Simulation Study of Conditional, Bootstrap, and t Confidence Intervals in Linear Regression

Two resampling procedures, the bootstrap (BS) and the conditional confidence interval (CCI), are compared with the standard t-interval for the slope parameter in simple linear regression with an error term that is not necessarily normal. The type of bootstrap confidence intervals computed are the widely used bias-corrected and accelerated (BC a ) intervals. The CCIs are found by an efficient method for inverting permutation tests. Normal, highly skewed, and heavy-tailed error distributions are considered. While the CCI and BC a intervals have similar asymptotic properties, for a moderate number of cases, the confidence intervals obtained from the CCI and BC a behave differently in terms of accuracy, power, length, and correctness. Across all conditions, the CCI is the most accurate interval and has very good power. The t-intervals are also very accurate across most of the conditions we studied, and have coverage closer to the nominal value than the BC a intervals.