Hypothesis tests in ordinal predictive models with optimal accuracy.

Area of Science:

• Statistics
• Machine Learning
• Biostatistics

Background:

• Multi-class ordinal discrimination is crucial for accurate prediction in real-world applications.
• Assessing multi-class classifiers often involves hypervolume under ROC manifolds (HUM), but existing statistical inference methods are computationally intensive.
• Efficient statistical inference is needed for optimal HUM with numerous predictors.

Purpose of the Study:

• To propose a computationally efficient jackknife empirical likelihood method for statistical inference in multi-class ordinal discrimination.
• To establish Wilks' theorem and provide power analysis under the Pitman alternative for the proposed method.
• To introduce a novel network-based algorithm for rapid computation of multi-sample U-statistics.

Main Methods:

• Jackknife empirical likelihood method.
• Establishment of Wilks' theorem and power analysis.
• Development of a network-based rapid computation algorithm for U-statistics.

Main Results:

• The proposed jackknife empirical likelihood method demonstrates superior performance compared to existing approaches.
• The method shows improved test size, statistical power, and significantly reduced implementation time.
• Simulations and analysis of a medical dataset confirm the method's effectiveness.

Conclusions:

• The jackknife empirical likelihood method offers a computationally efficient and powerful alternative for statistical inference in multi-class ordinal discrimination.
• The novel algorithm accelerates U-statistic computation, making complex analyses more feasible.
• The method provides new insights when applied to real-world medical data analysis.