an improved stability criterion for discrete time lur e systems with sector and slope restrictions this paper introduces an improved stability criterion for discrete time lur e systems with sector and slope restrictions for the stability criterion a lur e lyapunov functional candidate is constructed to include quadratic terms and integration terms with nonlinearities to handle the resulting integration terms in the lyapunov difference there is proposed a new bound lemma where the integration terms are relaxed into the second order terms by the geometric point of view in addition an appropriate weighting method uses slack variables from the sector and slope restrictions in the overall derivation the stabilization condition is formulated in terms of a parameterized linear matrix inequality plmi which is then converted into the linear matrix inequality an example illustrates that the proposed criterion presents a less conservative result than the previous criteria in the literature

brief paper a revisited tsypkin criterion for discrete time nonlinear lur e systems with monotonic sector restrictions this paper revisits a well known tsypkin criterion for stability analysis of discrete time nonlinear luroe systems when nonlinearities are monotonic and sector restricted by 0 1 where 1 is positive de nite it is shown by kapila and haddad that the system is absolutely stable if a function g 0 z 1 1 mi 1 z 1 k ng z is strictly positive real wherek is nonnegative diagonal and g z represents a transfer function of the linear part of the luroe system with invertible or identically zero g 0 this paper extends this criterion when 1 is positive diagonal by choosing a new lyapunov function to obtain an lmi criterion from a frequency domain interpretation of this lmi criterion another su cient criterion is generated which establishes that the system is absolutely stable if a function g 0 z 1 1 mi 1 z 1 k 1 z k n g z is strictly positive real wherek andk are nonnegative diagonal and orthogonal to each other 1998 elsevier science ltd all rights reserved

semiparametric analysis of random effects linear models from binary panel data andersen 1970 considered the problem of inference on random effects linear models from binary response panel data he showed that inference is possible if the disturbances for each panel member are known to be white noise with the logistic distribution and if the observed explanatory variables vary over time a conditional maximum likelihood estimator consistently estimates the model parameters up to scale the present paper shows that inference remains possible if the disturbances for each panel member are known only to be time stationary with unbounded support and if the explanatory variables vary enough over time a conditional version of the maximum score estimator manski 1975 1985 consistently estimates the model parameters up to scale

reflection subgroups of coxeter systems let w r be a coxetcr system and t ij w wrw denote the corresponding set of reflections for u e w define n w tv tlf tw l w h w ere i denotes the length function of w r the principal result 3 3 of this paper is that if w is a reflection subgroup of w i e w w n t then e ti n z n w 1 is a set of coxeter generators for w in particular w is a coxeter group in 6 v deodhar gives a geometric proof of this last fact using properties of the root system of w it is easily seen that the coxeter gcncrators for w defined by deodhar coincide with those described above the idea of the proof here is that n may be regarded as a cocycle with n r r rer and coxeter systems are characterized among groups generated by involutions r by the existence of such a cocycle one then checks that w h n w n w w e w gives a suitable cocycle for w the same argument applies to a wider class of reflection systems g x characterized by the cxistcncc of a certain cocycle and so we give the proof for these the coxeter systems are precisely the reflection systems g x in which x consists of involutions the arrangement of this paper is as follows in section 2 we describe the main facts about reflection systems closely paralleling 1 chap iv sect 11 in section 3 we prove that reflection subgroups of a reflection system are themselves reflection systems in a canonical way 3 3 and obtain some additional facts about their canonical generators 3 4 3 11 in section 4 we specialize to the case of a coxeter system and give a geometric criterion 4 4 for a set of reflections to be the set of canonical generators of a reflection subgroup in terms of the inner products of the

lmi based stability criteria for discrete time lur e systems with monotonic sector and slope restricted nonlinearities this note presents new lmi based stability criteria for the discrete time multivariable lur e system with nonlinearities that are monotonic sector and slope restricted corresponding lur e lyapunov functions are constructed for such a system the new criteria are expressed in a reasonably general form that can be applied to both non diagonal and diagonal nonlinearities we explicitly compare the new approach to the existing lmi based popov like criteria in the literature and express the results in terms of an integral quadratic constraint iqc the applications of the new criteria to some control problems and strategies are briefly discussed numerical examples are included to show their performance and they are shown to be less conservative than the previous results

nonparametric identification in nonseparable panel data models with generalized fixed effects abstract this paper extends the familiar notion of fixed effects to nonlinear structures with infinite dimensional unobservables like preferences the main result is that a generalized version of differencing identifies local average responses lars in nonseparable structures in contrast to existing results this does not require either substantial restrictions on functional form or independence between the persistent unobservables and the explanatory variables of interest and it requires only two time periods on the other hand the results are confined to the subpopulation of stayers chamberlain 1982 i e the population for which the explanatory variables do not change over time we extend the basic framework to include time trends and dynamics in the explanatory variables and we show how distributional effects as well as average partial effects are identified our approach also allows endogeneity in the transitory unobservables furthermore we show that this new identification principle can be applied to well known objects like the slope coefficient in the semiparametric panel data binary choice model with fixed effects finally we suggest estimators for the local average response and average partial effect and we analyze their large and finite sample behavior

instrumental variable models for discrete outcomes single equation instrumental variable models for discrete outcomes are shown to be set identifying not point identifying for the structural functions that deliver the values of the discrete outcome bounds on identified sets are derived for a general nonparametric model and sharp set identification is demonstrated in the binary outcome case point identification is typically not achieved by imposing parametric restrictions the extent of an identified set varies with the strength and support of instruments and typically shrinks as the support of a discrete outcome grows the paper extends the analysis of structural quantile functions with endogenous arguments to cases in which there are discrete outcomes

a less conservative stability criterion for discrete time lur e systems with sector and slope restrictions this paper proposes a less conservative stability criterion for discrete time lur e systems with sector and slope restrictions by constructing a novel lyapunov functional compared with the lyapunov functional in the literature this paper fully utilizes the sector and slope restrictions in our lyapunov functional which includes integral terms involved with the sector restriction of the nonlinearities phi y i and phi y i 1 integral terms involved with the slope restriction between phi y i and phi y i 1 and a quadratic term with an augmented vector related to available vectors for representing upper and lower bounds of all integral terms the positive definiteness of a matrix appearing in the quadratic term can be relaxed by utilizing the lower bounds of all integral terms based on the lyapunov functional an improved stability criterion is derived in terms of linear matrix inequalities numerical examples show the effectiveness of the proposed criterion

identification of nonseparable triangular models with discrete instruments identification of nonseparable triangular models we study the identification through instruments of a nonseparable function that relates a continuous outcome to a continuous endogenous variable using group and dynamical systems theories we show that full identification can be achieved under strong exogeneity of the instrument and a dual monotonicity condition even if the instrument is discrete when identified the model is also testable our results therefore highlight the identifying power of strong exogeneity when combined with monotonicity restrictions

weighted minimum mean square distance from independence estimation in this paper we introduce a family of semi parametric estimators suggested by manski s minimum mean square distance from independence estimator we establish the strong consistency asymptotic normality and consistency of bootstrap estimates of the sampling distribution and the asymptotic variance of these estimators this abstract was borrowed from another version of this item

absolute stability criteria for multiple slope restricted monotonic nonlinearities absolute stability criteria such as the classical popov criterion guarantee stability for a class of sector bounded nonlinearities although the sector restriction bounds the admissible class of the nonlinearities the local slope of the nonlinearity may be arbitrarily large in this paper the authors derive absolute stability criteria for multiple slope restricted time invariant monotonic nonlinearities like the popov criterion in the single input single output case the authors results provide a simple graphical interpretation involving a straight line in a modified popov plane

infinite reduced words lattice property and braid graph of affine weyl groups abstract in this paper we establish a bijection between the infinite reduced words of an affine weyl group and certain biclosed sets of its positive system and determine all finitely generated biclosed sets in the positive system of an affine weyl group using these results we show firstly that the biclosed sets in the standard positive system of rank 3 affine weyl groups when ordered by inclusion form a complete algebraic ortholattice and secondly that the generalized braid graphs of those coxeter groups are connected which can be thought of as an infinite version of tit s solution to the word problem

nonparametric identification in panels using quantiles abstract this paper considers identification and estimation of ceteris paribus effects of continuous regressors in nonseparable panel models with time homogeneity the effects of interest are derivatives of the average and quantile structural functions of the model we find that these derivatives are identified with two time periods for stayers i e for individuals with the same regressor values in two time periods we show that the identification results carry over to models that allow location and scale time effects we propose nonparametric series methods and a weighted bootstrap scheme to estimate and make inference on the identified effects the bootstrap proposed allows inference for function valued parameters such as quantile effects uniformly over a region of quantile indices and or regressor values an empirical application to engel curve estimation with panel data illustrates the results

bootstrapping general empirical measures it is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions mathscr f and based on a probability measure p holds a s if and only if mathscr f in mathrm clt p and int f 2 dp infty where f sup f in mathscr f f and it holds in probability if and only if mathscr f in mathrm clt p thus for a large class of statistics no local uniformity of the clt about p is needed for the bootstrap to work consistency of the bootstrap the bootstrapped law of large numbers is also characterized these results are proved under certain weak measurability assumptions on mathscr f

a less conservative lmi condition for stability of discrete time systems with slope restricted nonlinearities many conditions have been found for the absolute stability of discrete time lur e systems in the literature it is advantageous to find convex searches via lmis where possible in this technical note we construct two less conservative lmi conditions for discrete time systems with slope restricted nonlinearities the first condition is derived via lyapunov theory while the second is derived via the theory of integral quadratic constraints iqcs and noncausal zames falb multipliers both conditions are related to the jury lee criterion most appropriate for systems with such nonlinearities and the second generalizes it numerical examples demonstrate a significant reduction in conservatism over competing approaches

small roots low elements and the weak order in coxeter groups abstract in this article we provide a new finite class of elements in any coxeter system w s called low elements they are defined from brink and howlett s small roots which are strongly linked to the automatic structure of w s our first main result is to show that they form a garside shadow in w s i e they contain s and are closed under join for the right weak order and by taking suffixes these low elements are the key to prove that all finitely generated artin tits groups have a finite garside family this result was announced in a note with p dehornoy in comptes rendus mathematiques 9 in which the present article was referred to under the following working title monotonicity of dominance depth on root systems and applications the proof is based on a fundamental property enjoyed by small roots and which is our second main result the set of small root is bipodal for a natural number n we define similarly n low elements from n small roots and conjecture that the set of n small roots is bipodal implying the set of n low elements is a garside shadow we prove this conjecture for affine coxeter groups and coxeter groups whose graph is labelled by 3 and to prove the latter we extend the root poset on positive roots to a weak order on the root system and define a bruhat order on the root system and study the paths in those orders in order to establish a criterion to prove bipodality involving only finite dihedral reflection subgroups

minimum distance from independence estimation of nonseparable instrumental variables models abstract i develop a semiparametric minimum distance from independence estimator for a nonseparable instrumental variables model an independence condition identifies the model for many types of discrete and continuous instruments the estimator is taken as the parameter value that most closely satisfies this independence condition implementing the estimator requires a quantile regression of the endogenous variables on the instrument so the procedure is two step with a finite or infinite dimensional nuisance parameter in the first step i prove consistency and establish asymptotic normality for a parametric but flexibly nonlinear outcome equation the consistency of the nonparametric bootstrap is also shown i illustrate the use of the estimator by estimating the returns to schooling using data from the 1979 national longitudinal survey

a multivariable extension of the tsypkin criterion using a lyapunov function approach for analyzing the stability of discrete time systems containing a feedback nonlinearity the tsypkin criterion is the closest analog to the popov criterion which is used for analyzing such systems in continuous time traditionally the proof of this criterion is based upon input output properties and function analytic methods in this paper we extend the tsypkin criterion to multivariable systems containing an arbitrary number of monotonic sector bounded memoryless time invariant nonlinearities along with providing a lyapunov function proof for this classical result

leapfrog estimation of a fixed effects model with unknown transformation of the dependent variable abstract this paper considers a fixed effects panel version of the linear transformation model in which the dependent variable is h yt for an unspecified strictly monotonic h examples of the model include the multiple spell proportional hazards model and dependent variable transformation models e g the box cox model with fixed effects a semiparametric estimator called the leapfrog estimator is introduced and shown to be n consistent and asymptotically normal the leapfrog estimator allows for h to vary over time and for heteroskedasticity across observational units related semiparametric estimators are considered and a general covariance result for estimators based on second order u processes is presented

average and quantile effects in nonseparable panel models nonseparable panel models are important in a variety of economic settings including discrete choice this paper gives identification and estimation results for nonseparable models under time homogeneity conditions that are like time is randomly assigned or time is an instrument partial identification results for average and quantile effects are given for discrete regressors under static or dynamic conditions in fully nonparametric and in semiparametric models with time effects it is shown that the usual linear fixed effects estimator is not a consistent estimator of the identified average effect and a consistent estimator is given a simple estimator of identified quantile treatment effects is given providing a solution to the important problem of estimating quantile treatment effects from panel data bounds for overall effects in static and dynamic models are given the dynamic bounds provide a partial identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity the impact of t the number of time periods is shown by deriving shrinkage rates for the identified set as t grows we also consider semiparametric discrete choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds computationally convenient methods for semiparametric models are presented we propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples we give empirical illustrations

decomposition rules for conformal pairs associated to symmetric spaces and abelian subalgebras of z2 graded lie algebras we give uniform formulas for the branching rules of level 1 modules over orthogonal affine lie algebras for all conformal pairs associated to symmetric spaces we also provide a combinatorial interpretation of these formulas in terms of certain abelian subalgebras of simple lie algebras

embeddings of root systems ii permutation root systems abstract this paper studies a class of embeddings of permutation root systems with properties abstracting those of examples of embeddings of linear root systems over commutative rings as considered in the first paper in this series the root system of one coxeter group w regarded as a permutation representation is realized with its roots as sets of roots of another coxeter group w with action induced by an embedding of w in a completion of w

identification and estimation of average partial effects in irregular correlated random coefficient panel data models in this paper we study identification and estimation of a correlated random coefficients crc panel data model the outcome of interest varies linearly with a vector of endogenous regressors the coefficients on these regressors are heterogenous across units and may covary with them we consider the average partial effect ape of a small change in the regressor vector on the outcome cf chamberlain 1984 wooldridge 2005a chamberlain 1992 calculated the semiparametric efficiency bound for the ape in our model and proposed a n consistent estimator nonsingularity of the ape s information bound and hence the appropriateness of chamberlain s 1992 estimator requires i the time dimension of the panel t to strictly exceed the number of random coefficients p and ii strong conditions on the time series properties of the regressor vector we demonstrate irregular identification of the ape when t p and for more persistent regressor processes our approach exploits the different identifying content of the subpopulations of stayers or units whose regressor values change little across periods and movers or units whose regressor values change substantially across periods we propose a feasible estimator based on our identification result and characterize its large sample properties while irregularity precludes our estimator from attaining parametric rates of convergence its limiting distribution is normal and inference is straightforward to conduct standard software may be used to compute point estimates and standard errors we use our methods to estimate the average elasticity of calorie consumption with respect to total outlay for a sample of poor nicaraguan households

normalizers of parabolic subgroups in coxeter groups we shall describe a simple procedure for obtaining presentations of normalizers of parabolic subgroups of arbitrary coxeter groups in each case the normalizer is the semidirect product of the parabolic subgroup by a complement which acts by permuting the simple re ections this complement may be viewed in a natural way as a maximal subgroup of a certain groupoid for which we obtain a set of generators and de ning relations moreover the de ning relations are all derived from subgroupoids of ranks one and two so that the groupoid can be viewed as a generalization of a coxeter group

a categorification of hecke algebras with parameters 1 and v abstract we categorify the hecke algebra with parameters 1 and v using a variation of the category of soergel bimodules

stability criteria of sector and slope restricted lur e systems presents stability criteria of sector and slope restricted lur e systems in terms of linear matrix inequalities by fully exploiting inherent properties of sector and slope restrictions in the time domain interpreting the time domain criteria in the frequency domain furthermore supplies simpler expressions several examples show excellent performances of these criteria

identification and estimation of time varying nonseparable panel data models without stayers abstract this paper explores the identification and estimation of nonseparable panel data models we show that the structural function is nonparametrically identified when it is strictly increasing in a scalar unobservable variable the conditional distributions of unobservable variables do not change over time and the joint support of explanatory variables satisfies some weak assumptions to identify the target parameters existing studies assume that the structural function does not change over time and that there are stayers namely individuals with the same regressor values in two time periods our approach by contrast allows the structural function to depend on the time period in an arbitrary manner and does not require the existence of stayers in estimation part of the paper we propose parametric and nonparametric estimators that implement our identification results monte carlo studies indicate that our parametric estimator performs well in finite samples finally we extend our identification results to models with discrete outcomes and show that the structural function is partially identified

the asymptotic stability of nonlinear lur e systems with multiple slope restrictions the authors present the analysis of the asymptotic stability of multiple slope restricted nonlinear lur e systems by providing a lyapunov function they obtain a matrix language criterion in terms of algebraic riccati equations and linear matrix inequalities which are discussed at the point of computational issues additionally they consider the frequency domain interpretation of the result

nonparametric estimation of nonadditive random functions we present estimators for nonparametric functions that are nonadditive in unobservable random terms the distributions of the unobservable random terms are assumed to be unknown we show that when a nonadditive nonparametric function is strictly monotone in an unobservable random term and it satisfies some other properties that may be implied by economic theory such as homogeneity of degree one or separability the function and the distribution of the unobservable random term are identified we also present convenient normalizations to use when the properties of the function other than strict monotonicity in the unobservable random term are unknown the estimators for the nonparametric function and for the distribution of the unobservable random term are shown to be consistent and asymptotically normal we extend the results to functions that depend on a multivariate random term the results of a limited simulation study are presented

simulation and the asymptotics of optimization estimators on demontre un theoreme de limite centrale general pour des estimateurs definis par minimisation de la longueur d une fonction de critere aleatoire a valeurs vectorielles aucune hypothese de regularite suffisante n est imposee sur la fonction de critere pour que les resultats puissent etre appliques a une classe d estimlateurs de simulation assez large des analyses completes de deux estimateurs de simulation l un introduit par pakes l autre par mcfadden illustrent l application des theoremes generaux

locally parabolic subgroups in coxeter groups of arbitrary ranks abstract despite the significance of the notion of parabolic closures in coxeter groups of finite ranks the parabolic closure is not guaranteed to exist as a parabolic subgroup in a general case in this paper first we give a concrete example to clarify that the parabolic closure of even an irreducible reflection subgroup of countable rank does not necessarily exist as a parabolic subgroup then we propose a generalized notion of locally parabolic closure by introducing a notion of locally parabolic subgroups which involves parabolic ones as a special case and prove that the locally parabolic closure always exists as a locally parabolic subgroup it is a subgroup of parabolic closure and we give another example to show that the inclusion may be strict in general our result suggests that locally parabolic closure has more natural properties and provides more information than parabolic closure we also give a result on maximal locally finite locally parabolic subgroups in coxeter groups which generalizes a similar well known fact on maximal finite parabolic subgroups

an iv model of quantile treatment effects the ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications however in observational studies the variables of interest e g education prices are often endogenous making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes in order to address this problem we develop a model of quantile treatment effects qte in the presence of endogeneity and obtain conditions for identification of the qte without functional form assumptions the principal feature of the model is the imposition of conditions that restrict the evolution of ranks across treatment states this feature allows us to overcome the endogeneity problem and recover the true qte through the use of instrumental variables the proposed model can also be equivalently viewed as a structural simultaneous equation model with nonadditive errors where qte can be interpreted as the structural quantile effects sqe

identification of nonseparable models using instruments with small support i consider nonparametric identification of nonseparable instrumental variables models with continuous endogenous variables if both the outcome and first stage equations are strictly increasing in a scalar unobservable then many kinds of continuous discrete and even binary instruments can be used to point identify the levels of the outcome equation this contrasts sharply with related work by imbens and newey 2009 that requires continuous instruments with large support one implication is that assumptions about the dimension of heterogeneity can provide nonparametric point identification of the distribution of treatment response for a continuous treatment in a randomized controlled experiment with partial compliance

cross section and panel data estimators for nonseparable models with endogenous regressors we propose two new methods for estimating models with nonseparable errors and endogenous regressors the first method estimates a local average response one estimates the response of the conditional mean of the dependent variable to a change in the explanatory variable while conditioning on an external variable and then undoes the conditioning the second method estimates the nonseparable function and the joint distribution of the observable and unobservable explanatory variables an external variable is used to impose an equality restriction at two points of support on the conditional distribution of the unobservable random term given the regressor and the external variable our methods apply to cross sections but our lead examples involve panel data cases in which the choice of the external variable is guided by the assumption that the distribution of the unobservable variables is exchangeable in the values of the endogenous variable for members of a group

embeddings of root systems i root systems over commutative rings abstract this paper gives examples of embeddings of root systems of coxeter groups including sporadic embeddings of standard real root systems in other standard real root systems and for a general coxeter group an embedding of its universal symmetric root system over commutative rings into the standard real root system of a simply laced coxeter group