√2-Estimation for Smooth Eigenvectors of Matrix-Valued Functions

IF 2.4 2区 数学 Q2 BIOLOGY
Biometrika Pub Date : 2023-03-15 DOI:10.1093/biomet/asad018
Giovanni Motta, W. Wu, M. Pourahmadi
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引用次数: 0

Abstract

Modern statistical methods for multivariate time series rely on the eigendecomposition of matrix-valued functions such as time-varying covariance and spectral density matrices. The curse of indeterminacy or misidentification of smooth eigenvector functions has not received much attention. We resolve this important problem and recover smooth trajectories by examining the distance between the eigenvectors of the same matrix-valued function evaluated at two consecutive points. We change the sign of the next eigenvector if its distance with the current one is larger than the square root of 2. In the case of distinct eigenvalues, this simple method delivers smooth eigenvectors. For coalescing eigenvalues, we match the corresponding eigenvectors and apply an additional signing around the coalescing points. We establish consistency and rates of convergence for the proposed smooth eigenvector estimators. Simulation results and applications to real data confirm that our approach is needed to obtain smooth eigenvectors.
√2-矩阵值函数光滑特征向量的估计
多元时间序列的现代统计方法依赖于矩阵值函数的本征分解,如时变协方差和谱密度矩阵。光滑特征向量函数的不确定性或错误识别的诅咒没有得到太多关注。我们解决了这个重要问题,并通过检查在两个连续点上评估的同一矩阵值函数的特征向量之间的距离来恢复平滑轨迹。如果下一个特征向量与当前特征向量的距离大于2的平方根,我们将更改其符号。在特征值不同的情况下,这种简单的方法可以提供平滑的特征向量。对于聚结特征值,我们匹配相应的特征向量,并在聚结点周围应用额外的符号。我们建立了所提出的光滑特征向量估计的一致性和收敛速度。仿真结果和实际数据的应用证实了我们的方法需要获得平滑的特征向量。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Biometrika
Biometrika 生物-生物学
CiteScore
5.50
自引率
3.70%
发文量
56
审稿时长
6-12 weeks
期刊介绍: Biometrika is primarily a journal of statistics in which emphasis is placed on papers containing original theoretical contributions of direct or potential value in applications. From time to time, papers in bordering fields are also published.
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