Gaussian estimation of parametric spectral density with unknown pole

研究问题: 当参数谱密度在未知频率附近呈幂律行为时，如何联合估计极点位置与其他参数，尤其如何处理记忆参数估计的渐近分布？
方法与思路: 作者研究一种高斯估计方法，将未知极点频率与其余参数的渐近行为分别分析；摘要未说明目标函数与参数空间的具体形式。
材料陈述的贡献: 摘要称频率估计具有 $n$ -一致性并呈非标准极限行为，其余参数估计具有 $\sqrt{n}$ -一致性和渐近正态性。摘要称频率估计具有 $n$-一致性并呈非标准极限行为，其余参数估计具有 $\sqrt{n}$-一致性和渐近正态性。
阅读关注点: 应核对极点附近的谱形状、参数约束及估计方法定义，重点查看频率估计的非标准极限与其他参数正态推断所需条件。
阅读边界: 材料为大学仓储摘要且稿件版本未注明；摘要未给出正则条件或频率估计的具体极限分布，不能将所述速度推广至任意谱模型。

GPT-6.1 Sol · 高 · 2026-10-10

原文摘要

We consider a parametric spectral density with power-law behavior about a fractional pole at the unknown frequency $\omega$ . The case of known $\omega$ , especially $\omega =0$ , is standard in the long memory literature. When $omega$ is unknown, asymptotic distribution theory for estimates of parameters, including the (long) memory parameter, is significantly harder. We study a form of Gaussian estimate. We establish $n$ -consistency of the estimate of $\omega$ , and discuss its (non-standard) limiting distributional behavior. For the remaining parameter estimates,we establish $\sqrt{n}$ -consistency and asymptotic normality.We consider a parametric spectral density with power-law behavior about a fractional pole at the unknown frequency $\omega$. The case of known $\omega$, especially $\omega =0$, is standard in the long memory literature. When $omega$ is unknown, asymptotic distribution theory for estimates of parameters, including the (long) memory parameter, is significantly harder. We study a form of Gaussian estimate. We establish $n$-consistency of the estimate of $\omega$, and discuss its (non-standard) limiting distributional behavior. For the remaining parameter estimates,we establish $\sqrt{n}$-consistency and asymptotic normality.

摘要来源：White Rose Research Online 大学仓储摘要（稿件版本未注明）

笔记与分组

分类依据与纠错

Gaussian estimation of parametric spectral density with unknown pole

代码、数据与补充材料

极点频率未知时参数谱密度的高斯估计

原文摘要

同方向的基础文献

同方向的基础文献