nonlinear and nonparametric regression and instrumental variables we consider regression when the predictor is measured with error and an instrumental variable iv is available the regression function can be modeled linearly nonlinearly or nonparametrically our major new result shows that the regression function and all parameters in the measurement error model are identified under relatively weak conditions much weaker than previously known to imply identifiability in addition we exploit a characterization of the iv estimator as a classical correction for attenuation method based on a particular estimate of the variance of the measurement error this estimate of the measurement error variance allows us to construct functional nonparametric regression estimators making no assumptions about the distribution of the unobserved predictor and structural estimators that use parametric assumptions about this distribution the functional estimators uses simulation extrapolation or deconvolution kernels and the structural method uses bayesian markov chain monte carlo

nonparametric regression in the presence of measurement error summary in many regression applications the independent variable is measured with error when this happens conventional parametric and nonparametric regression techniques are no longer valid we consider two diverent approaches to nonparametric regression the first uses the simex simulation extrapolation method and makes no assumption about the distribution of the unobserved error prone predictor for this approach we derive an asymptotic theory for kernel regression which has some surprising implications penalised regression splines are also considered for fixed number of known knots the second approach assumes that the error prone predictor has a distribution of a mixture of normals with an unknown number of components and uses regression splines simulations illustrate the results

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

monte carlo methods for nonparametric regression with heteroscedastic measurement error nonparametric regression is a fundamental problem in statistics but challenging when the independent variable is measured with error among the first approaches was an extension of deconvoluting kernel density estimators for homescedastic measurement error the main contribution of this article is to propose a new simulation based nonparametric regression estimator for the heteroscedastic measurement error case similar to some earlier proposals our estimator is built on principles underlying deconvoluting kernel density estimators however the proposed estimation procedure uses monte carlo methods for estimating nonlinear functions of a normal mean which is different than any previous estimator we show that the estimator has desirable operating characteristics in both large and small samples and apply the method to a study of benzene exposure in chinese factory workers

on deconvolution with repeated measurements in a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known although in many applications it is unrealistic to make this assumption the problem is often insoluble without it however if additional data are available then it is possible to estimate consistently the unknown error density data are seldom available directly on the transformation but repeated or replicated measurements increasingly are becoming available such data consist of intrinsic values that are measured several times with errors that are generally independent working in this setting we treat the nonparametric deconvolution problems of density estimation with observation errors and regression with errors in variables we show that even if the number of repeated measurements is quite small it is possible for modified kernel estimators to achieve the same level of performance they would if the error distribution were known indeed density and regression estimators can be constructed from replicated data so that they have the same first order properties as conventional estimators in the known error case without any replication but with sample size equal to the sum of the numbers of replicates practical methods for constructing estimators with these properties are suggested involving empirical rules for smoothing parameter choice

blow up of periodic solutions to reducible quasilinear hyperbolic systems under general assumption we prove that the smooth solution to reducible quasilinear hyperbolic system with periodic initial data in general develop singularities in finite time provided that the total variation on one period of the initial data is small

using simex for smoothing parameter choice in errors in variables problems simex methods are attractive for solving curve estimation problems in errors in variables regression using parametric or semiparametric techniques however nonparametric approaches are generally of quite a different type being based on for example kernels local linear modeling ridging orthogonal series or splines all of these techniques involve the challenging and not well studied issue of empirical smoothing parameter choice we show that simex can be used effectively for selecting smoothing parameters when applying nonparametric methods to errors in variable regression in particular we suggest an approach based on multiple error inflated or remeasured data sets and extrapolation

low order approximations in deconvolution and regression with errors in variables summary we suggest two new methods which are applicable to both deconvolution and regression with errors in explanatory variables for nonparametric inference the two approaches involve kernel or orthogonal series methods they are based on defining a low order approximation to the problem at hand and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently of course both techniques could be employed to construct consistent estimators but in many contexts of importance e g those where the errors are gaussian consistency is from a practical viewpoint an unattainable goal we rephrase the problem in a form where an explicit interpretable low order approximation is available the information that we require about the error distribution the error in variables distribution in the case of regression is only in the form of low order moments and so is readily obtainable by a rudimentary analysis of indirect measurements of errors e g through repeated measurements in particular we do not need to estimate a function such as a characteristic function which expresses detailed properties of the error distribution this feature of our methods coupled with the fact that all our estimators are explicitly defined in terms of readily computable averages means that the methods are particularly economical in computing time

estimating a nonlinear function of a normal mean summary we derive a monte carlo amenable minimum variance unbiased estimator of a nonlinear function of a normal mean and the variance of the estimator applications to problems arising in the analysis of data measured with error are described

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

local polynomial regression and simulation extrapolation summary the paper introduces a new local polynomial estimator and develops supporting asymptotic theory for nonparametric regression in the presence of covariate measurement error we address the measurement error with cook and stefanski s simulation extrapolation simex algorithm our method improves on previous local polynomial estimators for this problem by using a bandwidth selection procedure that addresses simex s particular estimation method and considers higher degree local polynomial estimators we illustrate the accuracy of our asymptotic expressions with a monte carlo study compare our method with other estimators with a second set of monte carlo simulations and apply our method to a data set from nutritional epidemiology simex was originally developed for parametric models although simex is in principle applicable to nonparametric models a serious problem arises with simex in nonparametric situations the problem is that smoothing parameter selectors that are developed for data without measurement error are no longer appropriate and can result in considerable undersmoothing we believe that this is the first paper to address this difficulty

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

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

bayesian smoothing and regression splines for measurement error problems in the presence of covariate measurement error estimating a regression function nonparametrically is extremely difficult the problem being related to deconvolution various frequentist approaches exist for this problem but to date there has been no bayesian treatment in this article we describe bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error the regression function is modeled with smoothing splines and regression p splines two methods are described for exploration of the posterior the first called the iterative conditional modes icm is only partially bayesian icm uses a componentwise maximization routine to find the mode of the posterior it also serves to create starting values for the second method which is fully bayesian and uses markov chain monte carlo mcmc techniques to generate observations from the joint posterior distribution use of the mcmc approach has the advantage that interval estimates that directly model and

nonlinear generalized lifting line coupling algorithms for pre poststall flows numerical algorithms and solutions of generalized nonlinear lifting line theory over an elliptical wing are examined with emphasis on near poststall flows first a thorough analysis on the circulation based and angle of attack based correction methods and methods respectively highlights their respective numerical poststall characteristics the stability of the method is demonstrated producing single and multiple solutions in the pre and poststall regions respectively second artificial dissipation added to the method is shown to be an effective means of controlling the poststall flow region finally a strongly coupled algorithm is presented allowing to bypass the interpolation phase via the use of legendre polynomials the model sheds light on poststall flow behavior in agreement with several papers studying formation of stall cell patterns

adverse yaw control during roll for a class of optimal lift distributions lifting line theory has formed the basis of wing design understanding for nearly a century this theory has previously been used to develop a class of optimal lift distributions that minimize induc

confidence bands in non parametric errors in variables regression summary errors in variables regression is important in many areas of science and social science e g in economics where it is often a feature of hedonic models in environmental science where air quality indices are measured with error in biology where the vegetative mass of plants is frequently obscured by mismeasurement and in nutrition where reported fat intake is typically subject to substantial error to date in non parametric contexts the great majority of work has focused on methods for estimating the mean as a function with relatively little attention being paid to techniques for empirical assessment of the accuracy of the estimator we develop methodologies for constructing confidence bands our contributions include techniques for tuning parameter choice aimed at minimizing the coverage error of confidence bands

corrected score estimation via complex variable simulation extrapolation a monte carlo method of computing unbiased estimating equations for the analysis of data measured with error is described asymptotic distribution results are obtained for estimators derived from the monte carlo estimating equations the method is illustrated with examples applications and simulation studies the monte carlo estimating equations are corrected scores in the sense of nakamura and the proposed methods are closely related to the simulation method described by cook and stefanski