Maximin efficiency-robust tests and some extensions

The Maximin Efficiency-Robust Test idea of Gastwirth (1966) was to maximize the minimum asymptotic power (for fixed size) versus special local families of alternatives over some specially chosen families of score statistics. This approach is reviewed from a general decision-theoretical perspective, including some Bayesian variants. For two-sample censored-data rank tests and stochastically ordered but not proportional-hazard alternatives, the MERT approach leads to customized weighted-logrank tests for which the weights depend on estimated randomcensoring distributions. Examples include statistics which perform well against both Lehmann and logistic alternatives or against families of alternatives which include increasing, decreasing, and 'bathtub-shaped' hazards. A M S Sub~cot Classification: 62G20, 62E20