Automatic sparse estimation of the multi-sample mean vector for high-dimensional data

Scenarios involving high-dimensional, low-sample-size (HDLSS) data are now common in genomics, image analysis, and other modern scientific applications. While mean-vector estimation is fundamental, classical estimators often suffer from severe noise accumulation in such settings. To overcome this problem, we develop a tuning-free sparse estimator for the high-dimensional mean vector under a general multi-sample setting. We establish the consistency of the proposed estimator under mild conditions, without requiring normality or restrictive assumptions in high-dimensional settings. Furthermore, we develop a shrinkage estimator of the mean vector and apply the proposed methodology to high-dimensional discriminant analysis. Finally, we evaluate the performance of the proposed estimators through simulations and real data analysis.