| Abstrakt: |
In this article, we consider high-dimensional models based on dependent observations defined through autoregressive processes. For such models we develop an adaptive efficient estimation method via robust sequential model selection procedures. To this end, we first obtain Van Tree's inequality for such models and then, using this inequality, we probably for the first time obtain a sharp lower bound for the weighted robust risk in an explicit form given by the new Pinsker constant, which is represented through the nonparametric version of the Fisher information for this model. Then, using the weighted least squares method and sharp nonasymptotic oracle inequalities from Arkoun, Brua, and Pergamenchtchikov (2019), we develop an analytic tool to provide the efficiency property in the minimax sense for the proposed estimation procedure; that is, we show that the upper bound for its risk coincides with the obtained lower bound. It should be emphasized that this property is obtained without using sparse conditions and in the adaptive setting when the parameter dimension and model regularity are unknown. We then study the constructed procedures numerically using Monte Carlo simulations. [ABSTRACT FROM AUTHOR] |
