Estimation of the Number of Spiked Eigenvalues in a Covariance Matrix by Bulk Eigenvalue Matching Analysis

The spiked covariance model has gained increasing popularity in high-dimensional data analysis. A fundamental problem is determination of the number eigenvalues, K. For estimation K, most attention focused on use top eigenvalues sample matrix, and there little investigation into proper ways using bulk to estimate We propose a principled approach incorporating Our method imposes working residual which assumed be diagonal matrix whose entries are drawn from gamma distribution. Under this model, asymptotically close quantiles fixed parametric This motivates us two-step method: first step uses parameters distribution, second leverages these assist resulting estimator K? aggregates information large eigenvalues. show consistency under standard model. also confidence interval for extensive simulation studies that proposed robust outperforms existing methods range scenarios. apply analysis lung cancer microarray dataset 1000 Genomes dataset.