propose a simple heuristic to generate feasible solutions that provide lower bounds at each iteration we use a two phase method with different solvers at each phase despite the difficulty of the problem the numerical results from a series of computational experiments with various types of instances assess the good behavior of the algorithm in particular 75 of the instances were optimally solved with the lp relaxation of the model the remaining instances were optimally solved on a second phase most of them in small computation times

convergence of learning algorithms with constant learning rates the behavior of neural network learning algorithms with a small constant learning rate epsilon in stationary random input environments is investigated it is rigorously established that the sequence of weight estimates can be approximated by a certain ordinary differential equation in the sense of weak convergence of random processes as epsilon tends to zero as applications backpropagation in feedforward architectures and some feature extraction algorithms are studied in more detail

estimation of spatial autoregressive panel data models with fixed effects this paper establishes asymptotic properties of quasi maximum likelihood estimators for sar panel data models with fixed effects and sar disturbances a direct approach is to estimate all the parameters including the fixed effects because of the incidental parameter problem some parameter estimators may be inconsistent or their distributions are not properly centered we propose an alternative estimation method based on transformation which yields consistent estimators with properly centered distributions for the model with individual effects only the direct approach does not yield a consistent estimator of the variance parameter unless t is large but the estimators for other common parameters are the same as those of the transformation approach we also consider the estimation of the model with both individual and time effects

neural approximations for multistage optimal control of nonlinear stochastic systems two main approximations are used to solve a nonlinear quadratic gaussian lqg optimal control problem the control law is assigned a given structure in which a finite number of parameters have to be determined to minimize the cost function the chosen structure is that of a multilayer feedforward neural network and the control law is given a limited memory the errors resulting front both assumptions are discussed simulation results show that the proposed method may constitute a simple and effective tool for solving to a sufficient degree of accuracy optimal control problems traditionally regarded as difficult ones

efficient gmm estimation of spatial dynamic panel data models with fixed effects abstract in this paper we derive the asymptotic properties of gmm estimators for the spatial dynamic panel data model with fixed effects when n is large and t can be large but small relative to n the gmm estimation methods are designed with the fixed individual and time effects eliminated from the model and are computationally tractable even under circumstances where the ml approach would be either infeasible or computationally complicated the ml approach would be infeasible if the spatial weights matrix is not row normalized while the time effects are eliminated and would be computationally intractable if there are multiple spatial weights matrices in the model also consistency of the mle would require t to be large and not small relative to n if the fixed effects are jointly estimated with other parameters of interest the gmm approach can overcome all these difficulties we use exogenous and predetermined variables as instruments for linear moments along with several levels of their neighboring variables and additional quadratic moments we stack up the data and construct the best linear and quadratic moment conditions an alternative approach is to use separate moment conditions for each period which gives rise to many moments estimation we show that these gmm estimators are n t consistent asymptotically normal and can be relatively efficient we compare these approaches on their finite sample performance by monte carlo

a branch and cut algorithm for the profitable windy rural postman problem abstract in this paper we study the profitable windy rural postman problem this is an arc routing problem with profits defined on a windy graph in which there is a profit associated with some of the edges of the graph consisting of finding a route maximizing the difference between the total profit collected and the total cost this problem generalizes the rural postman problem and other well known arc routing problems and has real life applications mainly in snow removal operations we propose here a formulation for the problem and study its associated polyhedron several families of facet inducing inequalities are described and used in the design of a branch and cut procedure the algorithm has been tested on a large set of benchmark instances and compared with other existing algorithms the results obtained show that the branch and cut algorithm is able to solve large sized instances optimally in reasonable computing times

approximate newton methods for policy search in markov decision processes approximate newton methods are standard optimization tools which aim to maintain the benefits of newton s method such as a fast rate of convergence while alleviating its drawbacks such as computationally expensive calculation or estimation of the inverse hessian in this work we investigate approximate newton methods for policy optimization in markov decision processes mdps we first analyse the structure of the hessian of the total expected reward which is a standard objective function for mdps we show that like the gradient the hessian exhibits useful structure in the context of mdps and we use this analysis to motivate two gauss newton methods for mdps like the gauss newton method for non linear least squares these methods drop certain terms in the hessian the approximate hessians possess desirable properties such as negative definiteness and we demonstrate several important performance guarantees including guaranteed ascent directions invariance to afine transformation of the parameter space and convergence guarantees we finally provide a unifying perspective of key policy search algorithms demonstrating that our second gauss newton algorithm is closely related to both the em algorithm and natural gradient ascent applied to mdps but performs significantly better in practice on a range of challenging domains

stochastic approximation with averaging and feedback rapidly convergent on line algorithms consider the stochastic approximation x sub n 1 x sub n a sub n g x sub n spl xi sub n where 0 0 the averaging method is essentially off line in the sense that the actual sa iterate x sub n is not influenced by the averaging in many applications x sub n itself is of greatest interest since that is the operating parameter this paper deals with the problem of stochastic approximation with averaging and with appropriate feedback of the averages into the original algorithm it is shown both mathematically and via simulation that it works very well and has numerous advantages it is a clear improvement over the system x sub n by itself it is fairly robust and quite often it is much preferable to the use of the above averages without feedback the authors deal in particular with linear algorithms of the type appearing in parameter estimators adaptive noise cancellers channel equalizers adaptive control and similar applications the main development is for the constant parameter case because of its importance in applications but analogous results hold for the case where a sub n spl rarr 0

convergence of simultaneous perturbation stochastic approximation for nondifferentiable optimization we consider simultaneous perturbation stochastic approximation for function minimization the standard assumption for convergence is that the function be three times differentiable although weaker assumptions have been used for special cases however all work that we are aware of at least requires differentiability we relax the differentiability requirement and prove convergence using convex analysis

regret and convergence bounds for a class of continuum armed bandit problems we consider a class of multi armed bandit problems where the set of available actions can be mapped to a convex compact region of ropfd sometimes denoted as the ldquocontinuum armed banditrdquo problem the paper establishes bounds on the efficiency of any arm selection procedure under certain conditions on the class of possible underlying reward functions both finite time lower bounds on the growth rate of the regret as well as asymptotic upper bounds on the rates of convergence of the selected control values to the optimum are derived we explicitly characterize the dependence of these convergence rates on the minimal rate of variation of the mean reward function in a neighborhood of the optimal control the bounds can be used to demonstrate the asymptotic optimality of the kiefer wolfowitz method of stochastic approximation with regard to a large class of possible mean reward functions

convergence rate of moments in stochastic approximation with simultaneous perturbation gradient approximation and resetting the sequence of recursive estimators for function minimization generated by spall s 1998 simultaneous perturbation stochastic approximation spsa method combined with a suitable restarting mechanism is considered it is proved that this sequence converges under certain conditions with rate o n sup spl beta 2 for some spl beta 0 the best value being spl beta 2 3 where the rate is measured by the l sub q norm of the estimation error for any 1 spl les q spl infin the authors also present higher order spsa methods it is shown that the error exponent spl beta 2 can be arbitrarily close to 1 2 if the hessian matrix of the cost function at the minimizing point has all its eigenvalues to the right of 1 2 the cost function is sufficiently smooth and a sufficiently high order approximation of the derivative is used

correlation based tuning of decoupling multivariable controllers the iterative method labelled correlation based tuning cbt is considered in this paper for tuning linear time invariant multivariable controllers the approach allows one to tune some elements of the controller transfer function matrix to satisfy the desired closed loop performance while the other elements are tuned to mutually decouple the closed loop outputs decoupling is achieved by decorrelating a given reference with the non corresponding outputs the controller parameters are calculated either by solving a correlation equation decorrelation procedure or by minimizing a cross correlation function correlation reduction in addition the preferred way of exciting a 2x2 system for cbt is investigated via the accuracy of the estimated controller parameters it is shown that simultaneous excitation of both reference signals does not improve the accuracy of the estimated controller parameters compared to the case of sequential excitation in fact one must choose between low experimental cost simultaneous excitation and better accuracy of the estimated parameters sequential excitation the theoretical results are illustrated via three simulation studies

second order convergence analysis of stochastic adaptive linear filtering the convergence of an adaptive filtering vector is studied when it is governed by the mean square error gradient algorithm with constant step size we consider the mean square deviation between the optimal filter and the actual one during the steady state this quantity is known to be essentially proportional to the step size of the algorithm however previous analyses were either heuristic or based upon the assumption that successive observations were independent which is far from being realistic actually in most applications two successive observation vectors share a large number of components and thus they are strongly correlated in this work we deal with the case of correlated observations and prove that the mean square deviation is actually of the same order or less than the step size of the algorithm this result is proved without any boundedness or barrier assumption for the algorithm as it has been done previously in the literature to ensure the nondivergence our assumptions are reduced to the finite strong memory assumption and the finite moments assumption for the observation they are satisfied in a very wide class of practical applications

unified m estimation of fixed effects spatial dynamic models with short panels abstract it is well known that quasi maximum likelihood qml estimation of dynamic panel data dpd models with short panels depends on the assumptions on the initial values and a wrong treatment of them will result in inconsistency and serious bias the same issues apply to spatial dpd sdpd models with short panels in this paper a unified m estimation method is proposed for estimating the fixed effects sdpd models containing three major types of spatial effects namely spatial lag spatial error and space time lag the method is free from the specification of the distribution of the initial observations and robust against nonnormality of the errors consistency and asymptotic normality of the proposed m estimator are established a martingale difference representation of the underlying estimating functions is developed which leads to an initial condition free estimate of the variance of the m estimators monte carlo results show that the proposed methods have excellent finite sample performance

model free control model free control and the corresponding intelligent pid controllers ipids which already had many successful concrete applications are presented here for the first time in an unified manner where the new advances are taken into account the basics of model free control is now employing some old functional analysis and some elementary differential algebra the estimation techniques become quite straightforward via a recent online parameter identification approach the importance of ipis and especially of ips is deduced from the presence of friction the strange industrial ubiquity of classic pid s and the great difficulty for tuning them in complex situations is deduced via an elementary sampling from their connections with ipids several numerical simulations are presented which include some infinite dimensional systems they demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them

specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances this study develops a methodology of inference for a widely used cliff ord type spatial model containing spatial lags in the dependent variable exogenous variables and the disturbance terms while allowing for unknown heteroskedasticity in the innovations we first generalize the gmm estimator suggested in kelejian and prucha 1998 1999 for the spatial autoregressive parameter in the disturbance process we also define iv estimators for the regression parameters of the model and give results concerning the joint asymptotic distribution of those estimators and the gmm estimator much of the theory is kept general to cover a wide range of settings

adaptive stochastic approximation by the simultaneous perturbation method stochastic approximation sa has long been applied for problems of minimizing loss functions or root finding with noisy input information as with all stochastic search algorithms there are adjustable algorithm coefficients that must be specified and that can have a profound effect on algorithm performance it is known that choosing these coefficients according to an sa analog of the deterministic newton raphson algorithm provides an optimal or near optimal form of the algorithm however directly determining the required hessian matrix or jacobian matrix for root finding to achieve this algorithm form has often been difficult or impossible in practice the paper presents a general adaptive sa algorithm that is based on a simple method for estimating the hessian matrix while concurrently estimating the primary parameters of interest the approach applies in both the gradient free optimization kiefer wolfowitz and root finding stochastic gradient based robbins monro settings and is based on the simultaneous perturbation sp idea introduced previously the algorithm requires only a small number of loss function or gradient measurements per iteration independent of the problem dimension to adaptively estimate the hessian and parameters of primary interest aside from introducing the adaptive sp approach the paper presents practical implementation guidance asymptotic theory and a nontrivial numerical evaluation also included is a discussion and numerical analysis comparing the adaptive sp approach with the iterate averaging approach to accelerated sa

learning rules for neuro controller via simultaneous perturbation this paper describes learning rules using simultaneous perturbation for a neurocontroller that controls an unknown plant when we apply a direct control scheme by a neural network the neural network must learn an inverse system of the unknown plant in this case we must know the sensitivity function of the plant using a kind of the gradient method as a learning rule of the neural network on the other hand the learning rules described here do not require information about the sensitivity function some numerical simulations of a two link planar arm and a tracking problem for a nonlinear dynamic plant are shown

an efficient gmm estimator of spatial autoregressive models in this paper we consider gmm estimation of the regression and mrsar models with sar disturbances we derive the best gmm estimator within the class of gmm estimators based on linear and quadratic moment conditions the best gmm estimator has the merit of computational simplicity and asymptotic efficiency it is asymptotically as efficient as the ml estimator under normality and asymptotically more efficient than the gaussian qml estimator otherwise monte carlo studies show that with moderate sized samples the best gmm estimator has its biggest advantage when the disturbances are asymmetrically distributed when the diagonal elements of the spatial weights matrix have enough variation incorporating kurtosis of the disturbances in the moment functions will also be helpful

constrained optimization via stochastic approximation with a simultaneous perturbation gradient approximation this paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions of the optimization parameters it is shown that under application of the projection algorithm the parameter iterate converges almost surely to a kuhn tucker point the procedure is illustrated by a numerical example

gmm and 2sls estimation of mixed regressive spatial autoregressive models the gmm method and the classical 2sls method are considered for the estimation of mixed regressive spatial autoregressive models these methods have computational advantage over the conventional maximum likelihood method the proposed gmm estimators are shown to be consistent and asymptotically normal within certain classes of gmm estimators best ones are derived the proposed gmm estimators improve upon the 2sls estimators and are applicable even if all regressors are irrelevant a best gmm estimator may have the same limiting distribution as the ml estimator with normal disturbances

testing for serial correlation spatial autocorrelation and random effects using panel data abstract this paper considers a spatial panel data regression model with serial correlation on each spatial unit over time as well as spatial dependence between the spatial units at each point in time in addition the model allows for heterogeneity across the spatial units using random effects the paper then derives several lagrange multiplier tests for this panel data regression model including a joint test for serial correlation spatial autocorrelation and random effects these tests draw upon two strands of earlier work the first is the lm tests for the spatial error correlation model discussed in anselin and bera 1998 spatial dependence in linear regression models with an introduction to spatial econometrics in ullah a giles d e a eds handbook of applied economic statistics marcel dekker new york and in the panel data context by baltagi et al 2003 testing panel data regression models with spatial error correlation journal of econometrics 117 123 150 the second is the lm tests for the error component panel data model with serial correlation derived by baltagi and li 1995 testing ar 1 against ma 1 disturbances in an error component model journal of econometrics 68 133 151 hence the joint lm test derived in this paper encompasses those derived in both strands of earlier works in fact in the context of our general model the earlier lm tests become marginal lm tests that ignore either serial correlation over time or spatial error correlation the paper then derives conditional lm and lr tests that do not ignore these correlations and contrast them with their marginal lm and lr counterparts the small sample performance of these tests is investigated using monte carlo experiments as expected ignoring any correlation when it is significant can lead to misleading inference

dynamic structure neural networks for stable adaptive control of nonlinear systems an adaptive control technique using dynamic structure gaussian radial basis function neural networks that grow in time according to the location of the system s state in space is presented for the affine class of nonlinear systems having unknown or partially known dynamics the method results in a network that is economic in terms of network size for cases where the state spans only a small subset of state space by utilizing less basis functions than would have been the case if basis functions were centered on discrete locations covering the whole relevant region of state space additionally the system is augmented with sliding control so as to ensure global stability if and when the state moves outside the region of state space spanned by the basis functions and to ensure robustness to disturbances that arise due to the network inherent approximation errors and to the fact that for limiting the network size a minimal number of basis functions are actually being used adaptation laws and sliding control gains that ensure system stability in a lyapunov sense are presented together with techniques for determining which basis functions are to form part of the network structure the effectiveness of the method is demonstrated by experiment simulations

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

a new semiparametric spatial model for panel time series abstract this paper presents a semiparametric model for large dimension vector time series whose elements correspond to economic agents dependence between agents variables is characterized using a spatial model functions of agents economic distances provide restrictions that enable estimation of a vector autoregressive specification we present sufficient conditions for our model to generate stationary mixing series with finite higher order moments we estimate the model using a simple two step sieve least squares procedure where the sieve estimators are constructed to preserve shape restrictions on the functions of economic distance e g positive definiteness of a covariance function we provide rates of convergence for the sieve estimators t limiting distributions for the model s finite dimensional parameters and a bootstrap method for inference in an illustrative application we use this model to characterize how the comovement in output growth across us industrial sectors depends on the similarity of sectors technologies we also present a small monte carlo evaluation of our estimators

estimation of dynamic models with error components abstract observations on n cross section units at t time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit different assumptions about the initial conditions are a initial state fixed b initial state random c the unobserved individual effect independent of the unobserved dynamic process with the initial value fixed and d the unobserved individual effect independent of the unobserved dynamic process with initial value random asymptotic properties of the maximum likelihood and covariance estimators are obtained when t and when n the relationship between the pseudo and conditional maximum likelihood estimators is clarified a simple consistent estimator that is independent of the initial conditions and the way in which t or n is also suggested

qml estimation of dynamic panel data models with spatial errors abstract we propose quasi maximum likelihood qml estimation of dynamic panel models with spatial errors when the cross sectional dimension n is large and the time dimension t is fixed we consider both the random effects and fixed effects models and prove consistency and derive the limiting distributions of the qml estimators under different assumptions on the initial observations we propose a residual based bootstrap method for estimating the standard errors of the qml estimators monte carlo simulation shows that both the qml estimators and the bootstrap standard errors perform well in finite samples under a correct assumption on initial observations but may perform poorly when this assumption is not met

a branch and cut algorithm for the maximum benefit chinese postman problem the maximum benefit chinese postman problem mbcpp is an np hard problem that considers several benefits associated with each edge one for each time the edge is traversed with a service the objective is to find a closed walk with maximum benefit we propose an ip formulation for the undirected mbcpp and based on the description of its associated polyhedron we propose a branch and cut algorithm and present computational results on instances with up to 1 000 vertices and 3 000 edges

choosing the number of instruments properties of instrumental variable estimators are sensitive to the choice of valid instruments even in large cross section applications in this paper we address this problem by deriving simple mean square error criteria that can be minimized to choose the instrument set we develop these criteria for two stage least squares 2sls limited information maximum likelihood liml and a bias adjusted version of 2sls b2sls we give a theoretical derivation of the mean square error and show optimality in monte carlo experiments we find that the instrument choice generally yields an improvement in performance also in the angrist and krueger 1991 returns to education application when the instrument set is chosen in the way we consider it turns out that both 2sls and liml give similar large returns to education

quasi maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and t are large this paper investigates the asymptotic properties of quasi maximum likelihood estimators for spatial dynamic panel data with xed eects when both the number of individuals n and the number of time periods t are large we consider the case where t is asymptotically large relative to n the case where t is asymptotically proportional to n and the case where n is asymptotically large relative to t in the case where t is asymptotically large relative to n the estimators are p nt consistent and asymptotically normal with the limit distribution centered around 0 when n is asymptotically proportional to t the estimators are p nt consistent and asymptotically normal but the limit distribution is not centered around 0 and when n is large relative to t the estimators are consistent with rate t and have a degenerate limit distribution the estimators of the xed eects are p t consistent and asymptotically normal we also propose a bias correction for our estimators we show that when t grows faster than n 1 3 the correction will asymptotically eliminate the bias and yield a centered con dence interval

kernel estimation of hazard functions when observations have dependent and common covariates abstract we propose a hazard model where dependence between events is achieved by assuming dependence between covariates this model allows for correlated variables specific to observations as well as macro variables which all observations share this setup better fits many economic and financial applications where events are not independent nonparametric estimation of the hazard function is then studied kernel estimators proposed in nielsen and linton 1995 and linton et al 2003 are shown to have similar asymptotic properties compared with the i i d case mixing conditions ensure the asymptotic results follow these results depend on adjustments to bandwidth conditions simulations are conducted which verify the impact of dependence on estimators bandwidth selection accounting for dependence is shown to improve performance in an empirical application trade intensity in high frequency financial data is estimated

efficient estimation of models for dynamic panel data abstract in this paper we consider a dynamic model for panel data we show that under standard assumptions there are more moment conditions than are currently exploited in the literature some of these are linear but others are quadratic so that nonlinear gmm is required we also show that exogenous regressors generate a larger number of relevant moment conditions in a dynamic model than they would in a static model

multivariate stochastic approximation using a simultaneous perturbation gradient approximation the problem of finding a root of the multivariate gradient equation that arises in function minimization is considered when only noisy measurements of the function are available a stochastic approximation sa algorithm for the general kiefer wolfowitz type is appropriate for estimating the root the paper presents an sa algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite difference approximation of keifer wolfowitz type procedures theory and numerical experience indicate that the algorithm can be significantly more efficient than the standard algorithms in large dimensional problems

acceleration of stochastic approximation by averaging a new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated convergence with probability one is proved for a variety of classical optimization and identification problems it is also demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence

consistent estimation with a large number of weak instruments this paper analyzes the conditions under which consistent estimation can be achieved in instrumental variables iv regression when the available instruments are weak and the number of instruments k n goes to infinity with the sample size we show that consistent estimation depends importantly on the strength of the instruments as measured by r the rate of growth of the so called concentration parameter and also on k n in particular when k n the concentration parameter can grow even if each individual instrument is only weakly correlated with the endogenous explanatory variables and consistency of certain estimators can be established under weaker conditions than have previously been assumed in the literature hence the use of many weak instruments may actually improve the performance of certain point estimators more specifically we find that the limited information maximum likelihood liml estimator and the bias corrected two stage least squares b2sls estimator are consistent when k n r n 0 while the two stage least squares 2sls estimator is consistent only if k n r n 0 as n these consistency results suggest that liml and b2sls are more robust to instrument weakness than 2sls

maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods abstract a transformed likelihood approach is suggested to estimate fixed effects dynamic panel data models conditions on the data generating process of the exogenous variables are given to get around the issue of incidental parameters the maximum likelihood mle and minimum distance estimator mde are suggested both estimators are shown to be consistent and asymptotically normally distributed a hausman type specification test is suggested to test the fixed versus random effects specification or conditions on the data generating process of the exogenous variables monte carlo studies are conducted to evaluate the finite sample properties of the mle mde instrumental variable estimator iv and linear generalized method of moments estimator gmm it is shown that the likelihood approach appears to dominate the gmm approach both in terms of the bias and root mean square error of the estimators and the size and power of the test statistics

stochastic optimisation with inequality constraints using simultaneous perturbations and penalty functions we present a stochastic approximation algorithm based on penalty function method and a simultaneous perturbation gradient estimate for solving stochastic optimisation problems with general inequality constraints we present a general convergence result that applies to a class of penalty functions including the quadratic penalty function the augmented lagrangian and the absolute penalty function we also establish an asymptotic normality result for the algorithm with smooth penalty functions under minor assumptions numerical results are given to compare the performance of the proposed algorithm with different penalty functions

a globally convergent stochastic approximation by combining a constrained kiefer wolfowitz search with an automatic learning algorithm it is shown that asymptotically normal convergence of an estimator to a global optimum under reasonably lenient assumptions can be attained it is enough that the objective function be smooth and locally strictly convex at its minima the central conclusion is that if theta n is the estimate produced by the method shown at the nth decision epoch then for some global minimizer theta n 1 3 theta n theta is asymptotically normally distributed this coincides with the conventional kiefer wolfowitz convergence rate to a local optimum whereas this study was motivated by needs of machine learning the basic plan would seem applicable to root finding tasks and to other types of stochastic approximation algorithms

on bias inconsistency and efficiency of various estimators in dynamic panel data models abstract when a model for panel data includes lagged dependent explanatory variables then the habitual estimation procedures are asymptotically valid only when the number of observations in the time dimension t gets large usually however such datasets have substantial sample size in the cross section dimension n whereas t is often a single digit number results on the asymptotic bias n in this situation have been published a decade ago but hence far analytic small sample assessments of the actual bias have not been presented here we derive a formula for the bias of the least squares dummy variable lsdv estimator which has a o n 1 t 3 2 approximation error in a simulation study this is found to be remarkably accurate due to the small variance of the lsdv estimator which is usually much smaller than the variance of consistent generalized method of moments estimators a very efficient procedure results when we remove the bias from the lsdv estimator the simulations contain results for a particular operational corrected lsdv estimation procedure which in many situations proves to be much more efficient than various instrumental variable type estimators

on the asymptotic distribution of the moran i test statistic with applications by far the most popular test for spatial correlation is the one based on moran s 1950 i test statistic despite this the available results in the literature concerning the large sample distribution of this statistic are limited and have been derived under assumptions that do not cover many applications of interest in this paper we 3rst give a general result concerning the large sample distribution of moran i type test statistics we then apply this result to derive the large sample distribution of the moran i test statistic for a variety of important models in order to establishth ese results we also give a new central limit theorem for linear quadratic forms 2001 elsevier science s a all rights reserved jel classi cation c12 c21

modeling and control of stochastic systems with poorly known dynamics this paper is concerned with controlling poorly known systems for which only a simplified and rough model is available for control design there are many systems that cannot be reasonably probed for the sake of identification yet they are important for areas such as economy populations or medicine the ideas are developed around an alternative way to account for the bare modeling in a stochastic based setting and to heighten the control features for such a modified model the mathematical framework for the optimal control reveals important features such as the raising of a precautionary feedback policy of keep the action unchanged inaction for short on a certain state space region this feature is not seen in the robust approach but has been pointed out and permeates part of the economics literature the control problem relies on the viscosity solution for the hamilton jacobi bellman equation and the value of the problem is shown to be convex when specialized to the quadratic problem with discounted cost the exact solution inside the inaction region is given by a lyapunov type of equation and asymptotically for large state values by a riccati like equation this scenario bridges to the stochastic stability analysis for the controlled model the single control input is developed in full part analytically part numerically for the scalar case and an approximation is tested for the multidimensional case the advantage of the precautionary policy is substantial in some situations

new results for the directed profitable rural postman problem abstract we study a generalization of the directed rural postman problem where not all arcs requiring a service have to be visited provided that a penalty cost is paid if a service arc is not crossed the problem known as directed profitable rural postman problem looks for a tour visiting the selected set of service arcs while minimizing both traveling and penalty costs we add different valid inequalities to a known mathematical formulation of the problem and develop a branch and cut algorithm that introduces connectivity constraints both in a lazy and in a standard way we also propose a matheuristic followed by an improvement heuristic final refinement the matheuristic exploits information provided by a problem relaxation to select promising service arcs used to solve optimally directed rural postman problems the ex post refinement tries to improve the solution provided by the matheuristic using a branch and cut algorithm the method gets a quick convergence through the introduction of connectivity cuts that are not guaranteed to be valid inequalities and thus may exclude integer feasible solutions all proposed methods have been tested on benchmark instances found in literature and compared to state of the art algorithms results show that heuristic methods are extremely effective outperforming existing algorithms moreover our exact method is able to close in less than one hour all the 22 benchmark instances that have not been solved to optimality yet

model free control of nonlinear stochastic systems with discrete time measurements consider the problem of developing a controller for general nonlinear and stochastic systems where the equations governing the system are unknown using discrete time measurement this paper presents an approach for estimating a controller without building or assuming a model for the system such an approach has potential advantages in accommodating complex systems with possibly time varying dynamics the controller is constructed through use of a function approximator such as a neural network or polynomial this paper considers the use of the simultaneous perturbation stochastic approximation algorithm which requires only system measurements a convergence result for stochastic approximation algorithms with time varying objective functions and feedback is established it is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite difference gradient approximations