论文标题
不规则创新的时变一阶自回归过程
Time-varying first-order autoregressive processes with irregular innovations
论文作者
论文摘要
我们考虑具有不规则创新的时变一阶自回归模型，我们假设系数函数是hölder连续的。为了估算此功能，我们使用基于准最大可能性的方法。对这种方法的精确控制需要对某些弱依赖过程的极端进行精致的分析，我们的主要结果是对此类数量的集中不平等。基于我们的分析，得出了上层和匹配的最小值下限，显示了我们的估计器的最佳性。与常规情况不同，信息理论复杂性既取决于平滑度和附加形状参数，却表征了基础分布的不规则性。证明的结果和想法与与统计数据有关的经典和最新方法截然不同。
We consider a time-varying first-order autoregressive model with irregular innovations, where we assume that the coefficient function is Hölder continuous. To estimate this function, we use a quasi-maximum likelihood based approach. A precise control of this method demands a delicate analysis of extremes of certain weakly dependent processes, our main result being a concentration inequality for such quantities. Based on our analysis, upper and matching minimax lower bounds are derived, showing the optimality of our estimators. Unlike the regular case, the information theoretic complexity depends both on the smoothness and an additional shape parameter, characterizing the irregularity of the underlying distribution. The results and ideas for the proofs are very different from classical and more recent methods in connection with statistics and inference for locally stationary processes.
