Almost-Exact Statistical Inferences vs Statistical Practice

• Activity Number: 281
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics*
• Author(s): Tim Hesterberg*+
• Affiliation(s): Insightful Corporation
• Keywords: bootstrap ; tilting ; nonparametric ; inference ; confidence interval

Abstract

The standard statistical confidence interval is estimate +- t s, where s is a standard error and t is a quantile from Student's t-distribution. Note the use of t rather than normal quantiles, which in practice eliminates an O(1/n) term in coverage probabilities, while ignoring the much larger O(1/sqrt(n)) errors that result from bias, skewness, and unjustified parametric assumptions.

We use the term "almost-exact" for inferences which "do not rely on parametric assumptions," are second-order correct--coverage errors or differences between actual and nominal p-values are O(1/n).

We introduce new "ABC-tilting" intervals, and compare them to existing almost-exact procedures, including bootstrap-BCa, bootstrap-t, ABC, and bootstrap-tilting, based on reliability, accuracy, computational requirements, and confidence interval length and variability. The tilting intervals are superior.

Our ultimate goal is to change statistical practice, so that accurate inferences augment or replace standard methods whenever accuracy matters. S-PLUS code is available for all intervals; please see www.insightful.com/Hesterberg. This work is supported by NSF SBIR Phase II grant DMI-0078706.