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A density based empirical likelihood approach for testing bivariate normality.

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Summary
This summary is machine-generated.

This study introduces a new method for testing bivariate normality using density-based empirical likelihood. The novel approach effectively assesses data distribution, showing strong performance in simulations and real-world applications.

Keywords:
Bivariate normalityDensity estimationEmpirical likelihoodEntropyGoodness-of-fitHistogram density estimation

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Area of Science:

  • Statistics
  • Nonparametric Statistics
  • Biostatistics

Background:

  • One-dimensional normality tests like sample entropy, sieves, and Grenander estimation are established nonparametric tools.
  • Density-based empirical likelihood (EL) offers a standardized, distribution-free method for approximating optimal parametric likelihood ratio tests.
  • Extending these methods to bivariate settings presents significant challenges.

Purpose of the Study:

  • To address the difficulties in constructing density-based empirical likelihood ratio techniques for bivariate normality testing.
  • To propose and validate a novel approach for bivariate normality assessment.

Main Methods:

  • Development of a novel bivariate sample entropy expression.
  • Demonstration that the new expression aligns with bivariate histogram density estimation principles.
  • Application of Monte Carlo simulations to evaluate the proposed density-based empirical likelihood ratio tests.

Main Results:

  • The newly derived bivariate sample entropy satisfies established density estimation concepts.
  • The proposed density-based empirical likelihood ratio tests for bivariate normality exhibit excellent performance in finite sample sizes.
  • Successful application of the method to real-world data concerning biomarkers for myocardial infarction.

Conclusions:

  • The novel density-based empirical likelihood approach provides a robust solution for bivariate normality testing.
  • The method demonstrates practical utility and effectiveness, as shown by simulation and real data analysis.
  • This work extends powerful nonparametric testing methodologies to a crucial bivariate context.