Projection Test for Mean Vector in High Dimensions

This article studies the projection test for high-dimensional mean vectors via optimal projection. The idea of projection test is to project high-dimensional data onto a space of low dimension such that traditional methods can be applied. We first propose a new estimation for the optimal projection direction by solving a constrained and regularized quadratic programming. Then two tests are constructed using the estimated optimal projection direction. The first one is based on a data-splitting procedure, which achieves an exact t-test under normality assumption. To mitigate the power loss due to data-splitting, we further propose an online framework, which iteratively updates the estimation of projection direction when new observations arrive. We show that this online-style projection test asymptotically converges to the standard normal distribution. Various simulation studies as well as a real data example show that the proposed online-style projection test retains the Type I error rate well and is more powerful than other existing tests. Supplementary materials for this article are available online.



Work Title Projection Test for Mean Vector in High Dimensions
Open Access
  1. Wanjun Liu
  2. Xiufan Yu
  3. Wei Zhong
  4. Runze Li
  1. Data splitting
  2. One-sample mean problem
  3. Online-style estimation
  4. Power enhancement
  5. Regularization methods
License In Copyright (Rights Reserved)
Work Type Article
  1. Journal of the American Statistical Association
Publication Date December 12, 2022
Publisher Identifier (DOI)
Deposited March 29, 2023




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Work History

Version 1

  • Created
  • Added Projection_Test_for_Mean_Vector_in_High_Dimensions.pdf
  • Added Creator Wanjun Liu
  • Added Creator Xiufan Yu
  • Added Creator Wei Zhong
  • Added Creator Runze Li
  • Published
  • Updated Keyword, Publication Date Show Changes
    • Data splitting, One-sample mean problem, Online-style estimation, Power enhancement, Regularization methods
    Publication Date
    • 2022-01-01
    • 2022-12-12
  • Updated