almost equitable partitions and new necessary conditions for network controllability abstract in this paper we consider the controllability problem for multi agent networked control systems the main results of the paper are new graph theoretic necessary conditions for controllability involving almost equitable graph vertex partitions we generalize the known results on the role of graph symmetries and uncontrollability to weighted digraphs with multiple leaders and we also consider the broadcasted control scenario our results show that the internal structure of communities in a graph can induce obstructions to controllability that cannot be characterized by symmetry arguments alone and that in some cases depend on the number theoretic properties of the communities we show via examples that our results can be used to account for a large portion of uncontrollable inducing leader selections that could not have otherwise been accounted for using symmetry results

jeffreys prior analysis of the simultaneous equations model in the case with n 1 endogenous variables this paper analyzes the behavior of posterior distributions under the jereys prior in a simul taneous equations model the case under study is that of a general limited information setup with n 1 endogenous variables the jereys prior is shown to give rise to a marginal pos terior density which has cauchy like tails similar to that exhibited by the exactnite sample distribution of the corresponding liml estimator a stronger correspondence is established in the special case of a just identied orthonormal canonical model where the posterior density under the jereys prior is shown to have the same functional form as the density of thenite sample distribution of the liml estimator the work here generalizes that of chao and phillips j econ 87 1998 49 which gave analogous results for the special case of an equation with two endogenous variables c 2002 elsevier science b v all rights reserved jel classication c11 c31

instrumental variables regression with weak instruments this paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak here modeled as local to zero asymptotic representations are provided for various instrumental variable statistics including the two stage least squares tsls and limited information maximum likelihood liml estimators and their t statistics the asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument even in large samples tsls can be badly biased but liml is in many cases approximately median unbiased the theory suggests concrete quantitative guidelines for applied work these guidelines help to interpret angrist and krueger s 1991 estimates of the returns to education whereas tsls estimates with many instruments approach the ols estimate of 6 the more reliable liml and tsls estimates with fewer instruments fall between 8 and 10 with a typical confidence interval of 6 14

why are estimates of agricultural supply response so variable abstract estimates of the response of agricultural supply to movements in expected price display curiously large variation across crops regions and time periods we argue that this anomaly may be traced at least in part to the statistical properties of the commonly used econometric estimator which has infinite moments of all orders and may have a bimodal distribution we propose an alternative minimum expected loss estimator establish its improved sample properties and argue for its usefulness in the empirical analysis of agricultural supply response

some sampling properties of minimum expected loss melo estimators of structural coefficients abstract some sampling properties of zellner s 1978 melo estimates of structural coefficients of linear simultaneous equation models are examined by a series of sampling experiments the melo estimates appear to have more pronounced biases in estimating structural coefficients than the 2sls estimates however melo is found to outperform 2sls according to several criteria including mse and mae in a wide range of situations generated by varying structural coefficients the variance covariance matrix of structural disturbances and the sample size the magnitude of absolute sampling errors the estimation of the variance of structural disturbances and the large sample standard errors are also compared among ols 2sls and melo

inference on structural parameters in instrumental variables regression with weak instruments we consider the problem of making asymptotically valid inference on structural parameters in instrumental variables regression with weak instruments using the localto zero asymptotics of staiger and stock 1997 we derive the asymptotic distributions of lr and lm type statistics for testing simple hypotheses on structural parameters based on maximum likelihood and generalized method of moments estimation methods in contrast to the nonstandard limiting behavior of wald statistics the limiting distributions of certain lm and lr statistics are bounded by a chi square distribution with degrees of freedom given by the number of instruments further we show how to construct asymptotically valid confidence sets for structural parameters by inverting these statistics

zero forcing sets and controllability of dynamical systems defined on graphs in this technical note controllability of systems defined on graphs is discussed we consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph a one to one correspondence between the set of leaders rendering the network controllable and zero forcing sets is established to illustrate the proposed results special cases including path cycle and complete graphs are discussed moreover as shown for graphs with a tree structure the proposed results of the present technical note together with the existing results on the zero forcing sets lead to a minimal leader selection scheme in particular cases

robust synchronization of uncertain linear multi agent systems this paper deals with robust synchronization of uncertain multi agent networks given a network with for each of the agents identical nominal linear dynamics we allow uncertainty in the form of additive perturbations of the transfer matrices of the nominal dynamics the perturbations are assumed to be stable and bounded in h norm by some a priori given desired tolerance we derive state space formulas for observer based dynamic protocols that achieve synchronization for all perturbations bounded by this desired tolerance it is shown that a protocol achieves robust synchronization if and only if each controller from a related finite set of feedback controllers robustly stabilizes a given single linear system our protocols are expressed in terms of real symmetric solutions of certain algebraic riccati equations and inequalities and also involve weighting factors that depend on the eigenvalues of the graph laplacian for undirected network graphs we show that within the class of such dynamic protocols a guaranteed achievable tolerance can be obtained that is proportional to the quotient of the second smallest and the largest eigenvalue of the laplacian we also extend our results to additive nonlinear perturbations with l2 gain bounded by a given tolerance

upper and lower bounds for controllable subspaces of networks of diffusively coupled agents this technical note studies the controllability of diffusively coupled networks where some agents called leaders are under the influence of external control inputs first we consider networks where agents have general linear dynamics then we turn our attention to infer network controllability from its underlying graph topology to do this we consider networks with agents having single integrator dynamics for such networks we provide lower and upper bounds for the controllable subspaces in terms of the distance partitions and the maximal almost equitable partitions respectively we also provide an algorithm for computing the maximal almost equitable partition for a given graph and a set of leaders

limited information bayesian analysis of a simultaneous equation with an autocorrelated error term and its application to the u s gasoline market using markov chain monte carlo algorithms within the limited information bayesian framework we estimate the parameters of the structural equation of interest and test weak exogeneity in a simultaneous equation model with white noise as well as autocorrelated error terms a numerical example and an estimation of the supply and demand equations of the u s gasoline market show that if we ignore autocorrelation we obtain unreasonable posterior distributions of the parameters of interest also we find that the hypothesis of the asymmetric effect of the changes in oil price on the changes in gasoline price is rejected oil inventory has a significant negative effect on the gasoline price

path positivity and infinite coxeter groups abstract a coxeter graph is a connected graph each of whose edges is labeled with an integer 3 or with the adjacency matrix of a coxeter graph g denoted by a g aij is defined to be a square matrix of order v where a ij 2 cos p if the edge i j is labeled with the integer p and 0 if there is no edge joining vertex i with vertex j for any positive integer k we denote by pk the characteristic polynomial of the adjacency matrix of the path on k vertices a coxeter graph g is said to be path positive if for all positive integers k the matrix pk a g is entrywise nonnegative it is shown that with the exception of a few cases which are a b d e f h and i any coxeter graph is path positive the result can be interpreted as a new criterion for the infiniteness of a coxeter group

load balancing of dynamical distribution networks with flow constraints and unknown in outflows we consider a basic model of a dynamical distribution network modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge subject to unknown but constant inflows and outflows as a preparatory result it is shown how a distributed proportional integral controller structure associating with every edge of the graph a controller state will regulate the state variables of the vertices irrespective of the unknown constant inflows and outflows in the sense that the storage variables converge to the same value load balancing or consensus this will be proved by identifying the closed loop system as a port hamiltonian system and modifying the hamiltonian function into a lyapunov function dependent on the value of the vector of constant inflows and outflows in the main part of the paper the same problem will be addressed for the case that the input flow variables are constrained to take value in an arbitrary interval we will derive sufficient and necessary conditions for load balancing which only depend on the structure of the network in relation with the flow constraints crown copyright c 2013 published by elsevier b v all rights reserved

brief paper synchronization in networks of identical linear systems the paper investigates the synchronization of a network of identical linear state space models under a possibly time varying and directed interconnection structure the main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected the result can be interpreted as a generalization of classical consensus algorithms stronger conditions are shown to be sufficient but to some extent also necessary to ensure synchronization with the diffusive static output coupling often considered in the literature

bayesian and classical approaches to instrumental variable regression we establish relationships between certain bayesian and classical approaches to instrumental variable regression we determine the form of priors that lead to posteriors for structural parameters that have similar properties as classical 2sls and liml and in doing so provide some new insight especially in the context of weak instruments to the small sample behavior of bayesian and classical procedures using a reduced rank restriction on a multivariate linear model we determine the priors that give rise to posteriors that are identical in functional form to the sampling densities of the classical 2sls and liml estimators

disproof of a conjecture on the existence of the path recursive period for a connected graph abstract a sufficient and necessary condition on the existence of the path recursive period for a graph has been established in this paper this disproves the conjecture proposed in r shi path polynomials of a graph linear algebra appl 236 1996 181 187 some results presented in r shi path polynomials of a graph linear algebra appl 236 1996 181 187 r b bapat a k lal path positive graphs linear algebra appl 149 1991 125 149 have also been included

posterior distributions in limited information analysis of the simultaneous equations model using the jeffreys prior abstract this paper studies the use of the jeffreys prior in bayesian analysis of the simultaneous equations model sem exact representations are obtained for the posterior density of the structural coefficient in canonical sems with two endogenous variables for the general case with m endogenous variables and an unknown covariance matrix the laplace approximation is used to derive an analytic formula for the same posterior density both the exact and the approximate formulas we derive are found to exhibit cauchy like tails analogous to comparable results in the classical literature on liml estimation moreover in the special case of a two equation just identified sem in canonical form the posterior density of is shown to have the same infinite series representation as the density of the finite sample distribution of the corresponding liml estimator this paper also examines the occurrence first documented in kleibergen and van dijk 1994a of a nonintegrable asymptotic cusp in the posterior distribution of the coefficient matrix of the reduced form equations for the included endogenous regressors an explanation for this phenomenon is provided in terms of the jacobian of the mapping from the structural model to the reduced form this interpretation assists in understanding the success of the jeffreys prior in resolving this problem

bayesian specification analysis and estimation of simultaneous equation models using monte carlo methods bayesian procedures for specification analysis or diagnostic checking of modeling assumptions for structural equations of econometric models are developed and applied using monte carlo numerical methods checks on the validity of identifying restrictions exogeneity assumptions and other specifying assumptions are performed using posterior distributions for discrepancy vectors and functions representing departures from specifying assumptions several mappings or functions of reduced form coefficients are defined and their posterior distributions are computed a restricted reduced form approach is used to compute posterior distributions for structural parameters these procedures are applied in analyses of two econometric models

path positive graphs for any positive integer k let p denote the characteristic polynomial of the adjacency matrix of the path on k vertices we obtain certain results regarding t evaluated at a c the adjacency matrix of any given graph g for some special graphs g we describe the matrix p a g completely we call a graph g path positive if i a g is a nonnegative matrix for all positive integers k it is shown that if g is a connected graph with a vertex of degree at least four then g is path positive we conjecture that all connected graphs are path positive apart from a few exceptional cases described in the paper

controllability and observability of grid graphs via reduction and symmetries in this paper we investigate the controllability and observability properties of a family of linear dynamical systems whose structure is induced by the laplacian of a grid graph this analysis is motivated by several applications in network control and estimation quantum computation and discretization of partial differential equations specifically we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph for each eigenvalue based on its multiplicity and on suitable symmetries of the corresponding eigenvectors we provide necessary and sufficient conditions to characterize all and only the nodes from which the induced dynamical system is controllable observable we discuss the proposed criteria and show through suitable examples how such criteria reduce the complexity of the controllability respectively observability analysis of the grid

noncooperative disturbance decoupling a theory for disturbance decoupling problems has been well developed in the area of geometric control theory the aim of the present study is to introduce disturbance decoupling problems in a dynamic game context a noncooperative version of the disturbance decoupling problem is introduced and two different information structures are studied easily verifiable necessary and sufficient conditions for both problem types are obtained

disturbance decoupling problem for multi agent systems a graph topological approach abstract this paper studies the disturbance decoupling problem for multi agent systems with single integrator dynamics and a directed communication graph we are interested in topological conditions that imply the disturbance decoupling of the network and more generally guarantee the existence of a state feedback rendering the system disturbance decoupled in particular we will develop a class of graph partitions which can be described as a topological translation of controlled invariant subspaces in the context of dynamical networks then we will derive sufficient conditions in terms of graph partitions such that the network is disturbance decoupled as well as conditions guaranteeing solvability of the disturbance decoupling problem the proposed results are illustrated by a numerical example

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

on the normalization of structural equations properties of direction estimators in the general structural equation model only the direction of the vector of coefficients of the endogenous variables is determined the traditional normalization rule defines the coefficients that are of interest but should not be embodied in the estimation procedure we show that the properties of the traditionally defined ordinary least squares and two stage least squares estimators are distorted by their dependence on the normalization rule symmetrically normalized analogues of these estimators are defined and are shown to have essentially similar properties to those of the limited information maximum likelihood estimator exact distribution theory for the classical structural equation model in econometrics is notoriously complex and results for even the simplest cases have seemed too complicated to yield interesting analytical conclusions about the relative merits of different estimators thus anderson and sawa 1973 and anderson kunimoto and sawa 1982 for instance have resorted to extensive numerical tabulations of the exact densities to extract such information for the case of an equation with just two endogenous variables these tabulations suggest that in several respects the limited information maximum likelihood liml estimator is superior to the ordinary least squares ols and two stage least squares tsls estimators among others and these conclusions are supported by the higher order asymptotic results in anderson kunimoto and morimune 1986 and other work referenced there the basis for inference in this model is the joint distribution of the included endogenous variables represented by the reduced form together with the maintained hypothesis that a submatrix of the reduced form coefficient matrix has rank one less than its column dimension this condition determines the direction of a vector in rn where n 1 is the total number of endogenous variables in the equation but not its length thus some normalization rule is needed to determine the coefficient vector uniquely and the distribution theory referred to above has focused on results for the n coefficients remaining when the other is assumed to be unity in this paper we focus on the estimation of the direction of the n 1 dimensional coefficient vector in an unnormalized equation existing distribu tion results for the coefficients in a normalized equation are easily translated 1an earlier version of this paper bore the title on the interpretation of exact results for structural equation estimators my thanks to the referees and the co editor for comments on earlier versions of the paper that helped to both clarify the message and broaden the scope of the paper 1181

reaching a consensus in a dynamically changing environment a graphical approach this paper presents new graph theoretic results appropriate for the analysis of a variety of consensus problems cast in dynamically changing environments the concepts of rooted strongly rooted and neighbor shared are defined and conditions are derived for compositions of sequences of directed graphs to be of these types the graph of a stochastic matrix is defined and it is shown that under certain conditions the graph of a sarymsakov matrix and a rooted graph are one and the same as an illustration of the use of the concepts developed in this paper graph theoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied vicsek consensus problem

some further results on the exact small sample properties of the instrumental variable estimator we present new results on the exact small sample distribution of the instrumental variable estimator in particular we compare the small sample distribution to the asymptotic distribution

invariant bayesian inference in regression models that is robust against the jeffreys lindley s paradox we obtain the prior and posterior probability of a nested regression model as the hausdorff integral of the prior and posterior on the parameters of an encompassing linear regression model over a lower dimensional set that represents the nested model the hausdorff integral is invariant and therefore avoids the borel kolmogorov paradox basing priors and prior probabilities of nested regression models on the prior on the parameters of an encompassing linear regression model reduces the discrepancies between classical and bayesian inference like the jeffreys lindley s paradox we illustrate the analysis with examples of linear restrictions i e a linear regression model and non linear restrictions i e a cointegration and an autoregressive moving average model on the parameters of an encompassing linear regression model

improving bias and coverage in instrumental variable analysis with weak instruments for continuous and binary outcomes causal estimates can be obtained by instrumental variable analysis using a two stage method however these can be biased when the instruments are weak we introduce a bayesian method which adjusts for the first stage residuals in the second stage regression and has much improved bias and coverage properties in the continuous outcome case this adjustment reduces median bias from weak instruments to close to zero in the binary outcome case bias from weak instruments is reduced and the estimand is changed from a marginal population based effect to a conditional effect the lack of distributional assumptions on the posterior distribution of the causal effect gives a better summary of uncertainty and more accurate coverage levels than methods that rely on the asymptotic distribution of the causal estimate we discuss these properties in the context of mendelian randomization

the finite sample properties of simultaneous equations estimates and estimators bayesian and non bayesian approaches abstract after discussing the need for good finite sample estimation procedures for simultaneous equations models and showing the inadequacies of asymptotically justified estimators it is shown how the bayesian method of moments bmom provides an exact finite sample analysis of unrestricted reduced form systems then optimal finite sample estimates of structural coefficients are derived using three standard loss functions and they are compared to traditional bayesian optimal estimates monte carlo experimental evidence from four studies on the relative performance of bayesian and non bayesian estimators is reviewed with the finding that the performance of bayesian estimators is better