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Empirical likelihood ratio tests with power one.

Albert Vexler1, Li Zou1

  • 1Department of Biostatistics, The State University of New York at Buffalo, NY 14206, USA.

Statistics & Probability Letters
|November 10, 2018
PubMed
Summary

Sequential empirical likelihood ratio (ELR) tests offer power one, outperforming traditional t-statistic tests. These nonparametric tests demonstrate superior performance across various data distributions for sequential analysis.

Keywords:
62G1062G2062L0597K70Empirical likelihoodLaw of the iterated logarithmPower oneSequential testsVile and Wald inequalityt-statistic

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Area of Science:

  • Statistics
  • Statistical Inference
  • Nonparametric Statistics

Background:

  • Professor Robbins extended the Vile and Wald inequality for likelihood ratio sequential tests with power one.
  • The law of the iterated logarithm supports the optimal properties of these power one tests.

Purpose of the Study:

  • To propose and examine sequential empirical likelihood ratio (ELR) tests with power one.
  • To develop nonparametric one- and two-sided ELR tests.

Main Methods:

  • Development of sequential empirical likelihood ratio (ELR) tests.
  • Application of nonparametric statistical methods.
  • Comparison with classical nonparametric t-statistic-based tests.

Main Results:

  • The proposed sequential ELR tests achieve power one.
  • Nonparametric one- and two-sided ELR tests were successfully developed.
  • Sequential ELR tests demonstrated significant performance advantages over t-statistic tests.

Conclusions:

  • Sequential ELR tests provide a powerful alternative to traditional methods.
  • The developed nonparametric ELR tests are effective across diverse data distributions.
  • These findings advance the field of sequential hypothesis testing.