A diagnostic function for bootstrap confidence intervals

The standard intervals, a point estimate plus-or-minus some multiple of a standard error, are mainstays of statistical applications. They are relatively easy to calculate in most situations, while providing first-order asymptotic accuracy, but can be quite inaccurate in practice. The bca system of bootstrap confidence intervals offers second-order asymptotic accuracy, often a substantial improvement. They are based on an implied transformation to a normal translation family. Is this justified? I'll discuss a data-based diagnostic function that answers the question, after first reviewing the bca method.