three component nonlinear dynamical system generated by the new third order discrete spectral problem we propose a nonlinear model on a regular infinite one dimensional lattice it describes the three component dynamical system with modulated on site masses and is shown to admit a zero curvature representation the associated auxiliary spectral problem is basically of third order and gives rise to fairly complicated subdivision into domains of regularity of jost functions in the plane of complex spectral parameter as a result both the direct and the inverse scattering problems turn out to be substantially nontrivial the caudrey version of the direct and inverse scattering technique for the needs of model integration is adapted the simplest soliton solution is found

instrumental variable estimation of nonlinear models with nonclassical measurement error using control variables we consider nonlinear models with an independent variable that is measured with error the measurement error can be correlated with the true value i e the measurement error is allowed to be nonclassical we show that we can use a control variate estimator to estimate the parameters of interest if we are prepared to make an assumption of the joint distribution of the rst stage

backlund transformations as exact integrable time discretizations for the trigonometric gaudin model we construct a two parameter family of backlund transformations for the trigonometric classical gaudin magnet the approach follows closely the one introduced by sklyanin and kuznetsov 1998 j phys a math gen 31 2241 51 in a number of seminal papers and takes advantage of the intimate relation between the trigonometric and the rational case as in the paper by hone kuznetsov and one of the authors or 2001 j phys a math gen 34 2477 90 the backlund transformations are presented as explicit symplectic maps starting from their lax representation the expected connection with the xxz heisenberg chain is established and the rational xxx case is recovered in a suitable limit it is shown how to obtain a physical transformation mapping real variables into real variables the interpolating hamiltonian flow is derived and some numerical iterations of the map are presented

discrete integrable systems and deformations of associative algebras interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed theory of deformations for associative algebras is presented closed left ideal generated by the elements representing the multiplication table plays a central role in this theory deformations of the structure constants are generated by the deformation driving algebra and governed by the central system of equations it is demonstrated that many discrete equations such as discrete boussinesq equation discrete wdvv equation discrete schwarzian kp and bkp equations discrete hirota miwa equations for kp and bkp hierarchies are particular realizations of the central system an interaction between the theories of discrete integrable systems and discrete deformations of associative algebras is reciprocal and fruitful an interpretation of the menelaus relation discrete schwarzian kp equation discrete hirota miwa equation for kp hierarchy consistency around the cube as the associativity conditions and the concept of gauge equivalence for instance between the menelaus and kp configurations are particular examples

superposition principles associated with the moutard transformation an integrable discretization of a 2 1 dimensional sine gordon system superposition principles both linear and nonlinear associated with the moutard transformation are found on suitable reinterpretation these constitute an integrable discrete nonlinear system and its associated linear system further it is shown that in a particular form this system is an integrable discretization of a 2 1 dimensional sine gordon system solutions of the discrete nonlinear system are constructed by means of a discrete analogue of the moutard transformation included in these solutions are discrete analogues of the kink solutions of the continuous system

unobserved heterogeneity in auctions under restricted stochastic dominance abstract we study the identification of first price auctions with nonseparable unobserved heterogeneity in particular we extend hu et al 2013 by relaxing the first order stochastic dominance condition instead we assume restricted stochastic dominance relations among value quantile functions and show that the same relations pass to bid quantile functions an ordered tree summarizes these relations and provides a total ordering relying on the proposed restricted stochastic dominance ordering we extend a list of identification results in the empirical auction literature

identification of complete information games this paper establishes sufficient conditions for point identification of the utility functions in generalized complete information game models these models allow generalized interaction structures and generalized behavioral assumptions the generalized interaction structures allow that the dependence of an agent s utility function on the other agents actions can itself depend on characteristics of the agents including an endogenous network of connections among the agents the generalized behavioral assumptions relax the solution concept from nash equilibrium play to weaker solution concepts like rationalizability the results allow a non parametric specification of the unobservables

bounding parameter estimates with nonclassical measurement error abstract the bias introduced by errors in the measurement of independent variables has increasingly been a topic of interest among researchers estimating economic parameters however studies typically use the assumption of classical measurement error that is the variable of interest and its measurement error are uncorrelated and the expected value of the mismeasured variable is equal to the expected value of the true measure these assumptions often arise from convenience rather than conviction when a variable is bounded it is likely that the measurement error and the true value of the variable are negatively correlated we consider the case of a noisily measured variable with a negative covariance between the measurement error and the true value of the variable we show that asymptotically the parameter in a univariate regression is bounded between the ordinary least squares ols estimator and an instrumental variables iv estimator further we demonstrate that the ols bound can be improved in

separation of non negative mixture of non negative sources using a bayesian approach and mcmc sampling this paper addresses blind source separation in the case where both the source signals and the mixing coefficients are non negative the problem is referred to as non negative source separation and the main application concerns the analysis of spectrometric data sets the separation is performed in a bayesian framework by encoding non negativity through the assignment of gamma priors on the distributions of both the source signals and the mixing coefficients a markov chain monte carlo mcmc sampling procedure is proposed to simulate the resulting joint posterior density from which marginal posterior mean estimates of the source signals and mixing coefficients are obtained results obtained with synthetic and experimental spectra are used to discuss the problem of non negative source separation and to illustrate the effectiveness of the proposed method

bayesian regularization and nonnegative deconvolution for room impulse response estimation this paper proposes bayesian regularization and nonnegative deconvolution brand for accurately and robustly estimating acoustic room impulse responses for applications such as time delay estimation and echo cancellation similar to conventional deconvolution methods brand estimates the coefficients of convolutive finite impulse response fir filters using least square optimization however brand exploits the nonnegative sparse structure of acoustic room impulse responses with nonnegativity constraints and l sub 1 norm sparsity regularization on the filter coefficients the optimization problem is modeled within the context of a probabilistic bayesian framework and expectation maximization em is used to derive efficient update rules for estimating the optimal regularization parameters brand is demonstrated on two representative examples subsample time delay estimation in reverberant environments and acoustic echo cancellation the results presented in this paper show the advantages of brand in high temporal resolution and robustness to ambient noise compared with other conventional techniques

variants of non negative least mean square algorithm and convergence analysis due to the inherent physical characteristics of systems under investigation non negativity is one of the most interesting constraints that can usually be imposed on the parameters to estimate the non negative least mean square algorithm nnlms was proposed to adaptively find solutions of a typical wiener filtering problem but with the side constraint that the resulting weights need to be non negative it has been shown to have good convergence properties nevertheless certain practical applications may benefit from the use of modified versions of this algorithm in this paper we derive three variants of nnlms each variant aims at improving the nnlms performance regarding one of the following aspects sensitivity of input power unbalance of convergence rates for different weights and computational cost we study the stochastic behavior of the adaptive weights for these three new algorithms for non stationary environments this study leads to analytical models to predict the first and second order moment behaviors of the weights for gaussian inputs simulation results are presented to illustrate the performance of the new algorithms and the accuracy of the derived models

projected gradient methods for nonnegative matrix factorization nonnegative matrix factorization nmf can be formulated as a minimization problem with bound constraints although bound constrained optimization has been studied extensively in both theory and practice so far no study has formally applied its techniques to nmf in this letter we propose two projected gradient methods for nmf both of which exhibit strong optimization properties we discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach a simple matlab code is also provided

characterizations of δ volterra lattice a symmetric orthogonal polynomials interpretation abstract in this paper we introduce the volterra lattice which is interpreted in terms of symmetric orthogonal polynomials it is shown that the measure of orthogonality associated with these systems of orthogonal polynomials evolves in t like 1 x 2 1 t x where is a given positive borel measure moreover the volterra lattice is related to the toda lattice from miura or backlund transformations the main ingredients are orthogonal polynomials which satisfy an appell condition with respect to the forward difference operator and the characterization of the point spectrum of a jacobian operator that satisfies a volterra equation lax type theorem we also provide an explicit example of solutions of volterra and toda lattices and connect this example with the results presented in the paper

closed form estimation of nonparametric models with non classical measurement errors this paper proposes closed form estimators for nonparametric regressions using two measurements with non classical errors one administrative measurement has location scale normalized errors but the other survey measurement has endogenous errors with arbitrary location and scale for this setting of data combination we derive closed form identification of nonparametric regressions and practical closed form estimators that perform well with small samples applying this method to nhanes iii we study how obesity explains health care usage clinical measurements and self reports of bmi are used as two measurements with normalized errors and endogenous errors respectively we robustly find that health care usage increases with obesity

non point integrable symmetries for equations on the lattice we present a new class of non point groups of transformations for scalar evolution chain equations then we construct the class of differential equations on the lattice which admits such group transformations

approximate quasi likelihood estimation in models with surrogate predictors abstract we consider quasi likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error we review and extend four approaches to estimation in this problem all of them based on small measurement error approximations a taxonomy of the data sets likely to be available in measurement error studies is developed an asymptotic theory based on this taxonomy is obtained and includes measurement error and berkson error models as special cases

a difference analogue of the davey stewartson system discrete gram type determinant solution and lax pair we consider a difference difference davey stewartson system together with its bilinear structure we write some new gram type determinantal solutions taking into account a set of jacobi identities for determinants a bilinear backlund transformation is constructed and consequently a lax pair for the discrete system is derived

reduction groups and related integrable difference systems of nonlinear schrodinger type we extend the reduction group method to the lax darboux schemes associated with nonlinear schrodinger type equations we consider all possible finite reduction groups and construct corresponding lax operators darboux transformations hierarchies of integrable differential difference equations integrable partial difference systems and associated scalar partial difference equations

the generalized symmetry method for discrete equations the generalized symmetry method is applied to a class of completely discrete equations including the adler bobenko suris list assuming the existence of a generalized symmetry we derive a few integrability conditions suitable for testing and classifying the equations of this class those conditions are used at the end to test for integrability discretizations of some well known hyperbolic equations

extension of the module of invertible transformations classification of integrable systems we demonstrate that for the systems of equations which are invariant under a point group or possess conservation laws of the zeroth or first order a nontrivial extension of the module of invertible transformations is possible that simplifies greatly a classification of the integrable systems of equations here we present an exhaustive list and a classification of the second order systems of the formu t u xx f u v u x v x v t v xx g u v u x v x which possess the conservation laws of higher order the reduction group approach allows us to define the lax type representations for some new equations of our list

estimation for the nonlinear functional relationship on etudie les proprietes asymptotiques de l estimateur du maximum de vraisemblance pour le modele fonctionnel implicite

explicit auto transformations of integrable chains a construction scheme for explicit auto transformations of integrable discrete differential equations chains is presented these transformations are rather convenient to obtain the exact solutions for chains as well as associated partial differential systems on the other hand they exemplify new integrable discrete mappings their group properties are also of great interest the scheme is illustrated by several examples of integrable systems which contains the nonlinear schrodinger system and the landau lifshits model

instrumental variable treatment of nonclassical measurement error models while the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors in variables models with continuously distributed variables our main identifying assumption is that conditional on the value of the true regressors some measure of location of the distribution of the measurement error e g its mean mode or median is equal to zero the proposed approach relies on the eigenvalue eigenfunction decomposition of an integral operator associated with specific joint probability densities the main identifying assumption is used to index the eigenfunctions so that the decomposition is unique we propose a convenient sieve based estimator derive its asymptotic properties and investigate its finite sample behavior through monte carlo simulations

semiparametric latent variable model estimation with endogenous or mismeasured regressors a simple root n consistent asymptotically normal semiparametric estimator of the coefficient vector b in the latent variable specification y l f b x e is constructed the distribution of e is unknown and may be correlated with x or be conditionally heteroscedastic e g x can contain measurement error the function l can also be unknown the identification assumption is that e is uncorrelated with instruments u and that the conditional distribution of e given x and u does not depend on one of the regressors which has some special properties extensions to more general latent variable specifications are provided

transient and tracking performance bounds of the sign sign algorithm the paper provides a rigorous tracking analysis of the sign sign algorithm when used in the identification of a time varying plant with a white gaussian input the plant parameters vary according to a random walk model the assumptions allow nonstationarity of the plant input plant noise and increments of the plant parameters upper bounds are derived for the long term averages of the mean of the weight misalignment norm mean absolute error mean square weight misalignment and mean square error these bounds hold for all values of the algorithm step size all initial filter weight settings and all degrees of nonstationarity of the plant input plant noise and plant parameter increments lower bounds of the mean square weight misalignment and mean square error are also derived the step sizes that minimize the above bounds are derived a transient analysis of the algorithm is done in the case of a time invariant plant a tight lower bound of the convergence time is derived the above analytical results are supported by computer simulations

nonnegative least mean square algorithm dynamic system modeling plays a crucial role in the development of techniques for stationary and nonstationary signal processing due to the inherent physical characteristics of systems under investigation nonnegativity is a desired constraint that can usually be imposed on the parameters to estimate in this paper we propose a general method for system identification under nonnegativity constraints we derive the so called nonnegative least mean square algorithm nnlms based on stochastic gradient descent and we analyze its convergence experiments are conducted to illustrate the performance of this approach and consistency with the analysis

nonparametric estimation of non exchangeable latent variable models we propose a two step method to nonparametrically estimate multivariate models in which the observed outcomes are independent conditional on a discrete latent variable applications include microeconometric models with unobserved types of agents regime switching models and models with misclassification error in the first step we estimate weights that transform moments of the marginal distribution of the data into moments of the conditional distribution of the data for given values of the latent variable in the second step these conditional moments are estimated as weighted sample averages we illustrate the method by estimating a model of wages with unobserved heterogeneity on psid data

three dimensional integrable lattices in euclidean spaces conjugacy and orthogonality it is shown that the discrete darboux system descriptive of conjugate lattices in euclidean spaces admits constraints on the adjoint eigenfunctions which may be interpreted as discrete orthogonality conditions on the lattices thus it turns out that the elementary quadrilaterals of orthogonal lattices are cyclic orthogonal lattices on lines planes and spheres are discussed and the underlying integrable systems in one two and three dimensions are derived explicitly a discrete analogue of bianchi s ribaucour transformation is set down and particular orthogonal lattices are given as a by product discrete dini surfaces are obtained

sign sign lms convergence with independent stochastic inputs the sign sign adaptive least mean square lms identifier filter is a computationally efficient variant of the lms identifier filter it involves the introduction of signum functions in the traditional lms update term consideration is given to global convergence of parameter estimates offered by this algorithm to a ball with radius proportional to the algorithm step size for white input sequences specially from gaussian and uniform distributions

algorithms for nonnegative independent component analysis we consider the task of solving the independent component analysis ica problem x as given observations x with a constraint of nonnegativity of the source random vector s we refer to this as nonnegative independent component analysis and we consider methods for solving this task for independent sources with nonzero probability density function pdf p s down to s 0 it is sufficient to find the orthonormal rotation y wz of prewhitened sources z vx which minimizes the mean squared error of the reconstruction of z from the rectified version y sup of y we suggest some algorithms which perform this both based on a nonlinear principal component analysis pca approach and on a geodesic search method driven by differential geometry considerations we demonstrate the operation of these algorithms on an image separation problem which shows in particular the fast convergence of the rotation and geodesic methods and apply the approach to a musical audio analysis task

some new integrable systems constructed from the bi hamiltonian systems with pure differential hamiltonian operators abstract when both hamiltonian operators of a bi hamiltonian system are pure differential operators we show that the generalized kupershmidt deformation gkd developed from the kupershmidt deformation in 10 offers an useful way to construct new integrable system starting from the bi hamiltonian system we construct some new integrable systems by means of the generalized kupershmidt deformation in the cases of harry dym hierarchy classical boussinesq hierarchy and coupled kdv hierarchy we show that the gkd of harry dym equation gkd of classical boussinesq equation and gkd of coupled kdv equation are equivalent to the new integrable rosochatius deformations of these soliton equations with self consistent sources we present the lax pair for these new systems therefore the generalized kupershmidt deformation provides a new way to construct new integrable systems from bi hamiltonian systems and also offers a new approach to obtain the rosochatius deformation of soliton equation with self consistent sources

stochastic analysis of the filtered x lms algorithm in systems with nonlinear secondary paths this paper presents a statistical analysis of the filtered x lms algorithm behavior when the secondary path output of the adaptive filter includes a nonlinear element this system is of special interest for active acoustic noise and vibration control where a saturation nonlinearity models the nonlinear distortion introduced by the power amplifiers and transducers deterministic nonlinear recursions are derived for gaussian inputs for the transient mean weight mean square error and cross covariance matrix of the adaptive weight vector at different times the cross covariance results provide improved steady state predictions as compared with previous results for moderate to large step sizes monte carlo simulations show excellent agreement with the behavior predicted by the theoretical models the analytical and simulation results show that a small nonlinearity can have a significant impact on the adaptive filter behavior

instrumental variable estimation of nonlinear errors in variables models this paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of fourier transforms of conditional expectations of observable variables for parametrically specified regression functions we propose a root n consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged in nonparametric kernel density estimate both the identification and the estimation methodologies rely on fourier analysis and on the theory of generalized functions the finite sample properties of the estimator are investigated through monte carlo simulations

nonlinear superposition formulae for the differential difference analogue of the kdv equation and two dimensional toda equation in this paper nonlinear superposition formulae of the differential difference analogue of the kdv equation and two dimensional toda equation are proved rigorously some particular solutions of the differential difference analogue of the kdv equation are given as an illustrative application of the obtained result

on strong and weak backlund transformations the authors show on a set of examples containing the hierarchies of equations associated with the zakharov and shabat spectral problem 1972 the modified korteweg de vries burgers spectral problem and the chiral field equation that one can easily prove the strength or weakness of a backlund transformation for a whole hierarchy of equations by the use of the darboux matrix approach and thus with just the knowledge of half a backlund transformation

consistent model specification tests omitted variables and semiparametric functional forms in this paper we develop several consistent tests in the context of a nonparametric regression model these include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative one common feature to the construction of all these tests is the use of the central limit theorem for degenerate u statistics of order higher than two as a result they share the same advantages over most of the corresponding existing tests in the literature a they do not depend on any ad hoc modifications such as sample splitting random weighting etc b under the alternative hypotheses the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications

a class of integrable lattices and kp hierarchy we introduce a class of integrable l field first order lattices together with corresponding lax equations these lattices may be represented as a consistency condition for auxiliary linear systems defined on sequences of formal dressing operators this construction provides a simple way to build lattice miura transformations between one field lattice and l field l 2 ones we show that the lattices pertained to by the above class are in some sense compatible with kp flows and define the chains of constrained kadomtsev petviashvili lax operators

estimation of average treatment effects with misclassification this paper considers identification and estimation of the effect of a mismeasured binary regressor in a nonparametric or semiparametric regression or the conditional average effect of a binary treatment or policy on some outcome where treatment may be misclassified failure to account for misclassification is shown to result in attenua tion bias in the estimated treatment effect an identifying assumption that overcomes this bias is the existence of an instrument for the binary regressor that is conditionally independent of the treatment effect a discrete instrument suffices for nonparametric identification this paper provides conditions for identification and estimation of the av erage effect conditioned on covariates of a binary treatment program or pol icy on a scalar outcome when treatment may be misclassified more generally what is provided is an estimator of the effect of a binary regressor in a con ditional mean regression which may also include other regressors when the binary regressor is observed with error this equals the conditional average treatment effect given a weak unconfoundedness assumption misclassification occurs when a binary variable the treatment indicator is measured with error that is some units are reported to have received treat ment when they actually have not and vice versa for example in a returns to schooling analysis the outcome could be wages the binary variable could be attaining a college degree and misclassification could arise from school tran script reporting errors see e g kane and rouse 1995 and kane rouse and staiger 1999 bollinger 1996 considers misclassification of union status in wage equations if treatment is a job training program misclassification may arise if individuals assigned to the program fail to attend or if those not as signed obtain training elsewhere similarly for medical treatment individuals assigned a drug might fail to take it and those assigned a placebo might obtain treatment from another source more generally misclassification describes any binary variable that is sometimes mismeasured this paper first shows that misclassification causes attenuation bias in esti mated treatment effects analogous to the attenuation bias of classically mis measured variables in linear regression models additional assumptions on

instrumental variable estimator for the nonlinear errors in variables model abstract estimation for the nonlinear errors in variables model is considered it isassumed that additional information is available in the form of observations on instrumental variables an estimation procedure is presented for the parameters of the model asymptotic properties of the estimator are investigated

semiparametric comparison of regression curves the comparison of nonparametric regression curves is considered it is assumed that there are parametric possibly nonlinear transformations of the axes which map one curve into the other estimation and testing of the parameters in the transformations are studied the rate of convergence is n 1 2 although the nonparametric components of the model typically have a rate slower than that a statistic is provided for testing the validity of a given completely parametric model

partial identification of probability distributions with misclassified data abstract this paper addresses the problem of data errors in discrete variables when data errors occur the observed variable is a misclassified version of the variable of interest whose distribution is not identified inferential problems caused by data errors have been conceptualized through convolution and mixture models this paper introduces the direct misclassification approach the approach is based on the observation that in the presence of classification errors the relation between the distribution of the true but unobservable variable and its misclassified representation is given by a linear system of simultaneous equations in which the coefficient matrix is the matrix of misclassification probabilities formalizing the problem in these terms allows one to incorporate any prior information into the analysis through sets of restrictions on the matrix of misclassification probabilities such information can have strong identifying power the direct misclassification approach fully exploits it to derive identification regions for any real functional of the distribution of interest a method for estimating the identification regions and construct their confidence sets is given and illustrated with an empirical analysis of the distribution of pension plan types using data from the health and retirement study

nonlinear errors in variables estimation of some engel curves abstract the most common solution to the errors in variables problem for the linear regression model is the use of instrumental variable estimation however this methodology cannot be applied in the nonlinear regression framework in this paper we develop consistent estimators for nonlinear regression specifications when errors in variables are present we apply our methodology to estimation of engel curves on household data first we find that the lesser working specification of budget shares regressed on the log of income or expenditure should be generalized to higher order terms in log income also we find that errors in variables in either reported income or expenditure should be accounted for lastly and perhaps most interesting we find rather strong support for the gorman rank restriction on the matrix of coefficients for the polynomial terms in income

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

quad equations and auto backlund transformations of nls type systems treating an integrable quad equation along with its two generalized symmetries as a compatible system allows one to construct an auto backlund transformation for solutions of the related nls type system a fixed periodic reduction of the quad equation yields a quasi periodic reduction of its generalized symmetries that turns them into differential constraints compatible with the nls type system

integrable discretization of time and its application on the fourier pseudospectral method to the korteweg de vries equation this paper presents a new integrable discretization of the korteweg de vries kdv equation different from other discrete analogues we discretize the variable time and obtain an integrable differential difference system this system has the original kdv equation as a standard limit when the step size tends to zero the main idea is based on hirota s bilinear method and backlund transformation and can be applied to other integrable systems by applying the fourier pseudospectral method to the space variable we derive a new numerical scheme for the kdv equation numerical results are found to agree with the exact solution and the first five conservation quantities are preserved quite well

fixed point error analysis of the normalized ladder algorithm an attempt is made to analyze the fixed point error performance of the normalized ladder algorithm for autoregressive system identification assuming rounding arithmetic a preliminary simulation study of this algorithm has shown that the bias in the estimated reflection coefficients is much more predominant than the variance of the error in the estimate the study therefore is directed to find a model for predicting the bias in the estimated reflection coefficients the analysis shows that the roundoff errors associated with the square root operations in one of the algorithm equations are mainly responsible for the bias in the estimated reflection coefficients these errors arise because of the normalization procedure that makes the quantities under the square root operations very close to one two main results are presented in the paper 1 a simplified theoretical expression for predicting the average bias in the estimated reflection coefficients at any stage is derived 2 a recursive relation for the average error arising from the finite precision arithmetic in the squared residuals is derived this relation illustrates how the errors made in one stage affect the errors in the succeeding stages simulations are performed to check the theoretical models the experimental results agree very closely with the theoretical predictions

on the convergence of multiplicative update algorithms for nonnegative matrix factorization nonnegative matrix factorization nmf is useful to find basis information of nonnegative data currently multiplicative updates are a simple and popular way to find the factorization however for the common nmf approach of minimizing the euclidean distance between approximate and true values no proof has shown that multiplicative updates converge to a stationary point of the nmf optimization problem stationarity is important as it is a necessary condition of a local minimum this paper discusses the difficulty of proving the convergence we propose slight modifications of existing updates and prove their convergence techniques invented in this paper may be applied to prove the convergence for other bound constrained optimization problems

misclassification in binary choice models abstract bias from misclassification of binary dependent variables can be pronounced we examine what can be learned from such contaminated data first we derive the asymptotic bias in parametric models allowing misclassification to be correlated with observables and unobservables simulations and validation data show that the bias formulas are accurate in finite samples and in most situations imply attenuation second we examine the bias in a prototypical application erroneously restricting the covariance of misclassification and covariates aggravates the bias for all estimators we examine estimators that relax this restriction perform well if a model of misclassification or validation data is available

continuous symmetries of difference equations lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations in this article we review the results of a much more recent program the use of lie groups to study difference equations we show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners one is to use generalized symmetries acting on solutions of difference equations but leaving the lattice invariant the other is to restrict them to point symmetries but to allow them to also transform the lattice

a hierarchy of coupled korteweg de vries equations and the normalisation conditions of the hilbert riemann problem the authors discuss the normalisation conditions of the hilbert riemann problem which is of importance for the construction of the ladder of soliton solutions for a given spectral problem they provide the prescription for constructing the appropriate normalisation condition all this is applied to a new hierarchy of coupled korteweg de vries equations to find the soliton solution which displays some peculiar phenomena

nonlinear differential difference equations as backlund transformations shows that the best known nonlinear differential difference equations associated with the discrete schrodinger spectral problem and also with the discrete zakharov shabat spectral problem can be interpreted as backlund transformations for some continuous nonlinear evolution equations

equivalent classes of integrable nonlinear evolution equations and generalised miura transformations the authors write down the recursion operator which defines the class of integrable nonlinear evolution equations nee associated with a spectral problem sp for matrices of rank 2 depending quadratically on the spectral parameter then they show the existence of four different transformations which transform the given sp into the well known one of zakharov and shabat zs 1972 by composing these transformations they recover among others the so called elementary backlund transformations for the zs sp under some restrictions one is able to prove the complete equivalence of the given glass of nee to the one associated with the zs sp

semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors abstract this paper develops a framework for the analysis of semiparametric conditional moment models with endogenous and mismeasured causes which is of empirical importance we show that one set of valid instruments is sufficient to control for both endogeneity and measurement errors of the causes of interest which has been observed in linear parametric models two step consistent estimators of the parameters of interest are proposed we also show that the proposed estimators are consistent with a rate faster than n 1 4 under a certain metric and the proposed estimators of the finite dimensional unknown parameters obtain root n asymptotic normality monte carlo evidences show that the proposed estimators perform well under a variety of identification conditions an application to instrumental variables estimation of engel curves illustrates the usefulness of our method it supports that correcting for both endogeneity and measurement errors on total expenditure is substantial in estimating economically meaningful engel curves

identification of additive and polynomial models of mismeasured regressors without instruments abstract we show nonparametric point identification of a measurement error model with covariates that can be interpreted as invalid instruments our main contribution is to replace standard exclusion restrictions with the weaker assumption of additivity in the covariates measurement errors are ubiquitous and additive models are popular so our results combining the two should have widespread potential application we also identify a model that replaces the nonparametric function of the mismeasured regressor with a polynomial in that regressor and other covariates this allows for rich interactions between the variables at the expense of introducing a parametric restriction our identification proofs are constructive and so can be used to form estimators we establish root n asymptotic normality for one of our estimators

robust and consistent estimation of nonlinear errors in variables models this paper considers the consistent estimation of nonlinear errors in variables models it adopts the functional modeling approach by assuming that the true but unobserved regressors are random variables but making no parametric assumption on the distribution from which the latent variables are drawn this paper shows how the information extracted from the replicate measurements can be used to identify and consistently estimate a general nonlinear errors in variables model the identification is established through characteristic functions the estimation procedure involves nonparametric estimation of the conditional density of the latent variables given the measurements using the identification results at the first stage and at the second stage a semiparametric nonlinear least squares estimator is proposed the consistency of the proposed estimator is also established finite sample performance of the estimator is investigated through a monte carlo study

comment on the unnecessary assumption of statistical independence between reference signal and filter weights in feedforward adaptive systems minkoff see ieee trans signal processing vol 45 p 2993 3004 1997 presented a formulation in which the time evolving weight iteration equation for random signals is derived without the necessity of invoking the usual unsatisfactory assumption that is customarily made namely that the weights w and the reference signal x the weight iteration equation are statistically independent minkoff neglected however to give a physical argument for it that is in this derivation it is not necessary for w to be independent of x but only of xx which does not contain the phase information of x the off diagonal terms of xx contain only phase differences which could be produced by an infinite number of different arbitrary xs

the non autonomous ydkn equation and generalized symmetries of boll equations in this paper we study the integrability of a class of nonlinear non autonomous quad graph equations compatible around the cube introduced by boll in the framework of the generalized adler bobenko and suris abs classification we show that all these equations possess three point generalized symmetries which are subcases of either the yamilov discretization of the krichever novikov equation or of its non autonomous extension we also prove that all those symmetries are integrable as they pass the algebraic entropy test

nonparametric instrumental regression the focus of this paper is the nonparametric estimation of an instrumental regression function f defined by conditional moment restrictions that stem from a structural econometric model e y f z w 0 and involve endogenous variables y and z and instruments w the function f is the solution of an ill posed inverse problem and we propose an estimation procedure based on tikhonov regularization the paper analyzes identification and overidentification of this model and presents asymptotic properties of the estimated nonparametric instrumental regression function

bayesian moment based inference in a regression model with misclassification error we present a bayesian analysis of a regression model with a binary covariate that may have classification measurement error prior research demonstrates that the regression coefficient is only partially identified we take a bayesian approach which adds assumptions in the form of priors on the unknown misclassification probabilities the approach is intermediate between the frequentist bounds of previous literature and strong assumptions which achieve point identification and thus preferable in many settings we present two simple algorithms to sample from the posterior distribution when the likelihood function is not fully parametric but only satisfies a set of moment restrictions we focus on how varying amounts of information contained in a prior distribution on the misclassification probabilities change the posterior of the parameters of interest while the priors add information to the model they do not necessarily tighten the identified set however the information is sufficient to tighten bayesian inferences we also consider the case where the mismeasured binary regressor is endogenous we illustrate the use of our bayesian approach in a simulated data set and an empirical application investigating the association between narcotic pain reliever use and earnings

functional representation of the ablowitz ladik hierarchy the ablowitz ladik hierarchy alh is considered in the framework of the inverse scattering approach after establishing the structure of solutions of the auxiliary linear problems the alh which has been originally introduced as an infinite system of differential difference equations is presented as a finite system of difference functional equations the representation obtained when rewritten in terms of hirota s bilinear formalism is used to demonstrate relations between the alh and some other integrable systems the kadomtsev petviashvili hierarchy in particular

discrete time toda systems in this paper we discuss several concepts of the modern theory of discrete integrable systems including time discretization based on the notion of backlund transformation symplectic realizations of multi hamiltonian structures interrelations between discrete 1d systems and lattice 2d systems multi dimensional consistency as integrability of discrete systems interrelations between integrable systems of quad equations and integrable systems of laplace type pluri lagrangian structure as integrability of discrete variational systems all these concepts are illustrated by the discrete time toda lattices and their relativistic analogs

measurement bias and effect restoration in causal inference summary this paper highlights several areas where graphical techniques can be harnessed to address the problem of measurement errors in causal inference in particular it discusses the control of unmeasured confounders in parametric and nonparametric models and the computational problem of obtaining bias free effect estimates in such models we derive new conditions under which causal effects can be restored by observing proxy variables of unmeasured confounders with without external studies

the modified camassa holm equation backlund transformation and nonlinear superposition formula this paper is concerned with the modified camassa holm equation and its backlund transformation with the aid of reciprocal transformation and the associated modified camassa holm equation a backlund transformation which involves both dependent and independent variables is constructed for the modified camassa holm equation the related nonlinear superposition formula is worked out and applications of both backlund transformation and nonlinear superposition formula are considered

counting rotten apples student achievement and score manipulation in italian elementary schools abstract we derive bounds on the distribution of math and language scores of elementary school students in italy correcting for pervasive manipulation a natural experiment that randomly assigns external monitors to schools is used to deal with endogeneity of manipulation as well as its mismeasurement in the data bounds are obtained from properties of the statistical model used to detect classes with manipulated scores and from restrictions on the relationship between manipulation and true scores our results show that regional rankings by academic performance are reversed once manipulation is taken into account

backlund transformations for the nizhnik novikov veselov equation the backlund transformations for the nizhnik novikov veselov equation are presented it is shown that these transformations can be iterated and that the resulting sequence can be described by the volterra equations the relationships between the nizhnik novikov veselov equation and the volterra hierarchy are discussed

spectral transformations self similar reductions and orthogonal polynomials we study spectral transformations in the theory of orthogonal polynomials which are similar to darboux transformations for the schr dinger equation linear transformations of the stieltjes function with coefficients that are rational in the argument are constructed as iterations of the christoffel and geronimus transformations we describe a characteristic property of semi classical orthogonal polynomials scop on the uniform and the exponential lattice namely that all these polynomials can be obtained through simple quasi periodic and q periodic self similar closures of the chain of linear spectral transformations in the self similar setting a characterization of the laguerre hahn polynomials on linear and q linear lattices is obtained by considering rational transformations of the stieltjes function generated by transitions to the associated polynomials

regression models for choice based samples with misclassification in the response variable abstract in this paper we provide a general framework to deal with the presence of misclassification in the response variable in choice based samples the contaminated data sampling distribution is written as a function of the error free conditional distribution of the dependent variable given the covariates and the conditional misclassification probabilities of the observable variable of interest given its latent values we propose an extension of imbens econometrica 60 1992 1187 efficient generalized method of moments to estimate this model and outline a specification test to detect the presence of this sort of measurement error the performance of both the estimators and the test is investigated in a monte carlo simulation study which shows very encouraging results

construction scheme for discrete miura transformations a direct and elementary scheme for the construction of miura type transformations and discrete differential equations related to them scalar and vector is presented the scheme is illustrated using as examples the volterra and toda models a discrete differential analogue of the calogero degasperis equation is discussed in detail this example is used to show how to construct conservation laws higher symmetries and solutions for an equation obtained with the help of the scheme

estimation of nonlinear models with measurement error this paper presents a solution to an important econometric problem namely the root n consistent estimation of nonlinear models with measurement errors in the explanatory variables when one repeated observation of each mismeasured regressor is available while a root n consistent estimator has been derived for polynomial specifications see hausman ichimura newey and powell 1991 such an estimator for general nonlinear specifications has so far not been available using the additional information provided by the repeated observation the suggested estimator separates the measurement error from the true value of the regressors thanks to a useful property of the fourier transform the fourier transform converts the integral equations that relate the distribution of the unobserved true variables to the observed variables measured with error into algebraic equations the solution to these equations yields enough information to identify arbitrary moments of the true unobserved variables the value of these moments can then be used to construct any estimator that can be written in terms of moments including traditional linear and nonlinear least squares estimators or general extremum estimators the proposed estimator is shown to admit a representation in terms of an influence function thus establishing its root n consistency and asymptotic normality monte carlo evidence and an application to engel curve estimation illustrate the usefulness of this new approach

nonparametric identification of discrete choice models with lagged dependent variables abstract variation in covariates can be used to nonparametrically identify a discrete choice model with a lagged dependent variable and discrete unobserved heterogeneity kasahara and shimotsu 2009 browning and carro 2014 in some cases the number of support points of the unobserved heterogeneity distribution is restricted only by the number of points of support in the distribution of the covariates this paper provides conditions under which these models can be identified with continuous heterogeneity using continuous variation in the covariates the identification argument is related to that of honore and lewbel 2002 in that it requires a special regressor lewbel 1998 but it does not assume an additively separable latent index identification requires only 3 time periods neither stationarity nor time homogeneity is imposed and the distribution of the initial condition is not restricted apart from conditions required for the special regressor i demonstrate the result through a monte carlo simulation

bounding mean regressions when a binary regressor is mismeasured in this paper i examine identification and estimation of mean regression models when a binary regressor is mismeasured i prove that bounds for the model parameters are identified and provide simple estimators which are consistent and asymptotically normal when stronger prior information about the probability of misclassification is available the bounds can be made tighter again a simple estimator for these cases is provided all results apply to parametric and nonparametric models the paper concludes with a short empirical example

integrable symplectic maps associated with the zs akns spectral problem the darboux transformations dts associated with the well known zs akns spectral problem are regarded as discrete spectral problems two kinds of integrable symplectic maps are derived from them through nonlinearization procedures as an application they are used to calculate the finite genus solutions of some new integrable lattice models constructed from these dts

identification and estimation of nonlinear models with misclassification error using instrumental variables a general solution abstract this paper provides a general solution to the problem of identification and estimation of nonlinear models with misclassification error in a general discrete explanatory variable using instrumental variables the misclassification error is allowed to be correlated with all the explanatory variables in the model it is not enough to identify the model by simply generalizing the identification in the binary case with a claim that the number of restrictions is no less than that of the unknowns such a claim requires solving a complicated nonlinear system of equations this paper introduces a matrix diagonalization technique which allows one to easily find the unique solution of the system the solution shows that the latent model can be expressed as an explicit function of directly observed distribution functions therefore the latent model is nonparametrically identifiable and directly estimable using instrumental variables the results show that certain monotonicity restrictions on the latent model may lead to its identification with virtually no restrictions on the misclassification probabilities an alternative identification condition suggests that the nonparametric identification may rely on the belief that people always have a higher probability of telling the truth than of misreporting the nonparametric identification in this paper directly leads to a n consistent semiparametric estimator the monte carlo simulation and empirical illustration show that the estimator performs well with a finite sample and real data

identification and estimation of polynomial errors in variables models abstract methods of estimation of regression coefficients are proposed when the regression function includes a polynomial in a true regressor which is measured with error two sources of additional information concerning the unobservable regressor are considered either an additional indicator of the regressor itself measured with error or instrumental variables which characterize the systematic variation in the true regressor in both cases estimators are constructed by relating moments involving the unobserved variables to moments of observables these relations lead to recursion formulae for computation of the regression coefficients and nuisance parameters e g moments of the measurement error consistency and asymptotic normality of the estimated coefficients is demonstrated and consistent estimators of the asymptotic covariant matrices are provided

non invertible transformations of differential difference equations we discuss aspects of the theory of non invertible transformations of differential difference equations and in particular the notion of miura type transformation we introduce the concept of non miura type linearizable transformation and we present techniques that allow one to construct simple linearizable transformations and might help one to solve classification problems this theory is illustrated by the example of a new integrable differential difference equation depending on five lattice points interesting from the viewpoint of the non invertible transformation which relate it to an itoh narita bogoyavlensky equation

treatment effect estimation with covariate measurement error this paper investigates the effect that covariate measurement error has on a treatment effect analysis built on an unconfoundedness restriction in which there is conditioning on error free covariates the approach uses small parameter asymptotic methods to obtain the approximate effects of measurement error for estimators of average treatment effects the approximations can be estimated using data on observed outcomes the treatment indicator and error contaminated covariates without employing additional information from validation data or instrumental variables the results can be used in a sensitivity analysis to probe the potential effects of measurement error on the evaluation of treatment effects