City Research Online

Abstract

We introduce shrinkage estimators of the sample mean vector in high dimension. Our estimators share desirable properties relative to existing methods: they are distribution-free, consider bona-fide target estimators, and use simple estimators of the shrinkage intensities independent of the precision matrix which are (Formula presented.) consistent in high dimension. Unlike existing estimators that impose that the whitened data be an i.i.d. matrix, we only impose i.i.d. across sample observations. We require uniform boundedness of the first four moments, and the high-dimensional asymptotics are in a general Kolmogorov setting where (Formula presented.) as (Formula presented.), with (Formula presented.) the mean-vector dimension and (Formula presented.) the sample size. We consider as a target estimator either zero or the grand mean. Simulations show that our shrinkage estimators are competitive with a range of benchmark estimators, both when the theoretical assumptions are satisfied and violated. Finally, we apply our estimators to constructing mean-variance portfolios of a large number of stocks, and find that they deliver robust out-of-sample Sharpe ratios.

Publication Type:	Article
Additional Information:	This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Business & Economic Statistics on 15 Jun 2026 available online at: https://doi.org/10.1080/07350015.2026.2638490
Publisher Keywords:	Bona-fide estimator, High-dimensional asymptotics, Mean-variance portfolio, Mean-vector estimation, Shrinkage estimation
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HB Economic Theory
Departments:	Bayes Business School Bayes Business School > Faculty of Actuarial Science & Insurance
SWORD Depositor:	Symplectic Administrator

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