Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size

By Olivier Ledoit, Michael Wolf. 2002

426 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0a1cf2140c4d52a78aebaf85d83fb18bdb9b920a

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In Applied Mathematics

In Computational Theory and Mathematics

In Statistics and Probability

Citations in the corpus

Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing (2014, methodology): “[2, 3, 9, 14, 20, 21], so that LSS of the sample covariance matrices are approximated using either the CLT (1.”
Testing Cross-Sectional Correlation in Large Panel Data Models with Serial Correlation (2016, methodology): “New approaches have been considered in the statistics literature for the testing the diagonality of the sample covariance or correlation matrices; see Ledoit and Wolf [8], Schott [9] and Chen et al. [10], to mention a few.”
Eigenvectors of some large sample covariance matrix ensembles (2009, neutral): “The MarčenkoPastur equation has also generated a considerable amount of interest in statistics [13, 19], finance [17, 18], signal processing [12], and other disc iplines.”
Dimension reduction in regression without matrix inversion (2007, background): “While it works well for our application in §4, it is indeed possible that such fixed-p asymptotics may perform poorly when p → ∞ as n increases; see Ledoit & Wolf (2002).”
Quadratic Shrinkage for Large Covariance Matrices (2020, methodology): “But linearly shrinking the inverse eigenvalues is certainly no more worrisome than linearly shrinking the eigenvalues, an operation that has been well understood and accepted by researchers at least since Ledoit and Wolf (2004). Theorem 2.”
Two Sample Tests for High Dimensional Covariance Matrices (2012, methodology): “…assuming p/n i → c i ∈ [0 , ∞ ) and the normal distributions. high-dimensional There are also one sample tests for a high-dimensional variance–covariance Σ. Ledoit and Wolf (2002) and Chen, Zhang and Zhong (2010) introduced tests for Σ being sphericity and identity for normally distributed random…”
Tests for High-Dimensional Covariance Matrices (2010, methodology): “While direct substitution of by Sn brings invariance and optimal testing properties as shown in John (1971, 1972) and Nagao (1973) for normally distributed data when p is fixed, tests based on these statistics may not work for high-dimensional data as demonstrated in Ledoit and Wolf (2002).”
A note on testing the covariance matrix for large dimension (2005, methodology): “However, the method used by Ledoit and Wolf (2002) to prove these results under assumption (1.”
Global Testing and Large-Scale Multiple Testing for High-Dimensional Covariance Structures (2017, background): “Ledoit and Wolf (2002) showed that using p−1‖Σ̂− I‖2F leads to an inconsistent test in the high-dimensional setting and introduced a correction term − 1 np tr2(Σ̂) + p n .”
Test for Bandedness of High Dimensional Covariance Matrices with Bandwidth Estimation (2012, background): “Allowing divergent bandwidth in the hypothesis is an improvement over the sphericity test as considered in Ledoit and Wolf (2002) and Chen, Zhang and Zhong (2010).”
On the sphericity test with large-dimensional observations (2013, methodology): “Following the idea of [15], [9] proposed to use a family of well selected U-statistics to test the sphericity; however, as showed in our simulation study in Section 3, the powers of our corrected John’s test are slightly higher than this test in most cases.”
Fundamental limits of detection in the spiked Wigner model (2018, background): “…provided many insights, as have analyses based on more thoroughgoing usage of spectral data and/or more advanced optimization-based procedures (see Ledoit and Wolf, 2002; Amini and Wainwright, 2009; Berthet and Rigollet, 2013; Dobriban, 2017, and references therein), they do not characterize the…”
RAPTT: An Exact Two-Sample Test in High Dimensions Using Random Projections (2014, background): “…on simultaneous testing of means based on marginal tests in high dimensions; Benjamini and Hochberg (1995) worked on controlling false discovery rates in multiple testing; Ledoit and Wolf (2002); Chen et al. (2010); Li and Chen (2012) considered testing of covariance matrices in high dimensions.”
Some Tests Concerning the Covariance Matrix in High Dimensional Data (2005, methodology): “However, Ledoit and Wolf (2002) have porposed a modified version of Nagao’s test and have given its asymptotic null distribution when (p/n) → c > 0, where c is a constant but the non-null distribution is lacking.”