标题： 利用带噪声的非线性不可逆观测函数进行半参数回归估计 显示英文标题

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

摘要： 我们研究了一种半参数回归模型，其中观测值的非线性、不可逆函数带有噪声。我们将重点放在这一方法在基于角度测量的跟踪问题中的应用上。首先，我们研究了最小二乘估计量，并在温和假设下证明了其一致性和渐近正态性。接着，我们研究了半参数似然过程，并证明了模型的局部渐近正态性。这使得我们可以定义有效Fisher信息作为正则估计量渐近方差的一个下界，并证明参数似然估计量是正则且渐近有效的。最后，通过模拟实验验证了我们的理论结果。 显示英文摘要

摘要： 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.