an efficient semiparametric estimator for binary response models this paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function where this function can be characterized by an index the estimator is shown to be consistent asymptotically normally distributed and to achieve the semiparametric efficiency bound monte carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known and that the small sample behavior of the estimator in other cases is good

an approximate formula for the expected number of real zeros of a random polynomial abstract we study the expected number of real zeros of an algebraic polynomial of degree n whose coefficients are independent cauchy distributed random variables we present a formula for the expected number which has the advantage of being easy to use numerically this approach shows that the error term involved in the asymptotic estimate for the expected number of real zeros with this class of distribution for the coefficients is o 1

adaptive systems and time varying plants abstract the behaviour of four adaptive algorithms lms equation error output error identification and the goodwin ramadge caines adaptive control algorithm are examined in the face of plant parameter variations the key point to note is that persistency of excitation conditions in the time invariant parameter case guarantees exponential convergence then standard and newly developed lyapunov stability results allow us to guarantee tracking error and parameter error boundedness when the plant parameters are actually time varying

adaptive observer for multiple input multiple output mimo linear time varying systems for joint state parameter estimation in linear time varying ltv multiple input multiple output mimo systems an approach to the design of adaptive observers is proposed it is conceptually simple and computationally efficient its global exponential convergence is established for noise free systems in the presence of noises it is proved that the estimation errors are bounded and converge in the mean to zero if the noises are bounded and have zero means potential applications are fault detection and isolation and adaptive control

a new approach for secure communication using constrained hyperchaotic systems a new constrained hyperchaotic system is presented a secure communication scheme using the generated chaotic signals is proposed the crls estimator for nonlinear systems is used for chaos synchronization the crls estimator and the convergence of its nonlinear update phase are analyzed simulation results demonstrate the proposed secure scheme effectiveness in this paper a new technique is developed for a typical secure communication scheme in this approach we introduce the concept of constrained hyperchaotic systems to encrypt the carrier of the data signal to be transmitted at the transmitter end two different chaotic oscillators are coupled constrained and used as a new hyperchaotic system one of the outputs of the constrained hyperchaotic system is used as a carrier for the encrypted data then the outputs of the system including the modulated carrier are encrypted using a set of pre defined encryption rules at the receiving end and after decrypting the received outputs the discrete time constrained regularized least square crls estimator is used to reconstruct the constrained hyperchaotic signals and hence retrieve the transmitted data simulation results are presented to illustrate the capability of the crls estimator in reconstructing the states of the constrained hyperchaotic system moreover the proposed secure communication scheme is applied to transmit discrete images for which the quality of the transmission process is measured by the bit error rate ber

identification and estimation of triangular simultaneous equations models without additivity this paper uses control variables to identify and estimate models with nonseparable multidimensional disturbances triangular simultaneous equations models are considered with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable also for any control variable identification results are given for quantile average and policy effects bounds are given when a common support assumption is not satisfied estimators of identified objects and bounds are provided and a demand analysis empirical example is given

testing for monotonicity under endogeneity an application to the reservation wage function abstract this paper develops a test for monotonicity of nonparametric regression models under endogeneity which in its generality is novel in the literature the test statistic which is built upon a second order u process introduces correction terms based on control functions that purge the endogeneity the test has a non standard asymptotic distribution from which asymptotic critical values can directly be derived furthermore the test statistic is extended to accommodate multivariate exogenous regressors consistency against general alternatives is proved and the finite sample properties of the test are examined in a monte carlo experiment the test is used to formally assess the monotonicity of the reservation wage as a declining function of elapsed unemployment duration which has implications for underlying job search models this relationship is difficult to measure due to the simultaneity of both variables results for uk data indicate that reservation wage functions do in fact not decline monotonically thereby contradicting some partial equilibrium job search models

semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables this paper provides estimators of discrete choice models including binary ordered and multinomial response choice models the estimators closely resemble ordinary and two stage least squares the distribution of the model s latent variable error is unknown and may be related to the regressors e g the model could have errors that are heteroscedastic or correlated with regressors the estimator does not require numerical searches even for multinomial choice for ordered and binary choice models the estimator is root n consistent and asymptotically normal a consistent estimator of the conditional error distribution is also provided

efficient estimation of limited dependent variable models with endogenous explanatory variables abstract this paper discusses asymptotically efficient estimation of the parameters of limited dependent variable models with endogenous explanatory variables general results on asymptotic efficiency of two stage and amemiya gls estimators are derived and used to obtain a simple asymptotically efficient estimator of the structural coefficients this estimator can be calculated by applying gls to estimates of the reduced form coefficients that are obtained by using reduced form residuals as additional explanatory variables it is also shown that it is possible to obtain asymptotically efficient estimators of the other coefficients by a modified minimum chi square method

direct semiparametric estimation of single index models with discrete covariates abstract others have developed average derivative estimators of the parameter in the model e y x x g x where g is an unknown function and x is a random vector these estimators are noniterative and easy to compute but require that x be continuously distributed this article develops a noniterative easily computed estimator of for models in which some components of x are discrete the estimator is n consistent and asymptotically normal an application to data on product innovation by german manufacturers illustrates the estimator s usefulness

estimation of semiparametric models when the criterion function is not smooth we provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some nonparametric estimators that can themselves depend on the parameters to be estimated our results extend existing theories such as those of pakes and pollard 1989 andrews 1994a and newey 1994 we also show that bootstrap provides asymptotically correct confidence regions for the finite dimensional parameters we apply our results to two examples a hit rate and a partially linear median regression with some endogenous regressors

an adaptive estimation of dimension reduction space summary searching for an effective dimension reduction space is an important problem in regression especially for high dimensional data we propose an adaptive approach based on semiparametric models which we call the conditional minimum average variance estimation mave method within quite a general setting the mave method has the following advantages most existing methods must undersmooth the nonparametric link function estimator to achieve a faster rate of consistency for the estimator of the parameters than for that of the nonparametric function in contrast a faster consistency rate can be achieved by the mave method even without undersmoothing the nonparametric link function estimator the mave method is applicable to a wide range of models with fewer restrictions on the distribution of the covariates to the extent that even time series can be included because of the faster rate of consistency for the parameter estimators it is possible for us to estimate the dimension of the space consistently the relationship of the mave method with other methods is also investigated in particular a simple outer product gradient estimator is proposed as an initial estimator in addition to theoretical results we demonstrate the efficacy of the mave method for high dimensional data sets through simulation two real data sets are analysed by using the mave approach

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

limited information estimators and exogeneity tests for simultaneous probit models a two step maximum likelihood procedure is proposed for estimating simultaneous probit models and is compared to alternative limited information estimators conditions under which each estimator attains the cramer rao lower bound are obtained simple tests for exogeneity based on the new two step estimator are proposed and are shown to be asymptotically equivalent to one another and to have the same local asymptotic power as classical tests based on the limited information maximum likelihood estimator finite sample comparisons between the new and alternative estimators are presented based on some monte carlo evidence the performance of the proposed tests for exogeneity is also assessed

global stability of adaptive pole placement algorithms this paper presents direct and indirect adaptive control schemes for assigning the closed loop poles of a single input single output system in both the continuous and discrete time cases the resulting closed loop system is shown to be globally stable when driven by an external reference signal consisting of a sum of sinusoids in particular persistent excitation of the potentially unbounded closed loop input output data and hence convergence of a sequential least squares identification algorithm is proved the results are applicable to standard sequential least squares and least squares with covariance reset

quantile regression with censoring and endogeneity in this paper we develop a new censored quantile instrumental variable cqiv estimator and describe its properties and computation the cqiv estimator combines powell 1986 censored quantile regression cqr to deal with censoring with a control variable approach to incorporate endogenous regressors the cqiv estimator is obtained in two stages that are nonadditive in the unobservables the first stage estimates a nonadditive model with infinite dimensional parameters for the control variable such as a quantile or distribution regression model the second stage estimates a nonadditive censored quantile regression model for the response variable of interest including the estimated control variable to deal with endogeneity for computation we extend the algorithm for cqr developed by chernozhukov and hong 2002 to incorporate the estimation of the control variable we give generic regularity conditions for asymptotic normality of the cqiv estimator and for the validity of resampling methods to approximate its asymptotic distribution we verify these conditions for quantile and distribution regression estimation of the control variable our analysis covers two stage uncensored quantile regression with nonadditive first stage as an important special case we illustrate the computation and applicability of the cqiv estimator with a monte carlo numerical example and an empirical application on estimation of engel curves for alcohol

distributed output regulation of nonlinear multi agent systems via host internal model this note presents a host internal model h im approach to distributed output regulation of reaching nonlinear leader following consensus focusing on a basic nonlinear scenario of identical or homogeneous agents of a normal form it is shown that the problem is solvable as long as its interaction digraph contains a certain directed spanning tree a constructive lyapunov protocol is proposed by incorporating a single h im the result is also demonstrated by fitzhugh nagumo fhn and lorenz type nonlinear dynamic networks

identification of binary response models abstract this article studies identification of the threshold crossing model of binary response most research on binary response has considered specific estimators and tests the study of identification exposes the foundations of binary response analysis by making explicit the assumptions needed to justify different methods it also clarifies the connections between reduced form and structural analyses of binary response data assume that the binary outcome z is determined by an observable random vector x and by an unobservable scalar u through a model z 1 x u 0 also assume that fu x the probability distribution of u conditional on x is continuous and strictly increasing given these maintained assumptions we investigate the identifiability of given the following restrictions on the distributions fu x x x mean independence quantile independence index sufficiency statistical independence and statistical independence with the distribution known we find that mean independence has n

on adaptive state regulation an indirect adaptive state regulator consisting of an adaptive observer and an asymptotic feedback matrix synthesis is discussed in a rigorous analysis lyapunov stability of the resulting closed loop system without the need for external excitation possible global instabilities as well as global convergence subject to sufficient excitation are shown moreover the behavior of the closed loop system is analyzed for cases in which the true plant differs from the assumed linear time invariant model in that it is of higher order contains slight nonlinearities and time variation effects and is subject to plant and measurement disturbances

adaptive synchronization for generalized lorenz systems in literature it is conjectured that the states of the generalized lorenz system with an unknown parameter can not be estimated by adaptive observers in this paper we show that this unknown parameter and the states can actually be estimated simultaneously by some kind of adaptive observer the proof is obtained by constructing some exponential observer to achieve chaotic synchronization for the generalized lorenz system the result implies that more work needs to be done to apply generalized lorenz system in secure communication

optimal smoothing in single index models single index models generalize linear regression they have applications to a variety of fields such as discrete choice analysis in econometrics and dose response models in biometrics where high dimensional regression models are often employed single index models are similar to the first step of projection pursuit regression a dimension reduction method in both cases the orientation vector can be estimated root n consistently even if the unknown univariate function or nonparametric link function is assumed to come from a large smoothness class however as we show in the present paper the similarities end there in particular the amount of smoothing necessary for root n consistent orientation estimation is very different in the two cases we suggest a simple empirical rule for selecting the bandwidth appropriate to single index models this rule is studied in a small simulation study and an application in binary response models

estimation of marginal effects in semiparametric selection models with binary outcomes this paper addresses the estimation of a semiparametric sample selection index model where both the selection rule and the outcome variable are binary since the marginal effects are often of primary interest and are difficult to recover in a semiparametric setting we focus on developing an estimator for the marginal effects this marginal effect estimator uses only observations where the selection probability is above a certain threshold a key innovation is that this high probability set is adaptive to the data we establish the large sample properties of the marginal effect estimator as well as those for an index estimator upon which it depends monte carlo studies show that these estimators perform well in finite samples

local asymptotic stability via averaging for time varying systems with unbounded dynamics with respect to time the purpose of this note is to provide sufficient conditions for asymptotic stability for time varying systems whose dynamics are unbounded with respect to time an averaging approach is established that constitutes a generalization of the well known methodology adopted in the literature for systems whose dynamics are bounded with respect to time

semiparametric estimation of binary response models with endogenous regressors abstract in this paper we propose a two step semiparametric maximum likelihood sml estimator for the coefficients of a single index binary choice model with endogenous regressors when identification is achieved via a control function approach the first step consists of estimating a reduced form equation for the endogenous regressors and extracting the corresponding residuals in the second step the latter are added as control variates to the outcome equation which is in turn estimated by sml we establish the estimator s n consistency and asymptotic normality in a simulation study we compare the properties of our estimator with those of existing alternatives highlighting the advantages of our approach

persistence of excitation conditions and the convergence of adaptive schemes in the study of the behavior of adaptive filtering algorithms persistence of excitation of the input process arises as a sufficient condition for convergence and perhaps more importantly for convergence rate of the parameter estimates in this paper the underlying nature of the persistence requirement is presented and discussed relating its normal specification in terms of moment conditions with covariance decays etc to sample path properties deterministic and stochastic persistence conditions and persistence measures are treated as well as persistence conditions for output error equation error and adaptive control schemes

on the average number of real roots of a random algebraic equation on donne un estimateur du nombre espere d instants ou le polynome prend la valeur reelle k k n etant pas forcement nul

endogeneity in quantile regression models a control function approach this paper considers a linear triangular simultaneous equations model with conditional quantile restrictions the paper adjusts for endogeneity by adopting a control function approach and presents a simple two step estimator that exploits the partially linear structure of the model the first step consists of estimation of the residuals of the reduced form equation for the endogenous explanatory variable the second step is series estimation of the primary equation with the reduced form residual included nonparametrically as an additional explanatory variable this paper imposes no functional form restrictions on the stochastic relationship between the reduced form residual and the disturbance term in the primary equation conditional on observable explanatory variables the paper presents regularity conditions for consistency and asymptotic normality of the two step estimator in addition the paper provides some discussions on related estimation methods in the literature and on possible extensions and limitations of the estimation approach finally the numerical performance and usefulness of the estimator are illustrated by the results of monte carlo experiments and two empirical examples demand for fish and returns to schooling

fast extremum seeking on hammerstein plants partial plant knowledge may be used to develop model based extremum seekers however existing results rely on a type of time scale separation which leads to slow optimization relative to the plant dynamics in this work a fast model based extremum seeking scheme is proposed for a hammerstein plant and semi global stability results are provided the structure of a hammerstein plant is used to advantage in designing filters that enable the extremum seeker to act on a faster time scale than the plant dynamics this leads to fast convergence while maintaining semi global stability

conditions of parameter identification from time series we study the problem of synchronization based parameters identification of dynamical systems from time series through theoretical analysis and numerical examples we show that some recent research reports on this issue are not perfect or even incorrect long time full rank and finite time full rank conditions of gram matrix are pointed out which are sufficient for parameters identification of dynamical systems the influence of additive noise on the proposed parameter identifier is also investigated the mean filter is used to suppress the estimation fluctuation caused by the noise

adaptive observer for continuous descriptor systems we design an adaptive observer for a stable single input and single output continuous descriptor generalized state space or singular system under the assumption that the descriptor system is observable it is transformed into what we call descriptor observer canonical form this form also allows the descriptor variable to be represented by a linear combination of the 2n unknown parameters and the filtered input and output measurement we also show that the estimates converge to the true values when the bounded input satisfies the richness condition under the assumption that the system is controllable

censored regression quantiles with endogenous regressors this paper develops a semiparametric method for estimation of the censored regression model when some of the regressors are endogenous and continuously distributed and instrumental variables are available for them a distributional exclusion restriction is imposed on the unobservable errors whose conditional distribution is assumed to depend on the regressors and instruments only through a lower dimensional control variable here assumed to be the difference between the endogenous regressors and their conditional expectations given the instruments this assumption which implies a similar exclusion restriction for the conditional quantiles of the censored dependent variable is used to motivate a two stage estimator of the censored regression coefficients in the first stage the conditional quantile of the dependent variable given the instruments and the regressors is nonparametrically estimated as are the first stage reduced form residuals to be used as control variables the second stage estimator is a weighted least squares regression of pairwise differences in the estimated quantiles on the corresponding differences in regressors using only pairs of observations for which both estimated quantiles are positive i e in the uncensored region and the corresponding difference in estimated control variables is small the paper gives the form of the asymptotic distribution for the proposed estimator and discusses how it compares to similar estimators for alternative models

a comparison of higher order bias kernel density estimators abstract we consider many kernel based density estimators all theoretically improving bias from o h 2 as the smoothing parameter h 0 to o h 4 examples include higher order kernels variable kernel methods and transformation and multiplicative bias correction approaches we stress the similarities between what appear to be disparate approaches in particular we show how the mean squared errors of all methods have the same form our main practical contribution is a comparative simulation study that isolates the most promising approaches it remains debatable however as to whether even the best methods give worthwhile improvements at least for small to moderate sample exploratory purposes

on the number of real solutions of a random polynomial n it is known that the expected number of real zeros of p x is asymptotic to 2 r logn as n tends to infinity the expected number of real solutions of the equation pn x k or k level crossings of pn x where k ranges through a sequence k n such that k2n n o as n ec is also known the objective of this paper is to generalize the known results in two directions we relax the normality assumption for the coefficients by considering a general distribution with finite or infinite variance and obtain the result for the number of solutions of p x kn rather than its expected number the trade off is to obtain bounds fairly narrow for this number rather than the asymptotic value derived for the expected number of solutions in the normal case denote any positive absolute constant value not necessarily the same at each occurrence by c we summarize our results in the following four theorems 3 be the third absolute moment of aj 2 be the variance and j theorem 1 let r j and

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

identification in nonseparable models weak nonparametric restrictions are developed sufficient to identify the values of derivatives of structural functions in which latent random variables are nonseparable these derivatives can exhibit stochastic variation in a microeconometric context this allows the impact of a policy intervention as measured by the value of a structural derivative to vary across people who are identical as measured by covariates when the restrictions are satisfied quantiles of the distribution of a policy impact across people can be identified the identification restrictions are local in the sense that they are specific to the values of the covariates and the specific quantiles of latent variables at which identification is sought the conditions do not include the commonly required independence of latent variables and covariates they include local versions of the classical rank and order conditions and local quantile insensitivity conditions values of structural derivatives are identified by functionals of quantile regression functions and can be estimated using the same functionals applied to estimated quantile regression functions

persistency of excitation in the presence of possibly unbounded signals this note develops an explicit characterization of the concept of persistency of excitation for time invariant linear systems in the presence of possibly unbounded signals this result can be used to establish exponential convergence for a range of adaptive control algorithms a feature of our proof is a particular technique for dealing with the initial condition response

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

a discontinuity test for identification in triangular nonseparable models this paper presents a test for the validity of control variable approaches to identification in triangular nonseparable models assumptions commonly imposed to justify such methods include full independence of instruments and disturbances and existence of a reduced form that is strictly monotonic in a scalar disturbance we show that if the data has a particular structure namely that the distribution of the endogenous variable has a mass point at the lower or upper boundary of its support validity of the control variable approach implies a continuity condition on an identified function which can be tested empirically

uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing a new uniform expansion is introduced for sums of weighted kernel based regression residuals from nonparametric or semiparametric models this result is useful for deriving asymptotic properties of semiparametric estimators and test statistics with data dependent bandwidth random trimming and estimated weights an extension allows for generated regressors without requiring the calculation of functional derivatives example applications are provided for a binary choice model with selection including a new semiparametric maximum likelihood estimator and a new directional test for correct specification of the average structural function a supplement contains general results on uniform rates for kernel estimators additional applications and primitive sufficient conditions for high level assumptions

how many zeros of a random polynomial are real we provide an elementary geometric derivation of the kac integral formula for the expected number of real zeros of a random polynomial with independent standard normally distributed coefficients we show that the expected number of real zeros is simply the length of the moment curve 1 t tn projected onto the surface of the unit sphere divided by the probability density of the real zeros is proportional to how fast this curve is traced out we then relax kac s assumptions by considering a variety of random sums series and distributions and we also illustrate such ideas as integral geometry and the fubini study metric

stable model reference adaptive control in the presence of bounded disturbances the adaptive control of a linear time invariant plant in the presence of bounded disturbances is considered in addition to the usual assumptions made regarding the plant transfer function it is also assumed that the high frequency gain k p of the plant and an upper bound on the magnitude of the controller parameters are known under these conditions the adaptive controller suggested assures the boundedness of all signals in the overall system

uniform global asymptotic stability of adaptive cascaded nonlinear systems with unknown high frequency gains abstract we study adaptive tracking problems for nonlinear systems with unknown control gains we construct controllers that yield uniform global asymptotic stability for the error dynamics and hence tracking and parameter estimation for the original systems our result is based on a new explicit global strict lyapunov function construction we illustrate our work using a brushless dc motor turning a mechanical load we quantify the effects of time varying uncertainties on the motor electric parameters

semiparametric maximum likelihood estimation of polychotomous and sequential choice models abstract this article considers semiparametric estimation of discrete choice models the estimation method is a semiparametric maximum likelihood method which generalizes klein and spady 1993 to the estimation of polychotomous choice and sequential choice models special emphasis is on the estimation of models with indices of which the density function is not bounded away from zero issues on trimming indices the correction of asymptotic bias and issues of negative kernel density estimation a semiparametric efficiency bound is derived for the polychotomous choice model with index restrictions our estimator is shown to be n consistent asymptotically normal and almost asymptotically efficient monte carlo experiments are provided to evaluate the finite sample performance of the estimator

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

stability and robustness properties of a simple adaptive controller a low order adaptive tracking controller is proposed for linear time invariant plants with a relative degree not exceeding two the order of the plant is not required to be known a priori the algorithm is robustly stable with respect to small linear time invariant plant perturbations and bounded disturbances the robustness is achieved by using a projection of the parameter estimates in the control law an additional a priori information needed to design the controller is bounds on the plant parameters in the absence of plant perturbations and disturbances perfect tracking is obtained

on adaptive observers for state affine systems in this paper the problem of adaptive observer design for the class of state affine systems is discussed the discussion is based on recent results on adaptive observer with exponential rate of convergence obtained for multi input multi output linear time varying systems on the one hand and the well known kalman like design for state affine systems on the other in particular the relationship between both designs is emphasized showing how they can even be equivalent the interest of such an adaptive observer for state affine systems is illustrated by the example of state and parameter estimation for the lorenz chaotic system the observer performances are illustrated via simulation

persistent excitation in adaptive systems the importance of the concept of persistent excitation pe in adaptive identification and control has been recognized for some time recently it has become evident that it also plays a central role in many questions related to the robustness of adaptive systems there is every reason to believe that arguments involving this concept will continue to feature prominently in the analysis of most of the important problems of adaptive control hence there is a real need for a deeper understanding of the concept the paper is written with three objectives the first which is tutorial in nature is to provide a general framework for the discussion of persistent excitation and to collect results in the area which are scattered throughout the adaptive literature the second objective is to present some new results related to the uniform asymptotic stability u a s and robustness of adaptive systems and the relation of pe to the stability properties of a class of non linear systems the final objective is to di

brief strict lyapunov functions for time varying systems uniformly asymptotically stable periodic time varying systems for which is known a lyapunov function with a derivative along the trajectories non positive and negative definite in the state variable on non empty open intervals of the time are considered for these systems strict lyapunov functions are constructed

on independence conditions in nonseparable models observable and unobservable instruments this paper develops identification results employing independence conditions among unobservable variables the independence conditions are used to derive first stage nonseparable reduced form functions once constructed these reduced form functions are employed to express the derivatives of nonseparable structural functions in terms of the derivatives of the reduced form functions for models with simultaneity we obtain the new results by combining the independence assumptions together with parametric specifications and exclusion restrictions for models with triangularity we allow all functions to be nonparametric and nonseparable in unobservable random terms for the latter we provide several equivalence results and discuss some of the trade offs between observable and unobservable instruments

on the expected number of level crossings of a random polynomial there are many known asymptotic estimates for the expected number ofk level crossings of an algebraic polynomiala0 a1x a2x2 anxnwith normally distributed coefficients the present paper provides the estimate for the expected number of such level crossings when the coefficients are independent identically cauchy distributed random variables using a numerical approach we show that in the interval 1 1 by increasingkthe number ofk level crossings decreases while outside this interval this number is invariant as long ask o n since the cauchy distribution does not belong to the wide class of distributions of domain of attraction of the normal law the polynomials with cauchy distributed coefficients are interesting as they indicate the behaviour of polynomials for distribution outside this class