Adaptive Estimation of Causal Periodic Autoregressive Model

作者：Bentarzi M^*; Guerbyenne H; Merzougui M

来源：Communications in Statistics - Simulation and Computation, 2009, 38(8): 1592-1609.

DOI：10.1080/03610910903061006

• Adaptive estimation
• Asymptotic linearity
• Central sequence
• Local asymptotic normality
• Locally asymptotic minimax estimator
• Periodic autoregressive model

This article deals with the adaptive estimation of a periodic autoregressive model, with unspecified innovation density satisfying only some general technical assumptions. We first establish, while verifying the adapted sufficient conditions of Swensen (1985) to our model, the Local Asymptotic Normality (LAN), the Local Asymptotic Quadratic (LAQ), and the Local Asymptotic properties satisfied by its central sequence. Secondly, the Locally Asymptotically Minimax (LAM) estimators are constructed. Using these results, we construct the adaptive estimators of the unknown autoregressive parameters. The performances of the established estimators are shown, via simulation studies.

• 出版日期2009