自回归大数据模型的自适应高效鲁棒序贯分析
Adaptive efficient robust sequential analysis for autoregressive big data models
摘要：
在本文中，我们考虑通过自回归过程定义的依赖观测的高维模型。对于这样的模型，我们开发了一个自适应有效的估计方法，通过稳健的序贯模型选择程序。为此，首先利用Van Trees不等式，得到了鲁棒风险的一个精确的下界，该下界由著名的Pinsker常数给出.应该注意的是，对于这种模型，该常数是首次计算的。然后，利用加权最小二乘法和尖锐的非渐近预言不等式，我们提供了效率性质的极小极大意义下的估计程序，即我们建立，其风险的上界与所获得的下界一致。应该强调的是，这一性质是在不使用稀疏条件和参数维数和模型正则性未知的自适应设置中获得的。
英文摘要：
In this paper we consider high dimension models based on dependent observations defined through autoregressive processes. For such models we develop an adaptive efficient estimation method via the robust sequential model selection procedures. To this end, firstly, using the Van Trees inequality, we obtain a sharp lower bound for robust risks in an explicit form given by the famous Pinsker constant. It should be noted, that for such models this constant is calculated for the first time. Then, using the weighted least square method and sharp non asymptotic oracle inequalities we provide the efficiency property in the minimax sense for the proposed estimation procedure, i.e. we establish, 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.
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