In reply to Rick Wicklin.

HI Rick, thank you for your reply! I am testing on synthetic dataset so I have the true value from the preset true population probability distribution. This always falls outside the bound of the bootstrap values as both empirical and bootstrap will give an underestimating result. So BCa becomes worse than percentile method (where I manually add in twice the bias to correct the interval) since most of the times, its upper bound falls below the true value. Is there a way to compensate for the huge bias here?