Data depth trimming counterpart of the classical \(t\) (or \(T^2\)) procedure (Q609674)

Summary: The classical \(t\) (or \(T^2\) in high dimensions) inference procedure for unknown mean \(\mu: \overline X\pm t_\alpha(n-1) S_n/\sqrt n\) (or \(\{\mu: n(\overline x-\mu)'S^{-1}(\overline x-\mu)\leq \chi_{1-\alpha}^2(p)\})\) is so fundamental in statistics and so prevailing in practices; it is regarded as an optimal procedure in the mind of many practitioners. In this manuscript we present a new procedure based on data depth trimming and bootstrapping that can outperform the classical (or in high dimensions) confidence interval (or region) procedure.