The DOI matches its Crossref record; 43 of the 43 references it cites were found in a registry or an index.
High dimensional covariance matrix estimation using a factor model
Abstract
High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality p tends to [infinity] as the sample size n increases. Motivated by the Arbitrage Pricing Theory in finance, a multi-factor model is employed to reduce dimensionality and to estimate the covariance matrix. The factors are observable and the number of factors K is allowed to grow with p. We investigate the impact of p and K on the performance of the model-based covariance matrix estimator. Under mild assumptions, we have established convergence rates and asymptotic normality of the model-based estimator. Its performance is compared with that of the sample covariance matrix. We identify situations under which the factor approach increases performance substantially or marginally. The impacts of covariance matrix estimation on optimal portfolio allocation and portfolio risk assessment are studied. The asymptotic results are supported by a thorough simulation study.
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Cites
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Challenges of Big Data analysis
Fan, J., Han, F., & Liu, H. (2014) · National Science Review · doi:10.1093/nsr/nwt032 · Cited by 1,482
Regularized estimation of large covariance matrices
Bickel, P. J., & Levina, E. (2008) · The Annals of Statistics · doi:10.1214/009053607000000758 · Cited by 934
Large Covariance Estimation by Thresholding Principal Orthogonal Complements
Fan, J., Liao, Y., & Mincheva, M. (2013) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/rssb.12016 · Cited by 909
Self-citationCovariance regularization by thresholding
Bickel, P. J., & Levina, E. (2008) · The Annals of Statistics · doi:10.1214/08-aos600 · Cited by 893
Sparse permutation invariant covariance estimation
Rothman, A. J., Bickel, P. J., Levina, E., & Zhu, J. (2008) · Electronic Journal of Statistics · doi:10.1214/08-ejs176 · Cited by 560
Metadata
- Authors
- Fan, J., Fan, Y., & Lv, J.
- Venue
- Journal of Econometrics
- Publisher
- Elsevier BV
- Published
- 2008-11
- Volume
- 147
- Issue
- 1
- Pages
- 186-197
- ISSN
- 0304-4076 (ISSN-L)
- OpenAlex
- W2073681337
- Cited by
- 685
- References
- 43
- FWCI
- 41.99
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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