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Session 22. Multivariate stochastic modelling in finance, insurance and risk management
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Optimal Shrinkage Estimator for High Dimensional Mean Vector |
Ostap Okhrin, Humboldt-University of Berlin, Germany
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The talk is based on the joint work with Taras Bodnar and Nestor Parolya
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In this paper we derive the optimal linear shrinkage estimator
for the large dimensional mean vector using the random matrix theory. We
concentrate on the case when both the dimension \(p\) and the sample
size \(n\) tend to infinity such that their ratio tends to a constant
\(c\in(0,+\infty)\). Using weak assumptions on the underlying distribution
we find the asymptotic equivalents of the optimal shrinkage intensities
and estimate them consistently. The obtained non-parametric estimator is
of simple structure and is proven to minimize asymptotically the
quadratic loss with probability \(1\) in the case \(c\in(0,1)\). In the case
\(c\in(1,+\infty)\) we improve the derived estimator by setting the
feasible estimator for the precision covariance matrix. At the end, an
exhaustive simulation study is provided, where the proposed estimator is
compared with known benchmarks from the literature.
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