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A Uniform Bound on the Operator Norm of Sub-Gaussian Random Matrices and Its Applications

Grigory Franguridi, Hyungsik Roger Moon

arXiv 3 May 2019 · Econometrics · publishedEconometric Theory (2021)

arXiv:1905.01096 · PDF · DOI · OpenAlex · Extracted main text

Abstract

For an $N \times T$ random matrix $X(\beta)$ with weakly dependent uniformly sub-Gaussian entries $x_{it}(\beta)$ that may depend on a possibly infinite-dimensional parameter $\beta\in \mathbf{B}$, we obtain a uniform bound on its operator norm of the form $\mathbb{E} \sup_{\beta \in \mathbf{B}} ||X(\beta)|| \leq CK \left(\sqrt{\max(N,T)} + \gamma_2(\mathbf{B},d_\mathbf{B})\right)$, where $C$ is an absolute constant, $K$ controls the tail behavior of (the increments of) $x_{it}(\cdot)$, and $\gamma_2(\mathbf{B},d_\mathbf{B})$ is Talagrand's functional, a measure of multi-scale complexity of the metric space $(\mathbf{B},d_\mathbf{B})$. We illustrate how this result may be used for estimation that seeks to minimize the operator norm of moment conditions as well as for estimation of the maximal number of factors with functional data.

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27
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Vershynin, R (2018) High-dimensional probability: An introduction with applications in data science, volume 470.8368288%
2Bai, J. and Ng, S (2002) Determining the number of factors in approximate factor models0.73732100%
3Lataa, R (2005) Some estimates of norms of random matrices0.64422100%
4Moon, H. R. and Weidner, M (2017) Dynamic linear panel regression models with interactive fixed effects self0.64422100%
5Fernique, X (1976) Regularité des trajectoires des fonctions aléatoires gaussiennes0.64422100%
6Talagrand, M (2006) The generic chaining: upper and lower bounds of stochastic processes0.58531100%
7Geman, S (1980) A limit theorem for the norm of random matrices0.51121100%
8Bai, Z. D (2008) Methodologies in spectral analysis of large dimensional random matrices, a review0.40511100%
9Bai, Z. and Silverstein, J. W (2010) Spectral analysis of large dimensional random matrices, volume 200.40511100%
10Bandeira, A. S. and Van Handel, R (2016) Sharp nonasymptotic bounds on the norm of random matrices with independent entries0.40511100%

Showing the top 10 of 27 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Nuclear Norm Regularized Estimation of Panel Regression Models0.00011