nonparametric least squares estimation of a multivariate convex regression function this paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional we characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided we also consider a regression function which is known to be convex and componentwise nonincreasing and discuss the characterization computation and consistency of its least squares estimator

realisation and estimation of piecewise linear output error models piecewise linear systems in input output form can have different switching schedules in this article two categories instant and delayed switching are analysed even though a general piecewise linear state space model cannot be converted into input output form it is shown that it is possible to find state space models representing instant and delayed switching in addition a prediction error minimisation pem method for piecewise linear output error predictors is derived and it is concluded that the instant switching model candidate is not necessarily the most suitable for the parameter estimation procedure

smooth models of quiver moduli for any moduli space of stable representations of quivers certain smooth varieties compactifying projective space fibrations over the moduli space are constructed the boundary of this compactification is analyzed explicit formulas for the betti numbers of the smooth models are derived in the case of moduli of simple representations explicit cell decompositions of the smooth models are constructed

nonparametric identification and estimation of polychotomous choice models abstract in this paper we provide conditions guaranteeing the identification of nonparametric polychotomous choice models in these models neither the subutility function of observable attributes nor the distribution of the unobservable random terms is specified parametrically sets of nonparametric functions that possess properties that are often implied by economic theory and satisfy the restrictions required to identify the models are described we use the identification results to develop nonparametric strongly consistent estimators for the subutility function of observable attributes the results concern models in which the distribution of the unobservable random terms both depend and do not depend on the observable characteristics

breaking the curse of dimensionality in conditional moment inequalities for discrete choice models abstract this paper studies inference of preference parameters in semiparametric discrete choice models when these parameters are not point identified and the identified set is characterized by a class of conditional moment inequalities exploring the semiparametric modeling restrictions we show that the identified set can be equivalently formulated by moment inequalities conditional on only two continuous indexing variables such formulation holds regardless of the covariate dimension thereby breaking the curse of dimensionality for nonparametric inference based on the underlying conditional moment inequalities we further apply this dimension reducing characterization approach to the monotone single index model and to a variety of semiparametric models under which the sign of conditional expectation of a certain transformation of the outcome is the same as that of the indexing variable

piecewise linear identification for the rate independent and rate dependent duhem hysteresis models we consider the semilinear duhem model and develop an identification method for rate independent and rate dependent hysteresis for rate independent hysteresis we reparameterize the system in terms of the input signal so that the system has the form of a switching linear time invariant system with ramp plus step forcing for rate dependent hysteresis the system can be viewed as a switching linear time invariant system for triangle wave inputs least squares based methods are developed to identify the rate independent and rate dependent semilinear duhem models

stabilizing controllers for bilinear systems the problem of finding stabilizing feedback controllers for continuous bilinear systems where the controls act additively and multiplicatively simultaneously is treated the applicability of the quadratic control law of jacobson 5 and others is extended to the case when the a matrix has arbitary eigenvalues under certain conditions a class of bilinear systems common among biochemical flow systems is defined the dyadic bilinear systems a control scheme the so called division controller for dyadic bilinear systems is suggested the practicality of the control schemes is demonstrated on the problem of controlling the neutron level in a fission reactor

a smoothed maximum score estimator for the binary response model this paper describes a semiparametric estimator for binary response models in which there may be arbitrary heteroskedasticity of unknown form the estimator is obtained by maximizing a smoothed version of the objective function of c manski s maximum score estimator the smoothing procedure is similar to that used in kernel nonparametric density estimation the resulting estimator s rate of convergence in probability is the fastest possible under the assumptions that are made the centered normalized estimator is asymptotically normally distributed methods are given for consistently estimating the parameters of the limiting distribution and for selecting the bandwidth required by the smoothing procedure copyright 1992 by the econometric society

classifying representations by way of grassmannians let a be a finite dimensional algebra over an algebraically closed field criteria are given which characterize existence of a fine or coarse moduli space classifying up to isomorphism the representations of a with fixed dimension d and fixed squarefree top t next to providing a complete theoretical picture some of these equivalent conditions are readily checkable from quiver and relations of a in the case of existence of a moduli space unexpectedly frequent in light of the stringency of fine classification this space is always projective and in fact arises as a closed subvariety brassy of a classical grassmannian even when the full moduli problem fails to be solvable the variety grass t d is seen to have distinctive properties recommending it as a substitute for a moduli space as an application a characterization of the algebras having only finitely many representations with fixed simple top is obtained in this case of finite local representation type at a given simple t the radical layering j l m j l 1 m l 0 is shown to be a classifying invariant for the modules with top t this relies on the following general fact obtained as a byproduct proper degenerations of a local module m never have the same radical layering as m

nonparametric and distribution free estimation of the binary threshold crossing and the binary choice models in this paper it is shown that it is possible to identify binary threshold crossing models and binary choice models without imposing any parametric structure either on the systematic function of observable exogenous variables or on the distribution of the random term this identification result is employed to develop a fully nonparametric maximum likelihood estimator for both the function of observable exogenous variables and the distribution of the random term the estimator is shown to be strongly consistent and a two step procedure for its calculation is developed the paper also includes examples of economic models that satisfy the conditions that are necessary to apply the results

brief fast approximate identification of nonlinear systems in this paper a method is presented to extend the classical identification methods for linear systems towards nonlinear modelling of linear systems that suffer from nonlinear distortions a well chosen general nonlinear model structure is proposed that is identified in a two step procedure first a best linear approximation is identified using the classical linear identification methods in the second step the nonlinear extensions are identified with a linear least squares method the proposed model not only includes wiener and hammerstein systems it is also suitable to model nonlinear feedback systems the stability of the nonlinear model can be easily verified the method is illustrated on experimental data

observability and controllability of piecewise affine and hybrid systems we prove in a constructive way the equivalence between piecewise affine systems and a broad class of hybrid systems described by interacting linear dynamics automata and propositional logic by focusing our investigation on the former class we show through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems instead we propose practical numerical tests based on mixed integer linear programming

distribution free maximum likelihood estimator of the binary choice model1 is a given function of the exogenous variables z and unknown parameters 9 representing the systematic component of the utility difference and f is the distribution function of the random component of the utility difference this paper describes a method of estimating the parameters 9 without assuming any functional form for the distribution function f and proves that this estimator is consistent f is also consistently estimated the method uses maximum likelihood estimation in which the likelihood is maximized not only over the parameter 9 but also over a space which contains all distribution functions

on the discretization of single input single output bilinear systems prompted by the observation that the parameters of a discrete bilinear model structure corresponding to a time invariant continuous bilinear model structure are input dependent quantities this paper deduces a correction factor that relates the continuous and discrete time models the correction factor that is obtained analytically is shown to provide an exact discretization an approximation to the correction factor is also included which produces a satisfactory discretization provided realistic bounds are placed on the choice of the sampling interval building on the developed approach for discretizing a first order bilinear system the procedure is extended to the case of higher order systems the new approach differs from existing schemes in that a discrete time bilinear model structure is retained with consideration given to a first order model of a high temperature furnace application it is shown that the resulting parameter variation is significantly reduced when a bilinear model structure is re

irreducible components of varieties of representations the acyclic case the goals of this article are as follows 1 to determine the irreducible components of the affine varieties mathbf rep mathbf d lambda parametrizing the representations with dimension vector mathbf d where lambda traces a major class of finite dimensional algebras 2 to generically describe the representations encoded by the components the target class consists of those truncated path algebras lambda over an algebraically closed field k which are based on a quiver q without oriented cycles the main result characterizes the irreducible components of mathbf rep mathbf d lambda in representation theoretic terms and provides a means of listing them from quiver and loewy length of lambda combined with existing theory this classification moreover yields an array of generic features of the modules parametrized by the components such as generic minimal projective presentations generic sub and quotient modules etc our second principal result pins down the generic socle series of the modules in the components it does so for more general lambda in fact the information on truncated path algebras of acyclic quivers supplements the theory available in the special case where lambda kq filling in generic data on the mathbf d dimensional representations of q with any fixed loewy length

top stable degenerations of finite dimensional representations ii abstract let be a finite dimensional algebra over an algebraically closed field we exhibit slices of the representation theory of that are always classifiable in stringent geometric terms namely we prove that for any semisimple object t mod the class of those modules with fixed dimension vector say d and top t which do not permit any proper top stable degenerations possesses a fine moduli space this moduli space modulimax d t is a projective variety despite classifiability up to isomorphism the targeted collections of modules are representation theoretically rich indeed any projective variety arises as modulimax d t for suitable choices of d and t in tandem we give a structural characterization of the finite dimensional representations that have no proper top stable degenerations

non parametric analysis of a generalized regression model the maximum rank correlation estimator the paper considers estimation of a model yi d f x i 0 ui where the composite transformation d f is only specified that d r r is non degenerate monotonic and f r2 r is strictly monotonic in each of its variables the paper thus generalizes standard data analysis which assumes that the functional form of d f is known and additive the estimator which it proposes is the maximum rank correlation estimator which is non parametric in the functional form of d f and non parametric in the distribution of the error terms ui the estimator is shown to be strongly consistent for the parameters 0 up to a scale coefficient

application of multi level signals to the identification of direction dependent processes theoretical results for the output and the input output crosscorrelation function are derived for first order direction dependent processes perturbed using pseudo random maximum length ternary mlt signals with unsymmetrical signal levels the analytical results are valid if the process output is either always increasing or always decreasing when the input is at its median level of zero it is shown that although this is not normally the case for the whole of the signal period good approximations to the analytical results are obtained when it is the case for most of the signal period as can be achieved with a suitable choice of signal levels mlt signals with unequal spacing between signal levels can also be used to minimise the nonlinear distortion this is equivalent to compensating for the direction dependent behaviour of the system by preceding it with a static nonlinearity based on the theoretical and simulation results obtained a novel technique is proposed to allow the best linear approximation of the process to be estimated from the ratio between the amount of time when the output increases to that when it decreases the proposed method is shown to be applicable even when the number of signal levels is greater than three and is less susceptible to the effects of noise than the method of correlation analysis and least squares

limit cycles with chattering in relay feedback systems relay feedback has a large variety of applications in control engineering several interesting phenomena occur in simple relay systems in the paper scalar linear systems with relay feedback are analyzed it is shown that a limit cycle where part of the limit cycle consists of fast relay switchings can occur this chattering is analyzed in detail and conditions for approximating it by a sliding mode are derived a result on existence of limit cycles with chattering is given and it is shown that the limit cycles can have arbitrarily many relay switchings each period limit cycles with regular sliding modes are also discussed examples illustrate the results

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

semiparametric identification and heterogeneity in discrete choice dynamic programming models abstract empirical discrete choice dynamic programming models have become important empirical tools a question that arises in estimation and interpretation of the results from these specifications is which combination of data and assumptions are needed to overcome problems of heterogeneity selection and omited variables bias this paper addresses this question by considering nonparametric identification of a version of the model that allows for quite general forms of unobservable and information structures i show that the model can be identified under conditions similar to a static polychotomous choice model using a stochastic version of an identification of infinity argument utility can be identified up to a monotonic transformation of the observables under strong support conditions and two types of exclusion restriction the first type is similar to a standard static exclusion restriction a variable that influences the first period decision but does not enter the second period decision directly the second type requires a variable that does not affect the utility of the first option directly but is known during the first period and has predictive power on the choice during the second i also provide two specifications under which the full error structure can be identified this requires the additional assumption of stochastic innovations in the observables i then use the model to estimate schooling decisions in which students deciding whether to drop out of high school account for the option value of attending college

on degenerations and extensions of finite dimensional modules abstract we derive a cancellation theorem for degenerations of modules that says in particular that projective or injective common direct summands can always be neglected combining the cancellation result with the existence of almost split sequences we characterize the orbit closure of a module living on preprojective components by the fact that the dimension of the homomorphism space to any other module does not decrease for representation directed algebras whence in particular for path algebras of dynkin quivers we provide an alternative proof which shows in addition that any minimal degenerationnofmcomes from an exact sequence with middle termmwhose end terms add up ton by a careful examination the same is true for degenerations of matrix pencils having used so far the existence of certain extensions to obtain degenerations we then turn the tables and use degenerations to produce a lot of interesting short exact sequences in particular we show that any non simple indecomposable over a tame quiver is an extension of an indecomposable and a simple

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

semiparametric estimation of monotone and concace utility functions for polychotomous choice models this paper introduces a semiparametric estimation method for polychotomous choice models the method does not require a parametric structure for the systematic subutility of observable exogenous variables the distribution of the random terms is assumed to be known up to a finite dimensional parameter vector in contrast previous semiparametric methods of estimating discrete choice models have concentrated on relaxing parametric subutility parametrically specified the systematic subutility is assumed to possess properties such as monotonicity and concavity that are typically assumed in microeconomic theory the estimator for the systematic subutility and the parameter vector of the distribution is shown to be strongly consistent a computational technique to calculate the estimators is developed copyright 1991 by the econometric society

semiparametric estimation of a simultaneous game with incomplete information abstract this paper studies the problem of estimating the normal form payoff parameters of a simultaneous discrete game where the realization of such payoffs is not common knowledge the paper contributes to the existing literature in two ways first by making a comparison with the complete information case it formally describes a set of conditions under which allowing for private information in payoffs facilitates the identification of various features of the game second focusing on the incomplete information case it presents an estimation procedure based on the equilibrium properties of the game that relies on weak semiparametric assumptions and relatively flexible information structures which allow players to condition their beliefs on signals whose exact distribution function is unknown to the researcher the proposed estimators recover unobserved beliefs by solving a semiparametric sample analog of the population bayesian nash equilibrium conditions the asymptotic features of such estimators are studied for the case in which the distribution of unobserved shocks is known and the case in which it is unknown in both instances equilibrium uniqueness is assumed to hold only in a neighborhood of the true parameter value and for a subset z of realizations of the signals multiple equilibria are allowed elsewhere in the parameter space and no equilibrium selection theory is involved extensions to games where beliefs are conditioned on unobservables as well as general games with many players and actions are also discussed an empirical application of a simple capital investment game is included

identifying effects of multivalued treatments multivalued treatment models have typically been studied under restrictive assumptions ordered choice and more recently unordered monotonicity we show how treatment effects can be identified in a more general class of models that allows for multidimensional unobserved heterogeneity our results rely on two main assumptions treatment assignment must be a measurable function of threshold crossing rules and enough continuous instruments must be available we illustrate our approach for several classes of models

identification of piecewise affine systems via mixed integer programming this paper addresses the problem of identification of hybrid dynamical systems by focusing the attention on hinging hyperplanes and wiener piecewise affine autoregressive exogenous models in which the regressor space is partitioned into polyhedra with affine submodels for each polyhedron in particular we provide algorithms based on mixed integer linear or quadratic programming which are guaranteed to converge to a global optimum for the special case where the estimation data only seldom switches between the different submodels we also suggest a way of trading off between optimality and complexity by using a change detection approach

piecewise linear identification of non linear systems methods of identifying a series of piecewise linear models which approximate to a non linear system over some operating range are investigated spatial linear models and models with signal dependent parameters are considered

jump linear quadratic regulator with controlled jump rates deals with the class of continuous time linear systems with markovian jumps we assume that jump rates are controlled our purpose is to study the jump linear quadratic jlq regulator of the class of systems the structure of the optimal controller is established for a one dimensional 1 d system an algorithm for solving the corresponding set of coupled riccati equations of this optimal control problem is provided two numerical examples are given to show the usefulness of our results

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

semiparametric analysis of discrete response asymptotic properties of the maximum score estimator abstract this paper is concerned with the estimation of the model med y x x from a random sample of observations on sgn y x manski 1975 introduced the maximum score estimator of the normalized parameter vector in the present paper strong consistency is proved it is also proved that the maximum score estimate lies outside any fixed neighborhood of with probability that goes to zero at exponential rate

stability for an abelian category abstract the main goal of the article is to give the definition of algebraic stability that would permit us to consider stability not only for algebraic vector bundles or torsion free coherent sheaves but for the abelian category of coherent sheaves or for whatever abelian category we present an axiomatic description of the algebraic stability on an abelian category and prove some general results then the stability for coherent sheaves on a projective variety is constructed which generalizes gieseker stability stabilities for graded modules and for quiver representations are also discussed the constructions could be used for other abelian categories as well

stabilization of nonholonomic integrators via logic based switching this paper explains how to stabilize a nonholonomic integrator using a hybrid control law employing switching and logic results concerning asymptotic stability and exponential convergence to the origin are derived the notion of a positively invariant set is extended to hybrid systems and sufficient conditions for invariance are presented the verification of these conditions does not require the computation of the state trajectories and their use goes beyond the analysis of the system presented in this paper

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

brief wiener models of direction dependent dynamic systems analysis of systems with direction dependent dynamics is currently limited to cases in which the dynamics in the two directions of the output are first order results for such systems have been published for both pseudo random maximum length binary mlb and inverse repeat maximum length binary ir mlb inputs these relatively limited analytical results make it useful to examine alternative ways of modelling such systems and in this paper wiener models are considered for this purpose methods for optimising the wiener model parameters by matching the system and model cross correlation functions outputs and discrete fourier transforms of the outputs are considered and the results are compared these methods are also applied to a first order direction dependent system with a maximum length ternary mlt input for which no analytical results are currently available and to a second order system with an ir mlb input

survey paper direction dependent systems a survey in this paper a survey on systems which exhibit gains and or dynamics depending on the input or output direction is presented several examples of such systems covering a wide range of application areas and the causes of their direction dependent responses are given direction dependent systems are mathematically classified into three classes depending on their state space representation and switching function the related linear dynamic transient and steady state characteristics of these systems are investigated approaches to model direction dependent systems using wiener models piecewise linear models bilinear models and recurrent neural networks are described three application examples are used to illustrate the usefulness of the direction dependent description the advantages and disadvantages of direction dependent models as well as possible directions for future work are pointed out

identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity we extend the identification results for nonparametric simultaneous equations models in matzkin 2008 to situations where the observations on the vector of dependent variables might be limited and where the number of exogenous unobservable variables is larger than the number of dependent variables