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We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This two-sample test based on a nontrivial extension of the one-sample central limit theorem (Chernozhukov et al., 2017) provides a practically useful procedure with rigorous theoretical guarantees on its size and power assessment. In particular, the proposed test is easy to compute and does not require the independently and identically distributed assumption, which is allowed to have different distributions and arbitrary correlation structures. Further desired features include weaker moments and tail conditions than existing methods, allowance for highly unequal sample sizes, consistent power behavior under fairly general alternative, data dimension allowed to be exponentially high under the umbrella of such general conditions. Simulated and real data examples are used to demonstrate the favorable numerical performance over existing methods.
This work is motivated by learning the individualized minimal clinically important difference, a vital concept to assess clinical importance in various biomedical studies. We formulate the scientific question into a high-dimensional statistical probl
We consider testing for two-sample means of high dimensional populations by thresholding. Two tests are investigated, which are designed for better power performance when the two population mean vectors differ only in sparsely populated coordinates.
In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity, determining i
The analysis of record-breaking events is of interest in fields such as climatology, hydrology, economy or sports. In connection with the record occurrence, we propose three distribution-free statistics for the changepoint detection problem. They are
$ell_1$-penalized quantile regression is widely used for analyzing high-dimensional data with heterogeneity. It is now recognized that the $ell_1$-penalty introduces non-negligible estimation bias, while a proper use of concave regularization may lea