Performance Comparison of Traditional Bootstrap and Bias-Corrected and Accelerated Methods in Constructing Confidence Intervals for Non-Normal Data: A Simulation Study

الملخص

Bootstrap methods have emerged as powerful non-parametric tools for statistical inference, particularly when dealing with non-normal data distributions where traditional parametric assumptions fail. This simulation study compares the performance of traditional bootstrap and bias-corrected and accelerated (BCa) bootstrap methods in constructing confidence intervals for non-normal data. We conducted extensive Monte Carlo simulations across various non-normal distributions including exponential, chi-square, and beta distributions with different sample sizes (n = 30, 50, 100, 200). Performance metrics evaluated include coverage probability, interval width, and computational efficiency. Our results demonstrate that BCa bootstrap consistently outperforms traditional bootstrap methods, achieving coverage probabilities closer to the nominal 95% level across all tested distributions. The BCa method showed superior performance particularly for heavily skewed distributions and smaller sample sizes, with coverage probabilities ranging from 94.2% to 95.8% compared to 89.3% to 93.7% for traditional bootstrap. While BCa bootstrap requires approximately 15-20% more computational time, the improved accuracy justifies this cost. These findings provide valuable insights for practitioners dealing with non-normal data and contribute to the growing body of literature on robust statistical inference methods.