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Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding
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Published on: October 11, 2018

U-statistic with side information.

Ao Yuan1, Wenqing He, Binhuan Wang

  • 1Howard University, Washington DC 20059, USA.

Journal of Multivariate Analysis
|May 25, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces U-statistics incorporating side information via empirical likelihood, achieving smaller asymptotic variance and enhanced efficiency. While confidence intervals don't improve, simulations show significant variance reduction and better coverage for skewed data.

Keywords:
EfficiencyInformation boundSide informationU-statistic

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Area of Science:

  • Statistics
  • Statistical Inference

Background:

  • U-statistics are fundamental in statistical estimation.
  • Incorporating auxiliary information can potentially improve statistical properties.

Purpose of the Study:

  • To develop and analyze U-statistics that leverage side information using empirical likelihood.
  • To investigate the impact of side information on asymptotic variance and efficiency.

Main Methods:

  • Empirical likelihood method for U-statistics.
  • Theoretical analysis of asymptotic properties.
  • Simulation studies for finite sample performance.

Main Results:

  • Proposed U-statistics with side information demonstrate smaller asymptotic variance compared to existing methods.
  • Asymptotic efficiency is achieved, with weak limits admitting a convolution result.
  • U-likelihood ratio procedures and confidence intervals do not benefit from side information.

Conclusions:

  • Proper implementation of side information in U-statistics offers substantial asymptotic variance reduction.
  • U-empirical likelihood confidence intervals show superior performance over normal approximation for skewed distributions.
  • The study highlights the benefits and limitations of incorporating side information in statistical estimation.