Estimation of a multiplicative covariance structure in the large dimensional case

Hafner, Christian; Linton, Oliver; Tang, Haihan

doi:10.1920/wp.cem.2016.5216

Cited by 2 publications

(1 citation statement)

References 79 publications

(54 reference statements)

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“…For instance, El Karoui (2008), Bickel and Levina (2008), Cai and Liu (2011), and Fan, Liao, and Mincheva (2013) propose estimating the largedimension covariance matrix via the thresholding method. Among many others, Ledoit and Wolf (2012), Bailey, Pesaran, and Smith (2016) and Hafner, Linton, and Tang (2016) suggest using different shrinkage methods and provide a detailed computation algorithm. Lam and Fan (2009) and Cai, Zhang, and Zhou (2010), on the other hand, theoretically derive the asymptotic properties of the large covariance matrix estimator through shrinkage estimation using penalty functions.…”

Section: Andmentioning

confidence: 99%

Large System of Seemingly Unrelated Regressions: A Penalized Quasi-Maximum Likelihood Estimation Perspective

et al. 2019

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In this article, using a shrinkage estimator, we propose a penalized quasi-maximum likelihood estimator (PQMLE) to estimate a large system of equations in seemingly unrelated regression models, where the number of equations is large relative to the sample size. We develop the asymptotic properties of the PQMLE for both the error covariance matrix and model coefficients. In particular, we derive the asymptotic distribution of the coefficient estimator and the convergence rate of the estimated covariance matrix in terms of the Frobenius norm. The model selection consistency of the covariance matrix estimator is also established. Simulation results show that when the number of equations is large relative to the sample size and the error covariance matrix is sparse, the PQMLE outperforms other contemporary estimators.

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Section: Andmentioning

confidence: 99%

Large System of Seemingly Unrelated Regressions: A Penalized Quasi-Maximum Likelihood Estimation Perspective

et al. 2019

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Testing and Support Recovery of Correlation Structures for Matrix-Valued Observations with an Application to Stock Market Data

Chen¹,

Yang²,

Xu³

et al. 2020

Preprint

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Estimation of the covariance matrix of asset returns is crucial to portfolio construction. As suggested by economic theories, the correlation structure among assets differs between emerging markets and developed countries. It is therefore imperative to make rigorous statistical inference on correlation matrix equality between the two groups of countries. However, if the traditional vector-valued approach is undertaken, such inference is either infeasible due to limited number of countries comparing to the relatively abundant assets, or invalid due to the violations of temporal independence assumption. This highlights the necessity of treating the observations as matrix-valued rather than vector-valued. With matrix-valued observations, our problem of interest can be formulated as statistical inference on covariance structures under matrix normal distributions, i.e., testing independence and correlation equality, as well as the corresponding support estimations. We develop procedures that are asymptotically optimal under some regularity conditions. Simulation results demonstrate the computational and statistical advantages of our procedures over certain existing state-of-the-art methods. Application of our procedures to stock market data validates several economic propositions.

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Estimation of a multiplicative covariance structure in the large dimensional case

Cited by 2 publications

References 79 publications

Large System of Seemingly Unrelated Regressions: A Penalized Quasi-Maximum Likelihood Estimation Perspective

Large System of Seemingly Unrelated Regressions: A Penalized Quasi-Maximum Likelihood Estimation Perspective

Testing and Support Recovery of Correlation Structures for Matrix-Valued Observations with an Application to Stock Market Data

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