identification of mixture models using support variations abstract we consider the issue of identifying nonparametrically continuous mixture models in these models all observed variables depend on a common and unobserved component but are mutually independent conditional on it such a structure applies for instance to measurement error matching and auction models traditional approaches rely on parametric assumptions or strong functional restrictions we show that these models are actually identified nonparametrically if the supports of the observed variables move with the value of the unobserved component moreover this assumption is testable nonparametrically using tools from extreme value theory we develop an appropriate test and derive its asymptotic properties

optimal rates of convergence for deconvolving a density abstract suppose that the sum of two independent random variables x and z is observed where z denotes measurement error and has a known distribution and where the unknown density f of x is to be estimated one application is the estimation of a prior density for a sequence of location parameters a second application arises in the errors in variables problem for nonlinear and generalized linear models when one attempts to model the distribution of the true but unobservable covariates this article shows that if z is normally distributed and f has k bounded derivatives then the fastest attainable convergence rate of any nonparametric estimator of f is only log n k 2 therefore deconvolution with normal errors may not be a practical proposition other error distributions are also treated stefanski carroll 1987a estimators achieve the optimal rates the results given have versions for multiplicative errors where they imply that even optimal rates are exceptionally slow

periodic solutions of a second order ordinary differential equation a necessary and sufficient condition for nonresonance the nonlinearity g in 1 1 is a continuous function from r to r and the forcing term h is taken in l o 27r nonresonance means that 1 1 admits at least one solution x for any given h integrating eq 1 1 over a period one immediately sees that a necessary condition for nonresonance is that the function g be unbounded from above and from below on r it will appear later cf 1 6 that this unboundedness can be looked at as a condition relating the behaviour at infinity of the nonlinearity g with respect to the first eigenvalue 1 0 of the associated linear problem xf ax in 0 27r x 0 x 27r x 0 x1 271 1 2

traveling wave solutions for gause type predator prey systems with density dependence a heteroclinic orbit in r4 abstract this paper investigates the existence of traveling wave solutions for a class of diffusive gause type predator prey systems with linear density dependence for predator using the shooting method we establish the existence of a non negative traveling wave solution connecting a boundary equilibrium point to the coexistence equilibrium point with the help of topological method of wazewski theorem and lasalle s invariance principle

traveling waves for competitive lotka volterra systems with spatial diffusions and spatio temporal delays abstract this paper is concerned with the existence of traveling waves for reaction diffusion equations with spatio temporal delays our approach is to use the cross iteration technique and schauder s fixed point theorem the iterative technique can be established for a class of integral operators when the reaction terms satisfy new monotonicity conditions which is different from those in previous works the results can be well applied to a two species competitive lotka volterra system with more general kernel functions in order to overcome the difficulty of spatio temporal delays we need to use a basic result from a pde textbook existence of traveling waves which connect the trivial equilibrium and the positive equilibrium indicates that there is a transition zone moving the steady state with no species to the steady state with the coexistence of two species our results can extend some existing ones for two species diffusion competitive lotka volterra systems

regression discontinuity design with continuous measurement error in the running variable abstract since the late 90s regression discontinuity rd designs have been widely used to estimate local average treatment effects late when the running variable is observed with continuous measurement error identification fails assuming non differential measurement error we propose a consistent nonparametric estimator of the late when the discrepancy between the true running variable and its noisy measure is observed in an auxiliary sample of treated individuals and when there are treated individuals at any value of the true running variable two sided fuzzy designs we apply our method to estimate the effect of receiving unemployment benefits

bayesian semiparametric regression in the presence of conditionally heteroscedastic measurement and regression errors summary we consider the problem of robust estimation of the regression relationship between a response and a covariate based on sample in which precise measurements on the covariate are not available but error prone surrogates for the unobserved covariate are available for each sampled unit existing methods often make restrictive and unrealistic assumptions about the density of the covariate and the densities of the regression and the measurement errors for example normality and for the latter two also homoscedasticity and thus independence from the covariate in this article we describe bayesian semiparametric methodology based on mixtures of b splines and mixtures induced by dirichlet processes that relaxes these restrictive assumptions in particular our models for the aforementioned densities adapt to asymmetry heavy tails and multimodality the models for the densities of regression and measurement errors also accommodate conditional heteroscedasticity in simulation experiments our method vastly outperforms existing methods we apply our method to data from nutritional epidemiology

some aspects of measurement error in a censored regression model abstract when a linear model with a censored dependent variable is written as a regression model the model is nonlinear in the explanatory variables this means that when the explanatory variables are measured with error estimation by instrumental variables will not lead to consistent estimates of the parameters my approach to the problem involves assuming that the variables measured with error can be represented by a reduced form equation and estimating the parameters of the censored regression model by the least absolute deviations estimator this estimator is based on the median of the distribution of the dependent variable rather than the mean and the median is not affected by censoring in the lower tail hence the estimator is consistent under general conditions i also consider the problem of testing for the presence of measurement error

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

nonparametric prediction in measurement error models predicting the value of a variable y corresponding to a future value of an explanatory variable x based on a sample of previously observed independent data pairs x1 y1 xn yn distributed like x y is very important in statistics in the error free case where x is observed accurately this problem is strongly related to that of standard regression estimation since prediction of y can be achieved via estimation of the regression curve e y x when the observed xis and the future observation of x are measured with error prediction is of a quite different nature here if t denotes the future contaminated available version of x prediction of y can be achieved via estimation of e y t in practice estimating e y t can be quite challenging as data may be collected under different conditions making the measurement errors on xi and x nonidentically distributed we take up this problem in the nonparametric setting and introduce estimators which allow a highly adaptive approach to smoothing

regressions with berkson errors in covariates a nonparametric approach this paper establishes that so called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with berkson type measurement error in the regressors an estimator is proposed and proven to be consistent its practical performance and feasibility are investigated via monte carlo simulations as well as through an epidemiological application investigating the effect of particulate air pollution on respiratory health these examples illustrate that berkson errors can clearly not be neglected in nonlinear regression models and that the proposed method represents an effective remedy

nonparametric regression estimation in the heteroscedastic errors in variables problem in the classical errors in variables problem the goal is to estimate a regression curve from data in which the explanatory variable is measured with error in this context nonparametric methods have been proposed that rely on the assumption that the measurement errors are identically distributed although there are many situations in which this assumption is too restrictive nonparametric estimators in the more realistic setting of heteroscedastic errors have not been studied in the literature we propose an estimator of the regression function in such a setting and show that it is optimal we give estimators in cases in which the error distributions are unknown and replicated observations are available practical methods including an adaptive bandwidth selector for the errors in variables regression problem are suggested and their finite sample performance is illustrated through simulated and real data examples

the effect of measurement error summary measurement error causes the distribution generating data to differ from the distribution that is of substantive interest to understand the effect of measurement error on the information produced by statistical procedures it is thus necessary to understand the distortions induced by measurement error this paper sheds light on this by providing small error variance approximations to the distribution of variates subject to contamination by measurement error these provide the basis for the analysis of the properties of estimators and tests and less formal procedures when measurement error is present and the basis for the development of tests to detect measurement error and of models which incorporate its influence

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

simultaneous treatment of unspecified heteroskedastic model error distribution and mismeasured covariates for restricted moment models abstract we develop consistent and efficient estimation of parameters in general regression models with mismeasured covariates we assume the model error and covariate distributions are unspecified and the measurement error distribution is a general parametric distribution with unknown variance covariance we construct root n consistent asymptotically normal and locally efficient estimators using the semiparametric efficient score we do not estimate any unknown distribution or model error heteroskedasticity instead we form the estimator under possibly incorrect working distribution models for the model error error prone covariate or both empirical results demonstrate robustness to different incorrect working models in homoscedastic and heteroskedastic models with error prone covariates

nonresonance below the first eigenvalue for a semilinear elliptic problem let be a bounded open subset in hbox i r n with smooth boundary and let f x s be a real valued caratheodory function on upomega times hbox i r we consider the semilinear dirichlet problem

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

asymptotic stability of the critical pulled front in a lotka volterra competition model abstract we prove that the critical pulled front of lotka volterra competition systems is nonlinearly asymptotically stable more precisely we show that perturbations of the critical front decay algebraically with rate t 3 2 in a weighted l space our proof relies on pointwise semigroup methods and utilizes in a crucial way that the faster decay rate t 3 2 is a consequence of the lack of an embedded zero of the evans function at the origin for the linearized problem around the critical front

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

traveling wave solutions for diffusive predator prey type systems with nonlinear density dependence abstract traveling wave solution for a class of diffusive predator prey system with nonlinear density dependence is considered using methods of topological shooting we show the existence of a non negative traveling wave solution connecting a boundary equilibrium to the co existence steady state with the help of a wazewski like set together with lyapunov function constructed elaborately this means that the traveling wave solution established by huang 2012 can be preserved in the presence of the nonlinear density dependence for the predator and the results of huang 2012 are generalized

nonparametric identification and semiparametric estimation of classical measurement error models without side information virtually all methods aimed at correcting for covariate measurement error in regressions rely on some form of additional information e g validation data known error distributions repeated measurements or instruments in contrast we establish that the fully nonparametric classical errors in variables model is identifiable from data on the regressor and the dependent variable alone unless the model takes a very specific parametric form this parametric family includes but is not limited to the linear specification with normally distributed variables as a well known special case this result relies on standard primitive regularity conditions taking the form of smoothness constraints and nonvanishing characteristic functions assumptions our approach can handle both monotone and nonmonotone specifications provided the latter oscillate a finite number of times given that the very specific unidentified parametric functional form is arguably the exception rather than the rule this identification r

convolution without independence abstract widely used convolution and deconvolution techniques traditionally rely on independence assumptions often criticized as being strong we observe that the convolution theorem actually holds under a weaker assumption known as subindependence we show that this notion is arguably as weak as a conditional mean assumption we report various simple characterizations of subindependence and devise constructive methods to generate subindependent random variables we extend subindependence to multivariate settings and propose the new concepts of conditional and mean subindependence relevant to measurement error problems we finally introduce three tests of subindependence based on characteristic functions generalized method of moments and randomization respectively

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

method of moments estimation and identifiability of semiparametric nonlinear errors in variables models abstract this paper deals with a nonlinear errors in variables model where the distributions of the unobserved predictor variables and of the measurement errors are nonparametric using the instrumental variable approach we propose method of moments estimators for the unknown parameters and simulation based estimators to overcome the possible computational difficulty of minimizing an objective function which involves multiple integrals both estimators are consistent and asymptotically normally distributed under fairly general regularity conditions moreover root n consistent semiparametric estimators and a rank condition for model identifiability are derived using the combined methods of the nonparametric technique and fourier deconvolution

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

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

monotone waves for non monotone and non local monostable reaction diffusion equations abstract we propose a new approach for proving existence of monotone wavefronts in non monotone and non local monostable diffusive equations this allows to extend recent results established for the particular case of equations with local delayed reaction in addition we demonstrate the uniqueness modulo translations of obtained monotone wavefront within the class of all monotone wavefronts such a kind of conditional uniqueness was recently established for the non local kpp fisher equation by fang and zhao moreover we show that if delayed reaction is local then each monotone wavefront is unique modulo translations within the class of all non constant traveling waves our approach is based on the construction of suitable fundamental solutions for linear integral differential equations we consider two alternative scenarios in the first one the fundamental solution is negative typically holds for the mackey glass diffusive equations while in the second one the fundamental solution is non negative typically holds for the kpp fisher diffusive equations

estimation of linear and nonlinear errors in variables models using validation data abstract consistent estimators for linear and nonlinear regression models with measurement errors in variables in the presence of validation data are proposed the estimation procedures are based on least squares methods with regression functions replaced by wide sense conditional expectation functions the methods do not depend on distributional assumptions and are robust against the misspecification of a measurement error model they are computationally and analytically simpler than semiparametric methods based on nonparametric regression or density functions

local indirect least squares and average marginal effects in nonseparable structural systems we study the scope of local indirect least squares lils methods for nonparametrically estimating average marginal effects of an endogenous cause x on a response y in triangular structural systems that need not exhibit linearity separability or monotonicity in scalar unobservables one main finding is negative in the fully nonseparable case lils methods cannot recover the average marginal effect lils methods can nevertheless test the hypothesis of no effect in the general nonseparable case we provide new nonparametric asymptotic theory treating both the traditional case of observed exogenous instruments z and the case where one observes only error laden proxies for z

minimal speed selection of traveling waves to the lotka volterra competition model abstract in this paper the minimal speed determinacy of traveling wave fronts of a two species competition model of diffusive lotka volterra type is investigated first a cooperative system is obtained from the classical lotka volterra competition model then we apply the upper lower solution technique on the cooperative system to study the traveling waves as well as its minimal speed selection mechanisms linear or nonlinear new types of upper and lower solutions are established previous results for the linear speed selection are extended and novel results on both linear and nonlinear selections are derived

polynomial regression with errors in the variables a polynomial functional relationship with errors in both variables can be consistently estimated by constructing an ordinary least squares estimator for the regression coefficients assuming hypothetically the latent true regressor variable to be known and then adjusting for the errors if normality of the error variables can be assumed the estimator can be simplified considerably only the variance of the errors in the regressor variable and its covariance with the errors of the response variable need to be known if the variance of the errors in the dependent variable is also known another estimator can be constructed

measurement errors in quantile regression models abstract this paper develops estimation and inference for quantile regression models with measurement errors we propose an easily implementable semiparametric two step estimator when repeated measures for the covariates are available building on recent theory on z estimation with infinite dimensional parameters consistency and asymptotic normality of the proposed estimator are established we also develop statistical inference procedures and show the validity of a bootstrap approach to implement the methods in practice monte carlo simulations assess the finite sample performance of the proposed methods we apply the methods to the investment equation model using a firm level data with repeated measures of investment demand tobin s q we document strong heterogeneity in the sensitivity of investment to tobin s q and cash flow across the conditional distribution of investment the cash flow sensitivity is relatively larger at the lower part of the distribution providing evidence that these firms are more exposed to and dependent on fluctuations in internal finance

a design adaptive local polynomial estimator for the errors in variables problem local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature their simplest version the local constant estimator can be easily extended to the errors in variables context by exploiting its similarity with the deconvolution kernel density estimator the generalization of the higher order versions of the estimator however is not straightforward and has remained an open problem for the last 15 years we propose an innovative local polynomial estimator of any order in the errors in variables context derive its design adaptive asymptotic properties and study its finite sample performance on simulated examples we provide not only a solution to a long standing open problem but also provide methodological contributions to error in variable regression including local polynomial estimation of derivative functions

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

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

traveling wave solutions in a delayed diffusive competition system abstract in this paper we first investigate the existence of traveling wave fronts in a delayed diffusive competition system by constructing a pair of upper and lower solutions then we consider the asymptotic behavior of traveling wave solutions at the minus plus infinity by means of the bilateral laplace transform finally the monotonicity and uniqueness up to the translation of traveling wave solutions are also obtained by the strong comparison principle and the sliding method

constructing instruments for regressions with measurement error when no additional data are available with an application to patents and r d constructing instruments for regressions with measurement error when no additional data are available with an application to patents and r d

nonparametric regression with errors in variables the effect of errors in variables in nonparametric regression estimation is examined to account for errors in covariates deconvolution is involved in the construction of a new class of kernel estimators it is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution in fact there are two types of rates of convergence according to whether the error is ordinary smooth or super smooth it is also shown that these results hold uniformly over a class of joint distributions of the response and the covariate which is rich enough for many practical applications furthermore to achieve optimality we show that the convergence rates of all possible estimators have a lower bound possessed by the kernel estimators

on the optimal rates of convergence for nonparametric deconvolution problems deconvolution problems arise in a variety of situations in statistics an interesting problem is to estimate the density f of a random variable x based on n i i d observations from y x varepsilon where varepsilon is a measurement error with a known distribution in this paper the effect of errors in variables of nonparametric deconvolution is examined insights are gained by showing that the difficulty of deconvolution depends on the smoothness of error distributions the smoother the harder in fact there are two types of optimal rates of convergence according to whether the error distribution is ordinary smooth or supersmooth it is shown that optimal rates of convergence can be achieved by deconvolution kernel density estimators

nonparametric identification of dynamic models with unobserved state variables we consider the identification of a markov process wt x t when only wt a subset of the variables are observed in structural dynamic models wt includes the sequences of choice variables and observed state variables of an optimizing agent while xdenotes the sequence of serially correlated unobserved state variables in the non stationary case we show that the markov law of motion fwt x wt 1 x t 1 is identified from the observation of five periods of data wt 1 wt wt 1 wt 2 wt 3 under reason able assumptions in the stationary case only four observations wt 1 wt wt 1 wt 2 are required identification of fwt x t wt 1 x t 1 is a crucial input in methodologies for estimating markovian dynamic models based on the conditional choice probability ccp approach pioneered by hotz and miller

non linear determinacy of minimum wave speed for a lotka volterra competition model abstract for a reaction diffusion system that serves as a 2 species lotka volterra diffusive competition model suppose that the corresponding reaction system has one stable boundary equilibrium and one unstable boundary equilibrium then it is well known that there exists a positive number c called the minimum wave speed such that for each c larger than or equal to c the reaction diffusion system has a positive traveling wave solution of wave speed c connecting these two equilibria if and only if c c it has been shown that the minimum wave speed for this system is identical to another important quantity the asymptotical speed of population spread towards the stable equilibrium hence to find the minimum wave speed c not only is of the interest in mathematics but is of the importance in application it has been conjectured that the minimum wave speed can be determined by studying the eigenvalues of the unstable equilibrium called the linear determinacy in this paper we will show that the conjecture on the linear determinacy is not true in general

estimation of censored linear errors in variables models this paper deals with a linear errors in variables model where the dependent variable is censored a two step procedure is proposed to estimate the model and the corresponding asymptotic covariance matrices are derived the framework covers the usual error free tobit model as a special case it is shown that under normality and a certain identifying condition this model can be uniquely reduced to an error free censored regression model and hence the existing estimators for the tobit model can be used to obtain estimators for this model in particular the maximum likelihood estimator is derived in this way the small sample behavior of the two estimators and their sensitivities to misspecified identifying information are studied through monte carlo simulations

consistent estimation for some nonlinear errors in variables models abstract the issues of identification and estimation of nonlinear errors in variables models are explored the deficiencies of the conventional definition of identification are discussed and an alternative definition in terms of observed samples is suggested the consistency and asymptotic normality of minimum distance estimators are studied to simplify the computation a two step estimation procedure is also suggested in which a consistent estimate of a subset of parameters is first obtained and treated as if they were known in the second step estimation of the rest of the parameters conditions for the consistency of this two step estimator and its asymptotic variance covariance matrix are also derived

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

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

nonparametric errors in variables models with measurement errors on both sides of the equation abstract measurement errors are often correlated as in surveys where respondent s biases or tendencies to err affect multiple reported variables we extend schennach 2007 to identify moments of the conditional distribution of a true y given a true x when both are measured with error the measurement errors in y and x are correlated and the true unknown model of y given x has nonseparable model errors after showing nonparametric identification we provide a sieve generalized method of moments based estimator of the model and apply it to nonparametric engel curve estimation in our application measurement errors on the expenditures of a good y are by construction correlated with measurement errors in total expenditures x this problem which is present in many consumption data sets has been ignored in most demand applications we find that accounting for this problem casts doubt on hildenbrand s 1994 increasing dispersion assumption

traveling waves for a model of the belousov zhabotinsky reaction abstract following j d murray we consider a system of two differential equations that models traveling fronts in the noyes field theory of the belousov zhabotinsky bz chemical reaction we are also interested in the situation when the system incorporates a delay h 0 as we show the bz system has a dual character it is monostable when its key parameter r 0 1 and it is bistable when r 1 for h 0 r 1 and for each admissible wave speed we prove the uniqueness of monotone wavefronts next a concept of regular super solutions is introduced as a main tool for generating new comparison solutions for the bz system this allows to improve all previously known upper estimations for the minimal speed of propagation in the bz system independently whether it is monostable bistable delayed or not special attention is given to the critical case r 1 which to some extent resembles to the zeldovich 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