基于Welch方法凝聚谱的偏差与方差估计

Estimation of Deviation and Variance of MSC Based on Welch Method

在有限的数据量下,采用Welch方法可以使凝聚谱(MSC)估计量获得更小的偏差与方差,然而此时估计量的分布尚未导出,致使MSC估计量的偏差与方差无从获得。给出了四种偏差与方差的估计方法,即采用N_(d)(独立分段数)、N_(s)(总分段数)、N_(c1)(修正自由度法)和N_(c2)(参数估计法)修正非重叠情形下偏差与方差的计算公式,通过随机模拟比较四种方法在不同重叠率和分段数下的优劣,最后给出四种方法的适用范围:在25%重叠率下,使用N_(s)、N_(c1)和N_(c2)得到的估计值与实际值比较吻合;在50%重叠率下,使用N_(c1)和N_(c2)得到的估计值与实际值比较接近;而在75%的重叠率下,N_(c1)和N_(c2)分别需要在分段数超过11和5的情况下使用。

Under the limited amount of data,using Welch method can make the condensed spectrum(MSc)estimator obtain smaller deviation and variance.However,at this time,the distribution of the estimator has not been derived,so that the deviation and variance of MSC estimator cannot be obtained.In this paper,four methods were given,that is,using N_(d),N_(s),N_(c1),and N_(c2) to correct the calculation formula of deviation and variance in the case of non overlapping.Through random simulation,the advantages and disadvantages of the four methods under different overlap rates and segment numbers are compared,and finally the application scope of the four methods is given.For 25%overlapping ratio,the deviation and variance calculated by N_(s),N_(c1),and N_(c2) are closed to real values.2.For 50%overlapping ratio,N_(c1) and N_(c2) can get more precise estimates of the deviation and variance.3.For 75%overlapping ratio,N_(c1) and N_(c2) should be used when number of segments is more than 11 and 5,respectively.