In Principal Component Analysis (PCA), the dimension of the signal subspace is detected by counting the number of eigenvalues of a covariance matrix that are above a threshold. Random matrix theory provides accurate estimates for this threshold if the underlying data matrix has independent identically distributed columns. However, in time series analysis, the underlying data matrix has a Hankel or Toeplitz structure, and the columns are not independent. Using an empirical approach, we observe that the largest eigenvalue is fitted well by a Generalized Extreme Value (GEV) distribution, and we obtain accurate estimates for the thresholds to be used in a sequential rank detection test. In contrast to AIC or MDL, this provides a parameter that controls the probability of false alarm. Also a lower bound is presented for the rank detection rate of threshold-based detection for rank-1 problems.
|Title of host publication||28th European Signal Processing Conference (EUSIPCO 2020)|
|Place of Publication||Amsterdam (Netherlands)|
|Number of pages||5|
|Publication status||Published - 1 Aug 2020|
|Event||EUSIPCO 2020: The 28th European Signal Processing Conference - Amsterdam, Netherlands|
Duration: 18 Jan 2021 → 22 Jan 2021
Conference number: 28th
|Period||18/01/21 → 22/01/21|
|Other||Date change due to COVID-19 (former date August 24-28 2020)|
- structured Wishart matrix
- rank detection
- Generalized Extreme Value
van der Veen, A. J., Romme, J. P. A., & Cui, Y. (2020). Rank detection thresholds for Hankel or Toeplitz data matrices. In 28th European Signal Processing Conference (EUSIPCO 2020) (pp. 1911-1915). Eurasip.