High‐dimensional covariance matrix estimation
By Clifford Lam. 2019
83 citations recorded by the source corpus.
Covariance matrix estimation plays an important role in statistical analysis in many fields, including (but not limited to) portfolio allocation and risk management in finance, graphical modeling, and clustering for genes discovery in bioinformatics, Kalman filtering and factor analysis in economics. In this paper, we give a selective review of covariance and precision matrix estimation when the matrix dimension can be diverging with, or even larger than the sample size. Two broad categories of regularization methods are presented. The first category exploits an assumed structure of the covariance or precision matrix for consistent estimation. The second category shrinks the eigenvalues of a sample covariance matrix, knowing from random matrix theory that such eigenvalues are biased from the population counterparts when the matrix dimension grows at the same rate as the sample size.
Subfields: Artificial Intelligence, Statistics and Probability
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Citations in the corpus
- Sufficient Forecasting Using Factor Models (2015, methodology): “The advantage of this is that F̂ is estimated far more accurately, according to Fan et al. (2016). Note that the projectionmatrix Pwas constructed by using the additive spline model.”
- Using Principal Component Analysis to Estimate a High Dimensional Factor Model with High-Frequency Data (2017, unknown): “In a setting with low-frequency time series data, Fan et al. (2011) and Fan et al. (2013) suggest imposing the sparsity assumption on the residual covariance matrix.”
- Factor Models for Portfolio Selection in Large Dimensions: The Good, the Better and the Ugly (2019, methodology): “Based on the nature of approximate factor models, which assume that the covariance matrix Σu is sparse or with bounded eigenvalues, one natural candidate to use an estimator of Σu that imposes sparsity; for example, see Fan et al. (2013) for some proposals to this end. All these proposals apply some”