A multiple decision procedure for testing with ordered alternatives

Abstract

In testing hypotheses with ordered alternatives, the conclusion of an order restriction when rejecting the null hypothesis is very sensitive to the correctness of the assumed model. In other words, when the null hypothesis is rejected, there is no protection against the fact that both the null and the ordered alternatives might be false. In this thesis we suggest a novel method of providing this protection. This entails redefining the classical concept of hypothesis testing to one where multiple decisions are made: (1) Decide that there is not enough evidence against the null hypothesis, (2) there is a strong evidence in favor of the ordered alternative, or, (3) there is a strong evidence against both the null and the ordered alternatives. By simulations and examples, we show that this new procedure provides very substantial protections against false conclusions of the order restriction while reducing the power of the test very little when the ordering is correct.