Journal Article

EXACT AND ASYMPTOTICALLY ROBUST PERMUTATION TESTS

Romano, Joseph P., Chung, EunYi

2013

Overview

Given independent samples from P and Q, two-sample permutation tests allow one to construct exact level tests when the null hypothesis is P = Q. On the other hand, when comparing or testing particular parameters θ of P and Q, such as their means or medians, permutation tests need not be level α, or even approximately level α in large samples. Under very weak assumptions for comparing estimators, we provide a general test procedure whereby the asymptotic validity of the permutation test holds while retaining the exact rejection probability α in finite samples when the underlying distributions are identical. The ideas are broadly applicable and special attention is given to the k-sample problem of comparing general parameters, whereby a permutation test is constructed which is exact level α under the hypothesis of identical distributions, but has asymptotic rejection probability α under the more general null hypothesis of equality of parameters. A Monte Carlo simulation study is performed as well. A quite general theory is possible based on a coupling construction, as well as a key contiguity argument for the multinomial and multivariate hypergeometric distributions.

• Publisher: Institute of Mathematical Statistics,The Institute of Mathematical Statistics
• Subject: 62E20 / 62G10 / Asymptotic methods / Behrens–Fisher problem / coupling / Estimating techniques / Estimators / Hypotheses / Mathematical permutation / Mathematical problems / Monte Carlo simulation / Null hypothesis / permutation test / Permutation tests / Probabilities / Probability distribution / Random allocation / Sampling distributions / Statistical discrepancies / Statistical median / Statistics / Studies / Theoretical mathematics