Comparison of linear shrinkage estimators of a large covariance matrix in normal and non-normal distributions. (English) Zbl 1468.62087
Summary: The problem of estimating the large covariance matrix of both normal and non-normal distributions is addressed. In convex combinations of the sample covariance matrix and a positive definite target matrix, the optimal weight is estimated by exact or approximate unbiased estimators of the numerator and denominator of the optimal weight in normal or non-normal cases. A spherical and a diagonal matrices are two typical examples of target matrices, and the corresponding single shrinkage estimators are provided. A double shrinkage estimator which shrinks the sample covariance matrix toward the two target matrices is also suggested. The performances of single and double shrinkage estimators are numerically investigated through simulation and empirical studies.
MSC:
| 62-08 | Computational methods for problems pertaining to statistics |
| 62H12 | Estimation in multivariate analysis |
| 62J07 | Ridge regression; shrinkage estimators (Lasso) |
Keywords:
covariance matrix; double shrinkage; high dimension; large sample; non-normal distribution; normal distribution; linear shrinkage estimator; risk function; shrinkageReferences:
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