发帖
雷达卡
摘要翻译：
我们提出了一种数学上合理、计算上简单、基于样本特征值的方法，用于用相对较少的样本估计白噪声中高维信号的数目。考虑基于样本特征值的方案的主要动机是计算简单和对特征向量建模误差的鲁棒性，这些误差会对利用样本特征向量信息的估计器的性能产生不利影响。然而，我们要付出代价，丢弃样本特征向量中的信息；我们强调了一个基于样本特征值的弱/紧密间隔高维信号检测的基本渐近极限。这激发了我们对可识别信号的有效个数的启发式定义，该定义等于总体协方差矩阵的“信号”特征值的个数，该特征值超出噪声方差一个严格大于1+SQRT（系统维数/样本大小）的因子。基本渐近极限引起了一个尖锐的焦点，为什么当可用的样本太少以至于有效信号数小于实际信号数时，当使用任何基于样本特征值的检测方案时，包括本文提出的方案，模型阶的低估是不可避免的（在渐近意义上）。分析揭示了为什么增加更多的传感器只会加剧情况。数值仿真表明，该估计器在维数固定、大样本容量限制下能一致地估计出真实信号数，在维数固定、大样本容量限制下能一致地估计出有效可识别信号数，而在维数固定、大样本容量限制下能一致地估计出有效可识别信号数。
---
英文标题：
《Sample eigenvalue based detection of high dimensional signals in white
noise using relatively few samples》
---
作者：
N. Raj Rao and Alan Edelman
---
最新提交年份：
2007
---
分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
--
一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--
---
英文摘要：
We present a mathematically justifiable, computationally simple, sample eigenvalue based procedure for estimating the number of high-dimensional signals in white noise using relatively few samples. The main motivation for considering a sample eigenvalue based scheme is the computational simplicity and the robustness to eigenvector modelling errors which are can adversely impact the performance of estimators that exploit information in the sample eigenvectors. There is, however, a price we pay by discarding the information in the sample eigenvectors; we highlight a fundamental asymptotic limit of sample eigenvalue based detection of weak/closely spaced high-dimensional signals from a limited sample size. This motivates our heuristic definition of the effective number of identifiable signals which is equal to the number of "signal" eigenvalues of the population covariance matrix which exceed the noise variance by a factor strictly greater than 1+sqrt(Dimensionality of the system/Sample size). The fundamental asymptotic limit brings into sharp focus why, when there are too few samples available so that the effective number of signals is less than the actual number of signals, underestimation of the model order is unavoidable (in an asymptotic sense) when using any sample eigenvalue based detection scheme, including the one proposed herein. The analysis reveals why adding more sensors can only exacerbate the situation. Numerical simulations are used to demonstrate that the proposed estimator consistently estimates the true number of signals in the dimension fixed, large sample size limit and the effective number of identifiable signals in the large dimension, large sample size limit.
---
PDF链接：
https://arxiv.org/pdf/705.2605
京公网安备 11010802022788号
