Stochastic Simulation for Inference in Nonlinear Errors-in- Variables Models

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This project will study inference in simultaneous nonlinear error-in-variables models - identification, estimation, prediction and specification testing. The linkages between identifiability and nonlinearities in the measurement error model will be studied and appropriate sufficient identifiability conditions analyzed. The consequences of measurement errors on standard procedures for testing hypotheses, estimation and validation in nonlinear models will be studied. Parametric and semiparametric procedures are established for the estimation of nonlinear error-in-variables models. Modifications of Monte Carlo and residual-based stochastic simulations are developed to handle measurement error problems and adapted to not only prediction but also estimation and specification testing. The large-sample asymptotic theory for these procedures will be developed. Particular attention is given to the treatment of the measurement error generating process. The standard Gaussian white nose model for measurement errors is the starting point for the analysis. Analysis then continues to less restrictive and more appropriate measurement error models which are nonlinear and non-Gaussian. Simultaneous systems with limited dependent variables are used for a more specific examination of the applicability of the new techniques.