Bootstrap approach to inference and power analysis based on three test statistics for covariance structure models

Area of Science:

• Statistics
• Statistical Inference
• Covariance Structure Models

Background:

• Bootstrap inference is crucial for covariance structure models.
• Assessing Type I error, power, and sample-size is vital for model validity.
• Heavy-tailed data can compromise standard bootstrap inference.

Purpose of the Study:

• To investigate bootstrap inference for covariance structure models.
• To improve Type I error accuracy and power analysis.
• To develop a robust method for heavy-tailed data.

Main Methods:

• Utilized three test statistics for bootstrap inference.
• Proposed a downweighting procedure for transformed samples.
• Applied bootstrap methodology to assess Type I error, power, and sample-size.

Main Results:

• The downweighting and bootstrapping approach enhances Type I error accuracy.
• Transformed samples with downweighting satisfy key conditions for safe bootstrap inference.
• The proposed method offers a near-optimal procedure for model evaluation.

Conclusions:

• Combining downweighting and bootstrapping provides a robust inference method for covariance structure models, especially with heavy-tailed data.
• The enhanced methodology improves reliability in statistical testing and model assessment.
• A practical rule for managing bootstrap non-convergence issues is presented.