Higher‐order asymptotics of minimax estimators for time series
Higher‐order asymptotics of minimax estimators for time series
复制标题
时间序列极小极大估计量的高阶渐近
DOI：
10.1111/jtsa.12661
复制
发表时间：
2022
影响因子：
0.9
通讯作者：
Taniguchi Masanobu
中科院分区：
文献类型：
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作者：
Xu Xiaofei;Liu Yan;Taniguchi Masanobu
本文从高阶渐近理论的角度考虑时间序列的极大极小估计。在贝叶斯推理的框架下，我们重点研究了参数估计的贝叶斯估计和贝叶斯惠特尔估计。结果表明，这些估计是极小极大的贝叶斯风险的高阶偏差出现在他们的渐近展开。讨论了在参数空间边界上含参数的边值问题的极大极小问题。我们的理论发现是合理的模拟研究，即使当样本量很小。
We consider the minimax estimation of time series in view of higher‐order asymptotic theory. Under the framework of Bayesian inference, we focus on the Bayes estimator and the Bayesian Whittle estimator for parameter estimation. It is shown that these estimators are minimax with respect to the Bayes risk of higher‐order bias appeared in their asymptotic expansion. The minimax problem in the boundary issue with parameter on the boundary of parameter space is also discussed. Our theoretical discovery is justified by simulation studies even when the sample size is small.