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Projection Test for Mean Vector in High Dimensions.

Wanjun Liu1, Xiufan Yu2, Wei Zhong3

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|May 6, 2024
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Summary
This summary is machine-generated.

This study introduces an online projection test for high-dimensional data, improving statistical power and maintaining accuracy. The novel method effectively analyzes complex datasets by projecting them into lower dimensions.

Keywords:
Data splittingone-sample mean problemonline-style estimationpower enhancementregularization methods

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Area of Science:

  • Statistics
  • High-dimensional data analysis

Background:

  • Traditional statistical methods struggle with high-dimensional data.
  • Projection tests reduce dimensionality for easier analysis.

Purpose of the Study:

  • To develop a powerful and accurate projection test for high-dimensional mean vectors.
  • To address power loss issues in existing data-splitting projection methods.

Main Methods:

  • Proposed a novel estimation for optimal projection direction using constrained quadratic programming.
  • Developed two tests: one with data-splitting (exact t-test under normality) and an online version.
  • The online framework iteratively updates projection direction estimates with new data.

Main Results:

  • The online-style projection test asymptotically converges to a standard normal distribution.
  • Simulations and real-data analysis demonstrate the proposed test maintains type I error rates.
  • The online test shows superior statistical power compared to existing methods.

Conclusions:

  • The proposed online projection test is a robust and powerful tool for high-dimensional mean vector analysis.
  • This method offers a significant advancement over traditional and data-splitting approaches.
  • Effective for both theoretical statistical research and practical data analysis applications.