论文标题
估计频率接近零的光谱密度
Estimating the Spectral Density at Frequencies Near Zero
论文作者
论文摘要
传统上，估计[-π，π] $的某些$ w \的光谱密度函数$ f（w）$是由内核平滑进行期刊和相关技术的。内核平滑度与局部平均值（即，在宽度较小的窗口上的常数近似于$ f（w）$）的差异。尽管$ f（w）$是统一的连续且周期性的$2π$，但在本文中，我们认识到，$ W = 0 $有效地充当基础内核平滑问题的边界点，而对于$ W = \pmπ$，也是如此。众所周知，在边界点（或接近）的内核回归中，局部平均可能是次优的。作为替代方案，当$ w $处于（或接近）0或$ \pmπ$时，我们提出了周期图或log periodogram的本地多项式回归。 $ w = 0 $的情况非常重要，因为$ f（0）$是样本平均值的大样本差异；因此，估计$ f（0）$对于对平均值进行任何推断至关重要。
Estimating the spectral density function $f(w)$ for some $w\in [-π, π]$ has been traditionally performed by kernel smoothing the periodogram and related techniques. Kernel smoothing is tantamount to local averaging, i.e., approximating $f(w)$ by a constant over a window of small width. Although $f(w)$ is uniformly continuous and periodic with period $2π$, in this paper we recognize the fact that $w=0$ effectively acts as a boundary point in the underlying kernel smoothing problem, and the same is true for $w=\pm π$. It is well-known that local averaging may be suboptimal in kernel regression at (or near) a boundary point. As an alternative, we propose a local polynomial regression of the periodogram or log-periodogram when $w$ is at (or near) the points 0 or $\pm π$. The case $w=0$ is of particular importance since $f(0)$ is the large-sample variance of the sample mean; hence, estimating $f(0)$ is crucial in order to conduct any sort of inference on the mean.
