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We investigate a semiparametric regression model where one gets noisy nonlinear non invertible functions of the observations. We focus on theapplication to bearings-only tracking. We first investigate the least squaresestimator and prove its consistency and asymptotic normality under mildassumptions. We study the semiparametric likelihood process and prove localasymptotic normality of the model. This allows to define the efficient Fisherinformation as a lower bound for the asymptotic variance of regular estimators,and to prove that the parametric likelihood estimator is regular andasymptotically efficient. Simulations are presented to illustrate our results.

Semiparametric regression estimation using noisy nonlinear non invertible functions of the observations