generalizing weak instrument robust iv statistics towards multiple parameters unrestricted covariance matrices and identification statistics abstract we generalize the weak instrument robust score or lagrange multiplier and likelihood ratio instrumental variables iv statistics towards multiple parameters and a general covariance matrix so they can be used in the generalized method of moments gmm the gmm extension of moreira s 2003 a conditional likelihood ratio test for structural models econometrica 71 1027 1048 conditional likelihood ratio statistic towards gmm preserves its expression except that it becomes conditional on a statistic that tests the rank of a matrix we analyze the spurious power decline of kleibergen s 2002 pivotal statistics for testing structural parameters in instrumental variables regression econometrica 70 1781 1803 2005 testing parameters in gmm without assuming that they are identified econometrica 73 1103 1124 score statistic and show that an independent misspecification pre test overcomes it we construct identification statistics that reflect if the confidence sets of the parameters are bounded a power study and the possible shapes of confidence sets illustrate the analysis

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

new approach to information fusion steady state kalman filtering by the modern time series analysis method based on the autoregressive moving average arma innovation model a unified and general information fusion steady state kalman filtering approach is presented for the general multisensor systems with different local dynamic models and correlated noises it can handle the filtering smoothing and prediction fusion problems for state or signal the optimal fusion rule weighted by matrices is re derived as a weighted least squares wls fuser and is reviewed an optimal fusion rule weighted by diagonal matrices is presented which is equivalent to the optimal fusion rule weighted by scalars for components and it realizes a decoupled fusion the new algorithms of the steady state kalman estimator gains are presented in order to compute the optimal weights the formulas of computing the cross covariances among local estimation errors by lyapunov equations are presented the exponential convergence of the iterative solution of lyapunov equation is proved it is proved that the optimal fusion estimators under three weighted fusion rules are locally optimal but are globally suboptimal the proposed steady state kalman fusers can reduce the on line computational burden and are suitable for real time applications a simulation example for the 3 sensor steady state kalman tracking fusion estimators shows their effectiveness and correctness and gives the accuracy comparison of the fusion rules

behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations we establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations asymptotic to constant shifts in phase showing that long time behavior is governed by an associated second order formal whitham modulation system a key point is to identify the way in which initial perturbations translate to initial data for this formal system a task accomplished by detailed estimates on the linearized solution operator about the background wave notably our approach gives both a common theoretical treatment and a complete classification in terms of phase coupling or decoupling of general systems of conservation or balance laws encompassing cases that had previously been studied separately or not at all at the same time our refined description of solutions gives the new result of nonlinear asymptotic stability with respect to localized perturbations in the phase decoupled case further distinguishing behavior in the different cases an interesting technical aspect of our analysis is that for systems of conservation laws the whitham modulation description is of system rather than scalar form as a consequence of which renormalization methods such as have been used to treat the reaction diffusion case in general do not seem to apply

simulated moments estimation of markov models of asset prices this paper provides a simulated moments estimator sme of the parameters of dynamic models in which the state vector follows a time homogeneous markov process conditions are provided for both weak and strong consistency as well as asymptotic normality various tradeoffs among the regularity conditions underlying the large sample properties of the sme are discussed in the context of an asset pricing model this paper provides conditions for the consistency and asymptotic normality of a simulated moments estimator sme of the parameters of asset pricing models with time homogeneous markov representations of the stochastic forc ing process sme s for economic models have been proposed by mcfadden 1989 and pakes and pollard 1989 for i i d environments and by lee and ingram 1991 for a time series environment the sme for time series models examined in this paper is as follows the state vector yt that determines asset prices is assumed to follow a time homogeneous markov process whose transi tion function depends on an unknown parameter vector 3 0 asset prices and possibly other relevant data are observed as f yt 0 for some given function f of the underlying state and parameter vector in parallel a simulated state process y is generated analytically or numerically from the economic model and corresponding simulated observations f yj3 13 are taken for a given parameter choice f3 the parameter is chosen so as to match moments that is to minimize the distance between sample moments of the data f y 8030 and those of the simulated series f yt f3 in a sense to be made precise the proposed sme extends the generalized method of moments gmm estimator hansen 1982 to a large class of asset pricing models for which the moment restrictions of interest do not have analytic representations in terms of observable variables and the unknown parameter vector we provide conditions on the transition function of yt and the observation function f under which the sme of 030 is consistent and characterize the normalized asymptotic distribu tion of the estimator for two reasons neither the regularity conditions underly ing hansen s 1982 analysis of gmm estimators for time series models without

estimation and inference with weak semi strong and strong identification this paper analyzes the properties of standard estimators tests and confidence sets cs s for parameters that are unidentified or weakly identified in some parts of the parameter space the paper also introduces methods to make the tests and cs s robust to such identification problems the results apply to a class of extremum estimators and corresponding tests and cs s that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification this covers a class of models estimated using maximum likelihood ml least squares ls quantile generalized method of moments generalized empirical likelihood minimum distance and semi parametric estimators the consistency lack of consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions the asymptotic sizes in a uniform sense of standard and identification robust tests and cs s are established the results are applied to the arma 1 1 time series model estimated by ml and to the nonlinear regression model estimated by ls in companion papers the results are applied to a number of other models

stability and asymptotic behavior of periodic traveling wave solutions of viscous conservation laws in several dimensions under natural spectral stability assumptions motivated by previous investigations of the associated spectral stability problem we determine sharp lp estimates on the linearized solution operator about a multidimensional planar periodic wave of a system of conservation laws with viscosity yielding linearized l1 lp lp stability for all p geqq 2 and dimensions d geqq 1 and nonlinear l1 hs lp hs stability and l2 asymptotic behavior for p geqq 2 and d geqq 3 the behavior can in general be rather complicated involving both convective that is wave like and diffusive effects

sequential covariance intersection fusion kalman filter for multisensor system with unknown cross covariances among local estimation errors the batch covariance intersection bci fusion estimation algorithm requires the optimization of a multi dimensional nonlinear cost function which yields a larger computational burden and computational complexity a fast sequential covariance intersection sci kalman filtering algorithm is presented in this paper which only requires to solve the optimization problem of several one dimensional nonlinear cost functions it is equivalent to several two sensor covariance intersection ci kalman fusers and is a recursive two sensor ci kalman fuser its accuracy depends on the orders of sensors it is proved that the sci fuser is consistent and its accuracy is higher than that of each local estimator and is lower than that of the optimal kalman fuser with known cross covariances the geometric interpretation of accuracy relations based on the covariance ellipses is given and the properties of the covariance ellipses are rigorously proved two monte carlo simulation examples show the effectiveness of the proposed results show that the accuracies of the sci fusers are not very sensitive with respect to the orders of sensors and show that its actual accuracy is close to that of the optimal kalman fuser in general cases and its robust accuracy is close to that of the bci fuser so it has good performances

minimizing euclidian state estimation error for linear uncertain dynamic systems based on multisensor and multi algorithm fusion in this paper a multisensor linear dynamic system with model uncertainty and bounded noises is considered based on previously developed set valued estimation methods in terms of convex optimization we propose several efficient algorithms of centralized sensor fusion distributed sensor fusion and multi algorithm fusion to minimize the euclidian estimation error of the state vector obviously an ellipsoid box with a larger size cannot be in general guaranteed to contain another ellipsoid box with a smaller size since centers and shapes of the two ellipsoids boxes may be different from each other this fact and the complementary advantages of multiple sensors and multiple algorithms motivate us to construct multiple estimation ellipsoids boxes squashed along each entry of the state vector as much as possible respectively by using the technique of multiple differently weighted objectives then intersection fusion of these estimation ellipsoids boxes yields a final euclidian error minimized state estimate numerical examples show that the new method with multi algorithm at both the sensors and the fusion center can significantly reduce the euclidian estimation error of the state

generalized empirical likelihood tests in time series models with potential identification failure abstract we introduce test statistics based on generalized empirical likelihood methods that can be used to test simple hypotheses involving the unknown parameter vector in moment condition time series models the test statistics generalize those in guggenberger and smith 2005 generalized empirical likelihood estimators and tests under partial weak and strong identification econometric theory 21 4 667 709 from the i i d to the time series context and are alternatives to those in kleibergen 2005a testing parameters in gmm without assuming that they are identified econometrica 73 4 1103 1123 and otsu 2006 generalized empirical likelihood inference for nonlinear and time series models under weak identification econometric theory 22 3 513 527 the main feature of these tests is that their empirical null rejection probabilities are not affected much by the strength or weakness of identification more precisely we show that the statistics are asymptotically distributed as chi square under both classical asymptotic theory and weak instrument asymptotics of stock and wright 2000 gmm with weak identification econometrica 68 5 1055 1096 we also introduce a modification to otsu s 2006 statistic that is computationally more attractive a monte carlo study reveals that the finite sample performance of the suggested tests is very competitive

optimal linear estimation fusion i unified fusion rules this paper deals with data or information fusion for the purpose of estimation three estimation fusion architectures are considered centralized distributed and hybrid a unified linear model and a general framework for these three architectures are established optimal fusion rules based on the best linear unbiased estimation blue the weighted least squares wls and their generalized versions are presented for cases with complete incomplete or no prior information these rules are more general and flexible and have wider applicability than previous results for example they are in a unified form that is optimal for all of the three fusion architectures with arbitrary correlation of local estimates or observation errors across sensors or across time they are also in explicit forms convenient for implementation the optimal fusion rules presented are not limited to linear data models illustrative numerical results are provided to verify the fusion rules and demonstrate how these fusion rules can be used in cases with complete incomplete or no prior information

on the track to track correlation problem the testing of the hypothesis whether two tracks represent the same target is considered previous works in the literature assumed that the estimates of the same target s state from two track files are uncorrelated a test that includes their correlation is presented

conditional linear combination tests for weakly identified models we introduce the class of conditional linear combination tests which reject null hypotheses concerning model parameters when a data dependent convex combination of two identification robust statistics is large these tests control size under weak identification and have a number of optimality properties in a conditional problem we show that the conditional likelihood ratio test of moreira 2003 is a conditional linear combination test in models with one endogenous regressor and that the class of conditional linear combination tests is equivalent to a class of quasi conditional likelihood ratio tests we suggest using minimax regret conditional linear combination tests and propose a computationally tractable class of tests that plug in an estimator for a nuisance parameter these plug in tests perform well in simulation and have optimal power in many strongly identified models thus allowing powerful identification robust inference in a wide range of linear and nonlinear models without sacrificing efficiency if identification is strong

nonlocalized modulation of periodic reaction diffusion waves the whitham equation in a companion paper we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized modulation plus a localized l1 perturbation here we determine time asymptotic behavior under such perturbations showing that solutions consist of a leading order of a modulation whose parameter evolution is governed by an associated whitham averaged equation

optimal distributed kalman filtering fusion with singular covariances of filtering errors and measurement noises in this paper we present the globally optimal distributed kalman filtering fusion with singular covariances of filtering errors and measurement noises the following facts motivate us to consider the problem first the invertibility of estimation error covariance matrices is a necessary condition for most of the existing distributed fusion algorithms however it can not be guaranteed to exist in practice for example when state estimation for a given dynamic system is subject to state equality constraints the estimation error covariance matrices must be singular second the proposed fused state estimate is still exactly the same as the centralized kalman filtering using all sensor raw measurements moreover the existing performance analysis results on the distributed kalman filtering fusion for the multisensor system with feedback are also extended to the singular covariance matrices of filtering error the final numerical examples support the theoretical results and show an advantage of less computational burden

group decision making models for sequential tasks the sequential probability ratio test sprt and related drift diffusion model ddm are optimal for choosing between two hypotheses using the minimal average number of samples and relevant for modeling the decision making process in human observers this work extends these models to group decision making previous works have focused almost exclusively on group accuracy here we explicitly address group decision time first we derive explicit solutions for the error rate and probability distribution function of decision times for a group of independent possibly nonidentical decision makers using one of three simple rules race majority total and majority first we illustrate our solutions with a group of n i i d decision makers who each make an individual decision using the sprt based ddm then compare the performance of each group rule under different constraints we then generalize these group rules to the eta total and eta first schemes to demonstrate the flexibility and power of our approach in characterizing the performance of a group given the performance of its individual members

nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case abstract extending previous results of oh zumbrun and johnson zumbrun we show that spectral stability implies linearized and nonlinear stability of spatially periodic traveling wave solutions of viscous systems of conservation laws for systems of generic type removing a restrictive assumption that wave speed be constant to first order along the manifold of nearby periodic solutions key to our analysis is a nonlinear cancellation estimate observed by johnson and zumbrun along with a detailed understanding of the whitham averaged system the latter motivates a careful analysis of the bloch perturbation expansion near zero frequency and suggests factoring out an appropriate translational modulation of the underlying wave allowing us to derive the sharpened low frequency estimates needed to close the nonlinear iteration arguments

sensors optimal dimensionality compression matrix in estimation fusion when there exists the limitation of communication bandwidth between sensors and a fusion center one needs to optimally pre compress sensor outputs sensor observations or estimates before sensors transmission to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion this paper will give an analytic solution of the optimal linear dimensionality compression matrix for the single sensor case and analyze the existence of the optimal linear dimensionality compression matrix for the multisensor case as well as how to implement a gauss seidel algorithm to search for an optimal solution to linear dimensionality compression matrix

optimal dimensionality reduction of sensor data in multisensor estimation fusion when there exists the limitation of communication bandwidth between sensors and a fusion center one needs to optimally precompress sensor outputs sensor observations or estimates before the sensors transmission in order to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion or when an allowed performance loss constraint exists one needs to design the minimum dimension of sensor data this paper will answer the above questions by using the matrix decomposition pseudo inverse and eigenvalue techniques

gel statistics under weak identification abstract the central concern of this paper is the provision in a time series moment condition framework of practical recommendations of confidence regions for parameters whose coverage probabilities are robust to the strength or weakness of identification to this end we develop pearson type test statistics based on gel implied probabilities formed from general kernel smoothed versions of the moment indicators we also modify the statistics suggested in guggenberger and smith 2008 for a general kernel smoothing function importantly for our conclusions we provide gel time series counterparts to gmm and gel conditional likelihood ratio statistics given in kleibergen 2005 and smith 2007 our analysis not only demonstrates that these statistics are asymptotically conditionally pivotal under both classical asymptotic theory and weak instrument asymptotics of stock and wright 2000 but also provides asymptotic power results in the weakly identified time series context consequently the empirical null rejection probabilities of the associated tests and thereby the coverage probabilities of the corresponding confidence regions should not be affected greatly by the strength or otherwise of identification a comprehensive monte carlo study indicates that a number of the tests proposed here represent very competitive choices in comparison with those suggested elsewhere in the literature

stability of undercompressive shock profiles abstract using a simplified pointwise iteration scheme we establish nonlinear phase asymptotic orbital stability of large amplitude lax undercompressive overcompressive and mixed under overcompressive type shock profiles of strictly parabolic systems of conservation laws with respect to initial perturbations u 0 x e 0 1 x 3 2 in c 0 e 0 sufficiently small under the necessary conditions of spectral and hyperbolic stability together with transversality of the connecting profile this completes the program initiated by zumbrun and howard in k zumbrun p howard pointwise semigroup methods and stability of viscous shock waves indiana univ math j 47 4 1998 741 871 extending to the general undercompressive case results obtained for lax and overcompressive shock profiles in a szepessy z xin nonlinear stability of viscous shock waves arch ration mech anal 122 1993 53 103 t p liu pointwise convergence to shock waves for viscous conservation laws comm pure appl math 50 11 1997 1113 1182 k zumbrun p howard pointwise semigroup methods and stability of viscous shock waves indiana univ math j 47 4 1998 741 871 k zumbrun refined wave tracking and nonlinear stability of viscous lax shocks methods appl anal 7 2000 747 768 m r raoofi l 1 asymptotic behavior of perturbed viscous shock profiles thesis indiana univ 2004 c mascia k zumbrun pointwise green s function bounds and stability of relaxation shocks indiana univ math j 51 4 2002 773 904 c mascia k zumbrun stability of small amplitude shock profiles of symmetric hyperbolic parabolic systems comm pure appl math 57 7 2004 841 876 c mascia k zumbrun pointwise green s function bounds for shock profiles with degenerate viscosity arch ration mech anal 169 3 2003 177 263 c mascia k zumbrun stability of large amplitude shock profiles of hyperbolic parabolic systems arch ration mech anal 172 1 2004 93 131 c mascia k zumbrun stability of large amplitude shock profiles of general relaxation systems siam j math anal in press and for special weakly coupled respectively scalar diffusive dispersive undercompressive profiles in t p liu k zumbrun nonlinear stability of an undercompressive shock for complex burgers equation comm math phys 168 1 1995 163 186 t p liu k zumbrun on nonlinear stability of general undercompressive viscous shock waves comm math phys 174 2 1995 319 345 respectively p howard k zumbrun pointwise estimates for dispersive diffusive shock waves arch ration mech anal 155 2000 85 169 in particular together with spectral results of k zumbrun dynamical stability of phase transitions in the p system with viscosity capillarity siam j appl math 60 2000 1913 1924 our results yield nonlinear stability of large amplitude undercompressive phase transitional profiles near equilibrium of slemrod s model m slemrod admissibility criteria for propagating phase boundaries in a van der waals fluid arch ration mech anal 81 4 1983 301 315 for van der waal gas dynamics or elasticity with viscosity capillarity

optimal two sided invariant similar tests for instrumental variables regression this paper considers tests of the parameter on an endogenous variable in an instrumental variables regression model the focus is on determining tests that have some optimal power properties we start by considering a model with normally distributed errors and known error covariance matrix we consider tests that are similar and satisfy a natural rotational invariance condition we determine a two sided power envelope for invariant similar tests this allows us to assess and compare the power properties of tests such as the conditional likelihood ratio clr the lagrange multiplier and the anderson rubin tests we find that the clr test is quite close to being uniformly most powerful invariant among a class of two sided tests the finite sample results of the paper are extended to the case of unknown error covariance matrix and possibly nonnormal errors via weak instrument asymptotics strong instrument asymptotic results also are provided because we seek tests that perform well under both weak and strong instruments

a conditional likelihood ratio test for structural models this paper develops a general method for constructing exactly similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced form covariance matrix these tests are shown to be similar under weak instrument asymptotics when the reduced form covariance matrix is estimated and the errors are non normal the conditional test based on the likelihood ratio statistic is particularly simple and has good power properties like the score test it is optimal under the usual local to null asymptotics but it has better power when identification is weak

nonparametric analysis of random utility models abstract this paper considers two sided tests for the parameter of an endogenous variable in an instrumental variable iv model with heteroskedastic and autocorrelated errors we develop the finite sample theory of weighted average power wap tests with normal errors and a known long run variance a typical weight choice yields tests with power near zero for parts of the parameter space we propose two boundary conditions that yield two sided tests with hac errors the locally unbiased lu condition is related to the power around the null hypothesis and is a weaker requirement than unbiasedness the strongly unbiased su condition is more restrictive than lu but the associated wap tests are easier to implement the wap su tests can outperform several tests under the weak iv asymptotics as they make use of the data beyond the anderson rubin and score statistics

a method of simulated moments for estimation of discrete response models without numerical integration this paper proposes a simple modification of a conventional method of moments estimator for a discrete response model replacing response probabilities that require numerical integration with estimators obtained by monte carlo simulation this method of simulated moments msm does not require precise estimates of these probabilities for consistency and asymptotic normality relying instead on the law of large numbers operating across observations to control simulation error and hence can use simulations of practical size the method is useful for models such as high dimensional multinomial probit mnp where computation has restricted applications

pointwise nonlinear stability of nonlocalized modulated periodic reaction diffusion waves abstract in this paper extending previous results of 2 we obtain pointwise nonlinear stability of periodic traveling reaction diffusion waves assuming spectral linearized stability under nonlocalized perturbations more precisely we establish pointwise estimate of nonlocalized modulational perturbation under a small initial perturbation consisting of a nonlocalized modulation plus a localized perturbation decaying algebraically

pointwise stability estimates for periodic traveling wave solutions of systems of viscous conservation laws abstract in the previous paper 9 we showed time asymptotic behavior with detailed decaying rates of perturbations of periodic traveling reaction diffusion waves under small initial perturbations with a gaussian rate and an algebraic rate here we establish pointwise nonlinear stability up to an appropriate modulation of periodic traveling waves of systems of viscous conservation laws under small algebraic decaying initial data similar to the reaction diffusion equations by using bloch decomposition we start with pointwise bounds on the green function of the linearized operator about underlying solutions

optimal interval estimation fusion based on sensor interval estimates with confidence degrees the interval estimation fusion method based on sensor interval estimates and their confidence degrees is developed when sensor estimates are independent of each other a combination rule to merge sensor estimates and their confidence degrees is proposed moreover two optimization criteria minimizing interval length with an allowable minimum confidence degree or maximizing confidence degree with an allowable maximum interval length are suggested in terms of the two criteria an optimal interval estimation fusion can be obtained based on the combined intervals and their confidence degrees then we can extend the results on the combined interval outputs and their confidence degrees to obtain a conditional combination rule and the corresponding optimal fault tolerant interval estimation fusion in terms of the two criteria it is easy to see that marzullo s fault tolerant interval estimation fusion marzullo 1990 tolerating failures of continuous valued sensors acm transactions on computer system 8 4 284 304 is a special case of our method

pivotal statistics for testing structural parameters in instrumental variables regression we propose a novel statistic for testing the structural parameters in instrumental variables regression the statistic is straightforward to compute and has a limiting distribution that is pivotal with a degrees of freedom parameter that is equal to the number of tested parameters it therefore differs from the anderson rubin statistic whose limiting distribution is pivotal but has a degrees of freedom parameter that is equal to the number of instruments and the likelihood based wald likelihood ratio and lagrange multiplier statistics whose limiting distributions are not pivotal we analyze the relationship between the statistic and the concentrated likelihood of the structural parameters and show that its limiting distribution is not affected by weak instruments we discuss examples of the non standard shapes of the asymptotically pivotal confidence sets that can be constructed using the statistic and investigate its power properties to show its importance for practical purposes we apply the statistic to the angrist krueger 1991 data and find similar results as in staiger and stock 1997 this discussion paper has resulted in a publication in econometrica 2002 70 5 1781 1803

stability of periodic solutions of conservation laws with viscosity pointwise bounds on the green function we investigate stability of periodic traveling wave solutions of systems of conservation laws with viscosity within the abstract evans function framework established by r a gardner our main result generalizing the work of zumbrun and howard in the traveling front or pulse setting is to establish sharp pointwise bounds on the green function for the linearized evolution equations provided that an appropriate evans function condition applies to the linearized operator about the wave this condition is equivalent to a spectral stability criterion introduced by schneider in the context of periodic reaction diffusion waves an immediate consequence is that strong spectral stability in the sense of schneider implies linearized l1 l p asymptotic stability for all p 1 on the other hand we show that the strict version of schneider s condition generically fails in the conservation law setting leading to complicated new metastable behavior reminiscent of that seen for degenerate neutrally stable families in the traveling front or pulse case our results apply also to the reaction diffusion setting sharpening at the linearized level results obtained by schneider using weighted norm and bloch decomposition methods

nonlinear modulational stability of periodic traveling wave solutions of the generalized kuramoto sivashinsky equation abstract in this paper we consider the spectral and nonlinear stabilities of periodic traveling wave solutions of a generalized kuramoto sivashinsky equation in particular we resolve the long standing question of nonlinear modulational stability by demonstrating that spectrally stable waves are nonlinearly stable when subject to small localized integrable perturbations our analysis is based upon detailed estimates of the linearized solution operator which are complicated by the fact that the necessarily essential spectrum of the associated linearization intersects the imaginary axis at the origin we carry out a numerical evans function study of the spectral problem and find bands of spectrally stable periodic traveling waves in close agreement with previous numerical studies of frisch she thual bar nepomnyashchy chang demekhin kopelevich and others carried out by other techniques we also compare predictions of the associated whitham modulation equations which formally describe the dynamics of weak large scale perturbations of a periodic wave train with numerical time evolution studies demonstrating their effectiveness at a practical level for the reader s convenience we include in an appendix the corresponding treatment of the swift hohenberg equation a nonconservative counterpart of the generalized kuramoto sivashinsky equation for which the nonlinear stability analysis is considerably simpler together with numerical evans function analyses extending spectral stability analyses of mielke and schneider

distributed fusion estimation with communication bandwidth constraints this technical note is concerned with the distributed kalman filtering problem for a class of networked multi sensor fusion systems nmfss with communication bandwidth constraints to satisfy finite communication bandwidth only partial components of the local vector estimation signals are transmitted to the fusion center fc at each time step where multiple binary variables are introduced to model this component transmitting process a novel compensation strategy is proposed to restructure the untransmitted components of each local estimate at the fc end and a recursive distributed fusion kalman filter dfkf is designed in the linear minimum variance sense moreover a simple suboptimal judgement criterion is proposed to determine a group of binary variables such that the mean square error of the designed dfkf is minimal at each time step an illustrative example is given to show the effectiveness of the proposed methods

technical communique distributed optimal component fusion weighted by scalars for fixed lag kalman smoother based on the optimal fusion criterion in the linear minimum variance sense a distributed optimal fusion fixed lag kalman smoother with a three layer fusion structure is given for the discrete time varying linear stochastic control systems with multiple sensors and correlated noises its components are estimated by scalar weighting fusion respectively it only requires in parallel a series of computations of the weighted scalars and avoids the computations of the weighted matrices so that the computational burden can obviously be reduced further the steady state fusion smoother is also given for the discrete time invariant linear stochastic control systems the scalar weights can be obtained by fusing once after all local estimations reach steady state it can reduce the online computational burden also the computation formulas of smoothing error cross covariance matrices are given two simulation examples show the performance

nonlinear weighted measurement fusion unscented kalman filter with asymptotic optimality for the general nonlinear systems a universal weighted measurement fusion wmf algorithm is presented via the taylor series expansion method based on the proposed fusion algorithm and the well known unscented kalman filter ukf the wmf ukf is presented it is proven that the proposed wmf ukf asymptotically approaches to the centralized measurement fusion ukf cmf ukf with the increase of the order of taylor series expansion so it has the asymptotical global optimality we find that wmf ukf has less computational cost than the cmf ukf does with the increase of the number of sensors two examples are given to show the effectiveness of the proposed algorithms

tests with correct size when instruments can be arbitrarily weak abstract this paper applies classical exponential family statistical theory to develop a unifying framework for testing structural parameters in the simultaneous equations model under the assumption of normal errors with known reduced form variance matrix the results can be divided into the limited information and full information categories in the limited information model it is possible to characterize the entire class of similar tests in a model with only one endogenous explanatory variable in the full information framework this paper proposes a family of similar tests for subsets of endogenous variables coefficients for both limited and full information models there exist power upper bounds for unbiased tests when the model is just identified the anderson rubin score and pseudo conditional likelihood ratio tests are optimal when the model is over identified the pseudo conditional likelihood ratio test has power close to the power envelope when identification is strong

distributed estimation constraints on the choice of the local models the following estimation problem is considered a coordinator must reconstruct the global probability density of a nonlinear random process conditioned on the noise corrupted observation history the coordinator can only access the local probability density produced by local processing of the observation history using a local model different from the process model it is shown that if the local model satisfies an algebraic constraint the coordinator can reconstruct the same conditional density of the state process as the one obtained if the observations were processed using the coordinator process model it is assumed that the random process is a nonlinear stochastic differential equation driven by a brownian motion and the observation process is corrupted by additive brownian motion which is identically modeled by the coordinator and the local processor

pointwise asymptotic behavior of modulated periodic reaction diffusion waves abstract by working with the periodic resolvent kernel and the bloch decomposition we establish pointwise bounds for the green function of the linearized equation associated with spatially periodic traveling waves of a system of reaction diffusion equations with our linearized estimates together with a nonlinear iteration scheme developed by johnson zumbrun we obtain l p behavior p 1 of a nonlinear solution to a perturbation equation of a reaction diffusion equation with respect to initial data in l 1 h 2 recovering and slightly sharpening results obtained by schneider using weighted energy and renormalization techniques we obtain also pointwise nonlinear estimates with respect to two different initial perturbations u 0 e 0 e x 2 m u 0 h 2 e 0 and u 0 e 0 1 x r r 2 u 0 h 2 e 0 respectively e 0 0 sufficiently small and m 1 sufficiently large showing that behavior is that of a heat kernel these pointwise bounds have not been obtained elsewhere and do not appear to be accessible by previous techniques

testing parameters in gmm without assuming that they are identified we propose a generalized method of moments gmm lagrange multiplier statistic i e the k statistic that uses the jacobian at the evaluated parameter value instead of the expected jacobian to obtain its limit behavior we use a novel assumption that brings gmm closer to maximum likelihood and which is easily satisfied the usual asymptotic x2 distribution of the k statistic then holds under a wider set of circumstances like weak and many instrument asymptotics and combinations thereof than the standard full rank case for the jacobian the behavior of the k statistic can be spurious around inflexion points and the maximum of the objective function since the moment conditions are then not satisfied combinations of the k statistic with statistics that test the validity of the moment equations overcome the spurious behavior we conduct a power comparison to test for the risk aversion parameter in a stochastic discount factor model and construct its confidence set for observed consumption growth and asset return series

an order insensitive sequential fast covariance intersection fusion algorithm the proposed sfci fusion algorithm can handle the problem of unknown cross correlation in local estimation errors the fusion accuracy of the proposed algorithm is not relevant to the fusion orders i e all fusion nodes can acquire identical result the fusion coefficients are straightforward to calculate owing to not require optimizing nonlinear cost function the proposed algorithm is computationally efficient and is therefore applicable for use in real time fusion systems in this article data cross correlation in distributed sensor system is investigated via an order insensitive sequential fast covariance intersection fusion algorithm among the existing approaches the common drawbacks are that the fusion results are sensitive to fusion orders and the computational burden is tremendous due to the optimization of multi dimensional nonlinear cost function in order to overcome these drawbacks a sequential fast covariance intersection sfci algorithm is presented the new fusion coefficients can be calculated straightforward by taking the reciprocal of the trace of the inverse variances as local fusion coefficients and using an iterative process for fusion step to revise the coefficient weight note that the proposed fusion algorithm is consistent and its accuracy is unrelated to the fusion order of the distributed system finally real radar data and simulation examples are provided to verify the effectiveness of the proposed algorithm