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Open AccessArticle

De-Biased Graphical Lasso for High-Frequency Data

Mathematics and Informatics Center and Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Entropy 2020, 22(4), 456; https://doi.org/10.3390/e22040456
Received: 6 February 2020 / Revised: 10 April 2020 / Accepted: 14 April 2020 / Published: 17 April 2020
This paper develops a new statistical inference theory for the precision matrix of high-frequency data in a high-dimensional setting. The focus is not only on point estimation but also on interval estimation and hypothesis testing for entries of the precision matrix. To accomplish this purpose, we establish an abstract asymptotic theory for the weighted graphical Lasso and its de-biased version without specifying the form of the initial covariance estimator. We also extend the scope of the theory to the case that a known factor structure is present in the data. The developed theory is applied to the concrete situation where we can use the realized covariance matrix as the initial covariance estimator, and we obtain a feasible asymptotic distribution theory to construct (simultaneous) confidence intervals and (multiple) testing procedures for entries of the precision matrix. View Full-Text
Keywords: asymptotic mixed normality; factor model; high-dimensions; Malliavin calculus; precision matrix; sparsity asymptotic mixed normality; factor model; high-dimensions; Malliavin calculus; precision matrix; sparsity
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Koike, Y. De-Biased Graphical Lasso for High-Frequency Data. Entropy 2020, 22, 456.

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