https://utt.hal.science/hal-02883351Nikiforov, IgorIgorNikiforovLM2S - Laboratoire Modélisation et Sûreté des Systèmes - ICD - Institut Charles Delaunay - UTT - Université de Technologie de Troyes - CNRS - Centre National de la Recherche ScientifiqueAsymptotically Efficient Estimation of a Nonlinear Model of the Heteroscedasticity*HAL CCSD2012[INFO] Computer Science [cs][INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]VU VAN, Jean-Baptiste2020-06-29 09:31:202023-03-24 14:53:182020-06-29 09:31:20enConference papers10.3182/20120711-3-BE-2027.000451The paper is devoted to the estimation of a nonlinear parametric model of the heteroscedasticity. The heteroscedasticity occurs in regression when the measurement noise variance is non-constant. Sometimes, the noise variance can be represented as a parameterized function of independent variables, so-called variance function. The maximum likelihood estimation (MLE) of variance function parameters leads to a system of nonlinear equations. The iterative solution of these nonlinear equations is based entirely on a successful choice of initial conditions. Hence, in the practice, the nonlinear MLE is intractable. To overcome this difficulty, another linear quasi-MLE estimator is proposed. It is strongly consistent, asymptotically Gaussian and only slightly less efficient than the Cramer-Rao lower bound. By using this estimator as an initial condition, an asymptotically efficient estimation is obtained by using one-step non-iterative Newton method. This approach has been applied to the GPS navigation in the constrained (urban) environment.