The authors of the method suggest to use Fuller's modified IV estimator. Here function g can be either parametric or non-parametric.
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Despite this optimistic result, as of now no methods exist for estimating non-linear errors-in-variables models without any extraneous information. However there are several techniques which make use of some additional data: either the instrumental variables, or repeated observations.
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Both observations contain their own measurement errors, however those errors are required to be independent:. If this function could be known or estimated, then the problem turns into standard non-linear regression, which can be estimated for example using the NLLS method. All densities in this formula can be estimated using inversion of the empirical characteristic functions. In particular,.
In order to invert these characteristic function one has to apply the inverse Fourier transform, with a trimming parameter C needed to ensure the numerical stability. For example:.
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If not for the measurement errors, this would have been a standard linear model with the estimator. It turns out that all the expected values in this formula are estimable using the same deconvolution trick. From Wikipedia, the free encyclopedia. Regression models accounting for possible errors in independent variables. Method of moments — the GMM estimator based on the third- or higher- order joint cumulants of observable variables. Total least squares is an extension of Deming regression to the multivariable setting. This method is the simplest from the implementation point of view, however its disadvantage is that it requires to collect additional data, which may be costly or even impossible.
Li's conditional density method for parametric models. Schennach's estimator for a nonparametric model. Both expectations here can be estimated using the same technique as in the previous method. Annual Review of Economics. Journal of Statistical Planning and Inference. Econometric Analysis 5th ed. New Jersey: Prentice Hall. Chapter 5.
In Baltagi, B. A Companion to Theoretical Econometrics. Journal of Economic Perspectives. Measurement Error Models. Princeton University Press.
A somewhat more restrictive result was established earlier by Geary, R. Proceedings of the Royal Irish Academy. Journal of Econometrics. An earlier proof by Willassen contained errors, see Willassen, Y.
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Micro-Econometrics: Methods of Moments and Limited Dependent Variables
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