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A two-sample nonparametric test for one-sided location-scale alternative.

Hidetoshi Murakami1, Markus Neuhäuser2

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Summary
This summary is machine-generated.

This study introduces new one-sided location-scale tests designed for right-skewed data. These novel statistical tests enhance and stabilize power, offering strong competition to existing methods.

Keywords:
62G10Adaptive testLepage-type testmaximum test

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Area of Science:

  • Statistics
  • Statistical Inference
  • Hypothesis Testing

Background:

  • Variability often increases with location, and heteroscedasticity can signal treatment effects in randomized studies.
  • Location-scale tests are appropriate for analyzing data with both location and scale changes.
  • Existing methods often combine location and scale test statistics, but one-sided tests require specialized approaches.

Purpose of the Study:

  • To develop and evaluate novel one-sided location-scale tests.
  • To specifically address the challenges posed by right-skewed data common in real-world applications.
  • To introduce maximum and adaptive test statistics based on a new Lepage-type test.

Main Methods:

  • Introduction of a one-sided Lepage-type test statistic.
  • Development of maximum and adaptive test statistics utilizing the Lepage-type statistic.
  • Derivation of limiting distributions for the maximum test statistics.
  • Performance assessment via Monte Carlo simulations across various continuous distribution scenarios.

Main Results:

  • The proposed new test statistics significantly increase and stabilize statistical power.
  • New tests demonstrate strong performance, competing effectively with established location-scale tests.
  • Simulation results validate the effectiveness of the new methods for right-skewed data.

Conclusions:

  • The novel one-sided location-scale tests offer improved and reliable statistical power.
  • These tests are particularly advantageous for analyzing right-skewed data.
  • The developed methods provide valuable alternatives for statistical inference in relevant applications.