Adaptive estimator of the memory parameter and goodness-of-fit test using a multidimensional increment ratio statistic

Jean-Marc Bardet (1) , Béchir Dola (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

The increment ratio (IR) statistic was first defined and studied in Surgailis {\it et al.} (2007) for estimating the memory parameter either of a stationary or an increment stationary Gaussian process. Here three extensions are proposed in the case of stationary processes. Firstly, a multidimensional central limit theorem is established for a vector composed by several IR statistics. Secondly, a goodness-of-fit $\chi^2$-type test can be deduced from this theorem. Finally, this theorem allows to construct adaptive versions of the estimator and test which are studied in a general semiparametric frame. The adaptive estimator of the long-memory parameter is proved to follow an oracle property. Simulations attest of the interesting accuracies and robustness of the estimator and test, even in the non Gaussian case.

Mots clés: minimax adaptive estimator; Long-memory Gaussian processes; goodness-of-fit test; estimation of the memory parameter; minimax adaptive estimator.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-Marc Bardet, Béchir Dola. Adaptive estimator of the memory parameter and goodness-of-fit test using a multidimensional increment ratio statistic. Journal of Multivariate Analysis, 2012, 105, pp.222-240. ⟨hal-00522842v2⟩