PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Semiparametric regression estimation using noisy nonlinear non invertible functions of the observations
Elisabeth Gassiat and Benoit Landelle
arxiv 2008.

Abstract

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.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:4874
Deposited By:Elisabeth Gassiat
Deposited On:24 March 2009