Test for Bandedness of High Dimensional Covariance Matrices with Bandwidth Estimation

By Yumou Qiu, Songxi Chen. 2012

70 citations recorded by the source corpus.

Motivated by the latest effort to employ banded matrices to estimate a high-dimensional covariance Σ , we propose a test for Σ being banded with possible diverging bandwidth. The test is adaptive to the “large p , small n ” situations without assuming a specific parametric distribution for the data. We also formulate a consistent estimator for the bandwidth of a banded high-dimensional covariance matrix. The properties of the test and the bandwidth estimator are investigated by theoretical evaluations and simulation studies, as well as an empirical analysis on a protein mass spectroscopy data.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e5a3315b6756c169a7743436f601863e346674e4

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Citations in the corpus

Global Testing and Large-Scale Multiple Testing for High-Dimensional Covariance Structures (2017, methodology): “Qiu and Chen (2012) proposed a test based on a U -statistic which is an unbiased estimator of ∑ |i−j|≥k σ 2 i,j for testing bandedness of Σ. Compared with the test proposed in Cai and Jiang (2011), which is powerful for sparse alternatives, the test introduced in Qiu and Chen (2012) is powerful for…”
Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, methodology): “Qiu and Chen (2012) constructed an unbiased estimator of Σ|i−j|≥kσ 2 ij via certain U -statistic to test banded covariance structure H0 (k), motivated by the Frobenius distance-based tests in Chen et al. (2010).”
Covariance Regression Analysis (2017, unknown): “Furthermore, the banded covariance matrix is (σ j1 j2 I{| j1 − j2| ≤ m})p×p, which has attracted considerable attention in the existing literature (Cai and Jiang 2011; Qiu and Chen 2012).”
Likelihood Ratio Tests for High‐Dimensional Normal Distributions (2013, background): “(iii) Recently, some authors study similar problems under the nonparametric setting, for example, the works of Cai et al. (2013), Cai & Ma (2013), Chen et al. (2010), Li & Chen (2012), Qiu & Chen (2012) and Xiao & Wu (2013).”
Testing mutual independence in high dimension via distance covariance (2016, methodology): “Schott (2005), in contrast, used the L2-type statistic with pairwise Pearson correlations, which attained a standard normal limiting null distribution.”
High‐dimensional covariance matrix estimation (2019, background): “Qiu and Chen (2012) proposed a criterion leading to consistent estimation of the banding parameter, while both Li and Zou (2016) and Li et al. (2018) analyzed the Stein’s unbiased risk estimation (SURE) information criterion for a class of bandable covariance matrices, with minimizing such a…”