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.

中文翻译：

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时间序列极小极大估计量的高阶渐近

我们根据高阶渐近理论考虑时间序列的极小极大估计。在贝叶斯推理的框架下，我们主要关注贝叶斯估计器和用于参数估计的贝叶斯惠特尔估计器。结果表明，这些估计量对于在其渐近展开中出现的高阶偏差的贝叶斯风险而言是极小极大的。还讨论了参数在参数空间边界上的边界问题中的极小极大问题。即使样本量很小，我们的理论发现也可以通过模拟研究得到证明。