A numerical investigation of the accuracy of parametric bootstrap for discrete data

作者：Lloyd Chris J^*

来源：Computational Statistics & Data Analysis, 2013, 61: 1-6.

DOI：10.1016/j.csda.2012.09.015

• Bootstrap
• Exact test
• Nuisance parameters
• Tests of non-inferiority

Standard first order tests have size error that decreases as m(-1/2) where m is a measure of sample size. Parametric bootstrap tests use an exact calculation of the P-value, assuming nuisance parameters equal their null maximum likelihood estimates. It is commonly believed that their performance is driven by asymptotics, notwithstanding some confusion in the literature on asymptotic error rates.
For simple discrete models, parametric bootstrap tests can be calculated explicitly rather than simulated. Moreover, their accuracy can also be calculated exactly as a function of the nuisance parameter. This article reports the results of an intensive numerical investigation of the accuracy of first order and parametric bootstrap based tests, firstly of treatment effect in clinical trials, and secondly of association in simple logistic regression. We conclude that bootstrap tests have asymptotic size error that decreases at rate O(m(-1)) but that their excellent small sample performance has little to do with asymptotics.

• 出版日期2013-5