ASYMPTOTIC EFFICIENCY IN THE AUTOREGRESSIVE PROCESS DRIVEN BY A STATIONARY GAUSSIAN NOISE

Marius Soltane (1)

1 LMM - Laboratoire Manceau de Mathématiques

The first purpose of this article is to obtain a.s. asymptotic properties of the maximum likelihood estimator in the autoregressive process driven by a stationary Gaussian noise. The second purpose is to show the local asymptotic normality property of the likelihoods ratio in order to get a notion of asymptotic efficiency and to build an asymptotically uniformly invariant most powerful procedure for testing the significance of the autoregressive parameter.

Domaines: Statistiques [stat]; Mathématiques [math]

Marius Soltane. ASYMPTOTIC EFFICIENCY IN THE AUTOREGRESSIVE PROCESS DRIVEN BY A STATIONARY GAUSSIAN NOISE. 2018. ⟨hal-01899971⟩