### THE EXPANSION OF A SIMEX ESTIMATOR IN THE NONLINEAR ERRORS-IN-VARIABLES MODEL WITH SMALL MEASUREMENT ERRORS

**OLENA GONTAR AND HELMUT KÜCHENHOFF**

*Theory of Stochastic Processes*

*Vol. 14 (30), no. 1, 2008, pp. 39–48*

The nonlinear structural errors-in-variables model is investigated. We consider a Simex estimator with polynomial extrapolation function. The expansion of a Simex estimator is based on the asymptotic expansion of a naive estimator for small measurement errors. It is shown that the Simex estimator has an asymptotic deviation from a true value of the unknown parameter which is negligible compared with a measurement error variance, while the deviation of the naive estimator is proportional to the measurement error variance.

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