Semiparametric regression estimation using noisy nonlinear non invertible functions of the observations
Elisabeth Gassiat and Benoit Landelle
We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of
the observations. We focus on the application to bearings-only tracking. We first investigate
the least squares estimator and prove its consistency and asymptotic normality under mild assumptions.
We study the semiparametric likelihood process and prove local asymptotic normality of the model.
This allows to define the efficient Fisher information as a lower bound for the asymptotic variance of
regular estimators, and to prove that the parametric likelihood estimator is regular and asymptotically
efficient. Simulations are presented to illustrate our results.