aggregating local image descriptors into compact codes this paper addresses the problem of large scale image search three constraints have to be taken into account search accuracy efficiency and memory usage we first present and evaluate different ways of aggregating local image descriptors into a vector and show that the fisher kernel achieves better performance than the reference bag of visual words approach for any given vector dimension we then jointly optimize dimensionality reduction and indexing in order to obtain a precise vector comparison as well as a compact representation the evaluation shows that the image representation can be reduced to a few dozen bytes while preserving high accuracy searching a 100 million image data set takes about 250 ms on one processor core

higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

empirical likelihood ratio confidence regions than are those based on student s t statistic an effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable the method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain algorithms exist for finding the unique global minimum at a superlinear rate of convergence a byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points the multivariate empirical likelihood regions are justified for functions of several means such as variances correlations and regression parameters and for statistics with linear estimating equations an algorithm is given for computing profile empirical likelihoods for these statistics

controllable regions of linear systems with bounded inputs it is known that the controllable region of a general unstable system with bounded control is the cartesian product of the controllable region of its subsystem with antistable modes and that of its subsystem with stable and marginally stable modes while the controllable region of a system with only stable and marginally stable modes is well known to be the whole state space that of an antistable system is studied in this paper a necessary and sufficient condition for a state of an antistable system to be controllable is given the boundary of the controllable region is characterized

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

brief predictive pi control of linear plants under positional and incremental input saturations a predictive control strategy is developed for set point tracking of lti plants in the presence of joint positional and incremental rate input saturation constraints the resulting control algorithm is built so as to provide an integral action capable to asymptotically reject arbitrary constant disturbances this task is achieved by possibly modifying on line the set point in the case this becomes incompatible with constraints and disturbances when applied to asymptotically null controllable with bounded inputs ancbi plants viz all stabilizable linear systems with eigenvalues in the closed unit circle the control law is shown to globally provide set point tracking in the presence of arbitrary constant disturbances and initial state for non ancbi plants viz systems with exponentially unstable modes the control law features the mentioned properties locally viz in bounded regions of initial states and disturbances

semiglobal stabilization of linear discrete time systems subject to input saturation via linear feedback an are based approach we revisit the problem of semiglobal stabilization of linear discrete time systems subject to input saturation and give an algebraic riccati equation are based approach to the proof of a fact established earlier lin and saberi 1995 i e a linear discrete time system subject to input saturation is semiglobally stabilizable via linear feedback as long as the linear system in the absence of the saturation is stabilizable and detectable and all its open loop poles are located inside or on the unit circle moreover we drastically relax the requirements on the characteristic of the saturation elements as imposed in the earlier work

asymptotic optimality of empirical likelihood for testing moment restrictions we show by example that empirical likelihood and other commonly used tests for moment restrictions are unable to control the exponential rate at which the probability of a type i error tends to zero unless the possible distributions for the observed data are restricted appropriately from this it follows that for the optimality claim for empirical likelihood in kitamura 2001 to hold additional assumptions and qualifications are required under stronger assumptions than those in kitamura 2001 we establish the following optimality result i empirical likelihood controls the rate at which the probability of a type i error tends to zero and ii among all procedures for which the probability of a type i error tends to zero at least as fast empirical likelihood maximizes the rate at which the probability of a type ii error tends to zero for most alternatives this result further implies that empirical likelihood maximizes the rate at which the probability of a type ii error tends to zero for all alternatives among a class of tests that satisfy a weaker criterion for their type i error probabilities

stability of finite horizon model predictive control with incremental input constraints abstract model predictive control of discrete time nonlinear systems with incremental input constraints is proposed in this paper firstly the existence of the terminal set and terminal penalty is proven on the assumption that the considered system is twice continuously differentiable secondly properties of the optimal cost function are exploited it shows that the optimal cost function is positive semi definite continuous at the equilibrium and monotonically decreasing along the predicted trajectory the systems under control converge to the equilibrium since the optimal cost function is monotonically decreasing thirdly stability of nonlinear systems is proven in terms of the classical lyapunov theorem where an upper bound of the optimal cost function in the terminal set is chosen as a candidate lyapuonv function finally the system is asymptotically stable since the system state converges to the equilibrium and the system is stable

a riemannian framework for tensor computing tensors are nowadays a common source of geometric information in this paper we propose to endow the tensor space with an affine invariant riemannian metric we demonstrate that it leads to strong theoretical properties the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries null eigenvalues are at the infinity the geodesic between two tensors and the mean of a set of tensors are uniquely defined etc we have previously shown that the riemannian metric provides a powerful framework for generalizing statistics to manifolds in this paper we show that it is also possible to generalize to tensor fields many important geometric data processing algorithms such as interpolation filtering diffusion and restoration of missing data for instance most interpolation and gaussian filtering schemes can be tackled efficiently through a weighted mean computation linear and anisotropic diffusion schemes can be adapted to our riemannian framework through partial differential evolution equations provided that the metric of the tensor space is taken into account for that purpose we provide intrinsic numerical schemes to compute the gradient and laplace beltrami operators finally to enforce the fidelity to the data either sparsely distributed tensors or complete tensors fields we propose least squares criteria based on our invariant riemannian distance which are particularly simple and efficient to solve

a general result on the stabilization of linear systems using bounded controls we present two constructions of controllers that globally stabilize linear systems subject to control saturation we allow essentially arbitrary saturation functions the only conditions imposed on the system are the obvious necessary ones namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold one of the constructions is in terms of a neural network type one hidden layer architecture while the other one is in terms of cascades of linear maps and saturations

empirical likelihood based inference in conditional moment restriction models this paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions our estimator generalizes the maximum empirical likelihood estimator mele of qin and lawless 1994 using a kernel smoothing method we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood based procedure this yields a one step estimator which avoids estimating optimal instruments our likelihood ratio type statistic for parametric restrictions does not require the estimation of variance and achieves asymptotic pivotalness implicitly the estimation and testing procedures we propose are normalization invariant simulation results suggest that our new estimator works remarkably well in finite samples

null controllability of linear systems with constrained controls the paper considers the problem of steering the state of a linear time varying system to the origin when the control is subject to magnitude constraints necessary and sufficient conditions are given for global constrained controllability as well as a necessary and sufficient condition for the existence of a control satisfying the constraints which steers the system to the origin from a specified initial epoch x 0 t 0 the global result does not require zero to be an interior point of the control set omega and the theorem for constrained controllability at x 0 t 0 only requires that omega be compact not that it contain zero the results are compared to those available in the literature furthermore numerical aspects of the problem are discussed as is a technique for determining a steering control

asymptotically efficient estimation in the presence of heteroskedasticity of unknown form in a multiple regression model the residual variance is an unknown function of the explanatory variables and estimated by nearest neighbor nonparametric regression the resulting weighted least squares estimator of the regression coefficients is shown to be adaptive in the sense of having the same asymptotic distribution to first order as estimators based on knowledge of the actual variance function or a finite parameterization of it a similar result was established by carroll 1982 using kernel estimation and under substantially more restrictive conditions on the data generating process than ours extensions to various other models seem to be possible

a central limit theorem for generalized quadratic forms random variables of the form w n mathop sum limits 1 leqq i leqq n mathop sum limits text 1 leqq j leqq n w ijn x i x j are considered with x i independent not necessarily identically distributed and w ijn borel functions such that w ijn x i x j is square integrable and has vanishing conditional expectations e w ijn x i x j x i e w ijn x i x j x j 0 text a text s text a central limit theorem is proved under the condition that the normed fourth moment tends to 3 under some restrictions the condition is also necessary finally conditions on the individual tails of w ijn x i x j and an eigenvalue condition are given that ensure asymptotic normality of w n

a semiparametric maximum likelihood estimator this paper presents a procedure for analyzing a model in which the parameter vector has two parts a finite dimensional component 8 and a nonparametric component a the procedure does not require parametric modeling of but assumes that the true density of the data satisfies an index restriction the idea is to construct a parametric model passing through the true model and to estimate by setting the score for the parametric model to zero the score is estimated nonparametrically and the estimator is shown to be n consistent and asymptotically normal the estimator is then shown to attain the semiparametric efficiency bound characterized in begun et al 1983 for multivariate nonlinear regression simultaneous equations partially specified regression index regression censored regression switching regression and disequilibrium models in which the error densities are unknown

bartlett adjustment of empirical discrepancy statistics summary we introduce two classes of empirical discrepancy statistics that extend empirical likelihood and establish simple conditions under which they admit bartlett adjustment

high order local pooling and encoding gaussians over a dictionary of gaussians local pooling lp in configuration feature space proposed by boureau et al explicitly restricts similar features to be aggregated which can preserve as much discriminative information as possible at the time it appeared this method combined with sparse coding achieved competitive classification results with only a small dictionary however its performance lags far behind the state of the art results as only the zero order information is exploited inspired by the success of high order statistical information in existing advanced feature coding or pooling methods we make an attempt to address the limitation of lp to this end we present a novel method called high order lp ho lp to leverage the information higher than the zero order one our idea is intuitively simple we compute the first and second order statistics per configuration bin and model them as a gaussian accordingly we employ a collection of gaussians as visual words to represent the universal probability distribution of features from all classes our problem is naturally formulated as encoding gaussians over a dictionary of gaussians as visual words this problem however is challenging since the space of gaussians is not a euclidean space but forms a riemannian manifold we address this challenge by mapping gaussians into the euclidean space which enables us to perform coding with common euclidean operations rather than complex and often expensive riemannian operations our ho lp preserves the advantages of the original lp pooling only similar features and using a small dictionary meanwhile it achieves very promising performance on standard benchmarks with either conventional hand engineered features or deep learning based features

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

semi global stabilization of linear systems with position and rate limited actuators abstract it is shown that if a linear system is asymptotically null controllable with bounded controls then when subject to both actuator position and rate saturation it is semi globally stabilizable by linear state feedback if in addition the system is also detectable then it is semi global stabilizable via linear output feedback

regulator problem for linear systems with constraints on control and its increment or rate this paper discusses the problem of constraints on both control and its rate or increment for linear systems in state space form in both the continuous and discrete time domains necessary and sufficient conditions are derived for autonomous linear systems with constrained state increment or rate for the continuous time case such that the system evolves respecting incremental or rate constraints a pole assignment technique is then used to solve the inverse problem giving stabilizing state feedback controllers that respect non symmetrical constraints on both control and its increment or rate an illustrative example shows the application of the method on the double integrator problem

smooth minimum distance estimation and testing with conditional estimating equations uniform in bandwidth theory abstract to study the influence of a bandwidth parameter in inference with conditional moments we propose a new class of estimators and establish an asymptotic representation of our estimator as a process indexed by a bandwidth which can vary within a wide range including bandwidths independent of the sample size we study its behavior under misspecification we also propose an efficient version of our estimator we develop a procedure based on a distance metric statistic for testing restrictions on parameters as well as a bootstrap technique to account for the bandwidth s influence our new methods are simple to implement apply to non smooth problems and perform well in our simulations

efficient additive kernels via explicit feature maps large scale nonlinear support vector machines svms can be approximated by linear ones using a suitable feature map the linear svms are in general much faster to learn and evaluate test than the original nonlinear svms this work introduces explicit feature maps for the additive class of kernels such as the intersection hellinger s and 2 kernels commonly used in computer vision and enables their use in large scale problems in particular we 1 provide explicit feature maps for all additive homogeneous kernels along with closed form expression for all common kernels 2 derive corresponding approximate finite dimensional feature maps based on a spectral analysis and 3 quantify the error of the approximation showing that the error is independent of the data dimension and decays exponentially fast with the approximation order for selected kernels such as 2 we demonstrate that the approximations have indistinguishable performance from the full kernels yet greatly reduce the train test times of svms we also compare with two other approximation methods nystrom s approximation of perronnin et al 1 which is data dependent and the explicit map of maji and berg 2 for the intersection kernel which as in the case of our approximations is data independent the approximations are evaluated on a number of standard data sets including caltech 101 3 daimler chrysler pedestrians 4 and inria pedestrians 5

empirical likelihood estimation and consistent tests with conditional moment restrictions this paper is about efficient estimation and consistent tests of conditional moment restrictions we use unconditional moment restrictions based on splines or other approximating functions for this purpose empirical likelihood estimation is particularly appropriate for this setting because of its relatively low bias with many moment conditions we give conditions so that efficiency of estimators and consistency of tests is achieved as the number of restrictions grows with the sample size we also give results for generalized empirical likelihood generalized method of moments and nonlinear instrumental variable estimators

feedback control of linear discrete time systems under state and control constraints in this paper the problem of stabilizing linear discrete time systems under state and control linear constraints is studied based on the concept of positive invariance existence conditions of linear state feedback control laws respecting both the constraints are established these conditions are then translated into an algorithm of linear programming

an algebraic approach to bounded controllability of linear systems in this paper we present an algebraic approach to the proof that a linear system with matrices a b is null controllable using bounded inputs if and only if it is null controllable with unbounde

efficient information theoretic inference for conditional moment restrictions abstract the generalised method of moments estimator may be substantially biased in finite samples especially so when there are large numbers of unconditional moment conditions this paper develops a class of first order equivalent semi parametric efficient estimators and tests for conditional moment restrictions models based on a local or kernel weighted version of the cressie read power divergence family of discrepancies this approach is similar in spirit to the empirical likelihood methods of kitamura et al 2004 empirical likelihood based inference in conditional moment restrictions models econometrica 72 1667 1714 and tripathi and kitamura 2003 testing conditional moment restrictions annals of statistics 31 2059 2095 these efficient local methods avoid the necessity of explicit estimation of the conditional jacobian and variance matrices of the conditional moment restrictions and provide empirical conditional probabilities for the observations

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

regulator problem for linear discrete time systems with non symmetrical constrained control the regulator problem is studied for linear discrete time systems with non symmetrical constrained control i e systems described by the state equation x k 1 ax k bu k where u k and u k fx k necessary and sufficient conditions allowing us to obtain the largest non symmetrical polyhedral domain of positive invariance and contractivity with respect to motions of the system in the closed loop are established the case of symmetrically constrained control is obtained as a particular case

local log euclidean multivariate gaussian descriptor and its application to image classification this paper presents a novel image descriptor to effectively characterize the local high order image statistics our work is inspired by the diffusion tensor imaging and the structure tensor method or covariance descriptor and motivated by popular distribution based descriptors such as sift and hog our idea is to associate one pixel with a multivariate gaussian distribution estimated in the neighborhood the challenge lies in that the space of gaussians is not a linear space but a riemannian manifold we show for the first time to our knowledge that the space of gaussians can be equipped with a lie group structure by defining a multiplication operation on this manifold and that it is isomorphic to a subgroup of the upper triangular matrix group furthermore we propose methods to embed this matrix group in the linear space which enables us to handle gaussians with euclidean operations rather than complicated riemannian operations the resulting descriptor called local log euclidean multivariate gaussian l 2 emg descriptor works well with low dimensional and high dimensional raw features moreover our descriptor is a continuous function of features without quantization which can model the first and second order statistics extensive experiments were conducted to evaluate thoroughly l 2 emg and the results showed that l 2 emg is very competitive with state of the art descriptors in image classification

an algorithm to find maximal state constraint sets for discrete time linear dynamical systems with bounded controls and states an algorithm to find a polyhedral approximant to the maximal state constraint set given state and input bounds is suggested for linear discrete time dynamical systems

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

an information theoretic alternative to generalized method of moments estimation while optimally weighted gmm estimation has desirable large sample properties its small sample performance is poor in some applications we propose a computationally simple alternative for weakly dependent data generating mechanisms based on minimization of the kullback leibler information criterion conditions are derived under which the large sample properties of this estimator are similar to gmm i e the estimator will be consistent and asymptotically normal with the same asymptotic covariance matrix as gmm in addition we propose overidentifying and parametric restrictions tests as alternatives to analogous gmm procedures

image classification with the fisher vector theory and practice a standard approach to describe an image for classification and retrieval purposes is to extract a set of local patch descriptors encode them into a high dimensional vector and pool them into an image level signature the most common patch encoding strategy consists in quantizing the local descriptors into a finite set of prototypical elements this leads to the popular bag of visual words representation in this work we propose to use the fisher kernel framework as an alternative patch encoding strategy we describe patches by their deviation from an universal generative gaussian mixture model this representation which we call fisher vector has many advantages it is efficient to compute it leads to excellent results even with efficient linear classifiers and it can be compressed with a minimal loss of accuracy using product quantization we report experimental results on five standard datasets pascal voc 2007 caltech 256 sun 397 ilsvrc 2010 and imagenet10k with up to 9m images and 10k classes showing that the fv framework is a state of the art patch encoding technique

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

decentralized formation control of mobile agents a unified framework abstract this paper studies the formation control problem for systems consisting of multiple mobile agents that are described by first order differential equations and second order differential equations respectively the following issues are investigated bounded input disturbance and time delay in derivation of the main results a blend of graph theoretic and system theoretic tools is employed where local potential functions and lasalle s invariant principle play central roles finally numerical examples which support the analytical results very well are also included

guaranteed stability regions of linear systems with actuator saturation using the low and high gain technique the stability regions of input saturated linear systems are examined with attention focused on state feedback lq control the results describe hyper ellipsoidal domains which are subsets of the actual domain of attraction for the system this is not new the novelty is in the use of the low and high gain technique to reduce conservatism in the results in addition to the standard regulator the tracking case is treated and some comments are made regarding other extensions

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

structured weak semantic space construction for visual categorization visual features have been widely used for image representation and categorization however visual features are often inconsistent with human perception besides constructing explicit semantic space is still an open problem to alleviate these two problems in this paper we propose to construct structured weak semantic space for image representation exemplar classifier is first trained to separate each training image from other images for weak semantic space construction however each exemplar classifier separates one training image from other images and it only has limited semantic separability besides the outputs of exemplar classifiers are inconsistent with each other we jointly construct the weak semantic space using structured constraint this is achieved by imposing low rank constraint on the outputs of exemplar classifiers with sparsity constraint an alternative optimization procedure is used to learn the exemplar classifiers since the proposed method does not dependent on the initial image representation strategy we can make use of various visual features for efficient exemplar classifier training e g fisher vector based methods and convolutional neural networks based methods we apply the proposed structured weak semantic space based image representation method for categorization the experimental results on several public image data sets prove the effectiveness of the proposed method

output regulation for linear systems subject to input saturation the purpose of this paper is to examine the problem of controlling a linear time invariant system subject to input saturation in order to have its output track or reject a family of reference or disturbance signals produced by some external generator it is shown that a semiglobal framework for this problem is a natural one within this framework a set of solvability conditions are given and feedback laws that solve the problem are constructed the theory developed in this paper incorporates earlier results established for linear systems without input saturation

local gmm estimation of time series models with conditional moment restrictions this paper investigates statistical properties of the local generalized method of moments lgmm estimator for some time series models defined by conditional moment restrictions first we consider markov processes with possible conditional heteroskedasticity of unknown forms and establish the consistency asymptotic normality and semi parametric efficiency of the lgmm estimator second we undertake a higher order asymptotic expansion and demonstrate that the lgmm estimator possesses some appealing bias reduction properties for positively autocorrelated processes our analysis of the asymptotic expansion of the lgmm estimator reveals an interesting contrast with the ols estimator that helps to shed light on the nature of the bias correction performed by the lgmm estimator the practical importance of these findings is evaluated in terms of a bond and option pricing exercise based on a diffusion model for spot interest rate

assessing misspecified asset pricing models with empirical likelihood estimators abstract hansen and jagannathan 1997 compare misspecified asset pricing models based on least square projections on a family of admissible stochastic discount factors we extend their fundamental contribution by considering minimum discrepancy projections where misspecification is measured by a family of convex functions that take into account higher moments of asset returns the minimum discrepancy problems are solved on dual spaces producing a family of estimators that captures the least square problem as a particular case we derive the asymptotic distributions of the estimators for the cressie read family of discrepancies and illustrate their use with an assessment of the consumption asset pricing model

curvature properties of the algebraic riccati equation abstract we prove that the solution to the algebraic ricatti equation are is concave with respect to a nonnegative definite symmetric state weighting matrix q when the input weighting matrix r r t 0 we also prove that the solution to the are is concave with respect to a positive definite diagonal input weighting matrix r when q q t 0

efficient instrumental variables estimation of nonlinear models this paper considers asymptotically efficient instrumental variables estimation of nonlinear models in an i i d environment the class of models includes nonlinear simultaneous equations models and other models of interest a problem in constructing efficient instrumental variables estimators for such models is that the optimal instruments involve a conditional expectation calculation of which can require functional form assumptions for the conditional distribution of endogenous variables as well as integration nonparametric methods provide a way of avoiding this difficulty here it is shown that nonparametric estimates of the optimal instruments can give asymptotically efficient instrumental variables estimators also ways of choosing the nonparametric estimate in applications are discussed two types of nonparametric estimates of the optimal instruments are considered each involves nonparametric regression one by nearest neighbor and the other by series approximation the finite sample properties of the estimators are considered in a small sampling experiment involving an endogenous dummy variable model

information theoretic approaches to inference in moment condition models one step efficient gmm estimation has been developed in the recent papers of back and brown 1990 imbens 1993 and qin and lawless 1994 these papers emphasized methods that correspond to using owen s 1988 method of empirical likelihood to reweight the data so that the reweighted sample obeys all the moment restrictions at the parameter estimates in this paper we consider an alternative klic motivated weighting and show how it and similar discrete reweightings define a class of unconstrained optimization problems which includes gmm as a special case such klic motivated reweightings introduce m auxiliary tilting parameters where m is the number of moments parameter and overidentification hypotheses can be recast in terms of these tilting parameters such tests when appropriately conditioned on the estimates of the original parameters are often startlingly more effective than their conventional counterparts this is apparently due to the local ancillarity of the original parameters for the tilting parameters

duality relationships for entropy like minimization problems this paper considers the minimization of a convex integral functional over the positive cone of an l p space subject to a finite number of linear equality constraints such problems arise in spectral estimation where the bjective function is often entropy like and in constrained approximation the lagrangian dual problem is finite dimensional and unconstrained under a quasi interior constraint qualification the primal and dual values are equal with dual attainment examples show the primal value may not be attained conditions are given that ensure that the primal optimal solution can be calculated directly from a dual optimum these conditions are satisfied in many examples

stability of rate constrained robust pole placement adaptive control systems abstract this paper presents stability analysis for discrete time pole placement adaptive control systems with input rate saturation constraints it is shown that with appropriate design the robust adaptive control system is stable for a class of stable minimum phase plants in the sense that all the signals in the loop remain bounded in the presence of modelling uncertainties and disturbances if the plant is free from modelling uncertainties and disturbances and the control input rate remains unsaturated for a period of time then the closed loop adaptive control system will asymptotically be characterized by the desired closed loop poles within this period

piecewise linear lq control for systems with input constraints abstract a piecewise linear control plc law based on lq theory is derived ths law raises an lq gain as the controlled error converges towards the origin it can be computed off line and it guarantees that input bounds are never exceeded without causing input saturation a succession of positively invariant sets are defined of diminishing size and associated with each is the corresponding highest lq gain possible in the presence of the input bounds the formulation gives rise to an iteration function whose solution is a fixed point fp the fp defines the optimal gain and the invariant set which comprise ellipsoids fp existence uniqueness and convergence properties are proven we explain the algorithms for the generation and subsequent implementation of the plc law the notion of a switching function is introduced consideration is given to the computational aspects of the fp the plc scheme is demonstrated for the linearized dynamics of the simple pendulum and the puma 560 robot a discrete time plc law can also be derived using the discrete time algebraic riccati equation

dynamic output feedback compensation for linear systems with independent amplitude and rate saturations the positive real lemma provides the basis for constructing linear output feedback dynamic compensators for multi input plants with independent amplitude saturations fixed structure techniques are used to obtain full and reduced order feedback compensators along with a guaranteed domain of attraction these results are then applied to the problem of rate saturation by using a feedback type model rate saturation is modelled as an amplitude saturation the closed loop system with amplitude and rate saturation is then treated as a system with independent amplitude saturations

jackknife estimation of stationary autoregressive models abstract this paper explores the properties of jackknife methods of estimation in stationary autoregressive models some general results concerning the correct weights for bias reduction under various sampling schemes are provided and the asymptotic properties of a jackknife estimator based on non overlapping sub samples are derived for the case of a stationary autoregression of order p when the number of sub samples is either fixed or increases with the sample size at an appropriate rate the results of a detailed investigation into the finite sample properties of various jackknife and alternative estimators are reported and it is found that the jackknife can deliver substantial reductions in bias in autoregressive models this finding is robust to departures from normality arch effects and misspecification the median unbiasedness and mean squared error properties are also investigated and compared with alternative methods as are the coverage rates of jackknife based confidence intervals

a new class of asymptotically efficient estimators for moment condition models in this paper we propose a new class of asymptotically efficient estimators for moment condition models these estimators share the same higher order bias properties as the generalized empirical likelihood estimators and once bias corrected have the same higher order efficiency properties as the bias corrected generalized empirical likelihood estimators unlike the generalized empirical likelihood estimators our new estimators are much easier to compute a simulation study finds that our estimators have better finite sample performance than the two step gmm and compare well to several potential alternatives in terms of both computational stability and overall performance

an explicit description of null controllable regions of linear systems with saturating actuators we give simple exact descriptions of the null controllable regions for general linear systems with saturating actuators the description is in terms of a set of extremal trajectories of the anti stable subsystem for lower order systems or systems with only real eigenvalues this description is further simplified to result in explicit formulae for the boundaries of the null controllable regions

testing conditional moment restrictions let x z be a pair of observable random vectors we construct a new smoothed empirical likelihood based test for the hypothesis e g z x 0 w p 1 where g is a vector of known functions and an unknown finite dimensional parameter we show that the test statistic is asymptotically normal under the null hypothesis and derive its asymptotic distribution under a sequence of local alternatives furthermore the test is shown to possess an optimality property in large samples simulation evidence suggests that it also behaves well in small samples

semi global exponential stabilization of linear discrete time systems subject to input saturation via linear feedbacks abstract in this paper we show that a linear discrete time system subject to input saturation is semi globally exponentially stabilizable via linear state and or output feedback laws as long as the system in the absence of input saturation is stabilizable and detectable and has all its poles located inside or on the unit circle furthermore the semi globally stabilizing feedback laws are explicitly constructed the results presented here are parallel to our earlier results on the continuous time counterpart lin and saberi 1993