Non-Standard Rank Tests [Paperback]

This monograph extends the notion of locally most powerful rank tests to non-regular cases. Through this no- tion one is led in a natural way to non-standard rank tests. A nearly complete analysis of the finite sample and asymptotic properties of such rank tests is presented. Also an adaptive test procedure is proposed and studied, and the results of a Monte Carlo simulation are given which provide strong evidence that it should perform well in many practical situations. An appendix derives the limit experiments needed to investigate the asymptotic optimality of these non-standard rank tests under local alternatives. The results in the appendix should also be of separate interest.This monograph extends the notion of locally most powerful rank tests to non-regular cases. Through this no- tion one is led in a natural way to non-standard rank tests. A nearly complete analysis of the finite sample and asymptotic properties of such rank tests is presented. Also an adaptive test procedure is proposed and studied, and the results of a Monte Carlo simulation are given which provide strong evidence that it should perform well in many practical situations. An appendix derives the limit experiments needed to investigate the asymptotic optimality of these non-standard rank tests under local alternatives. The results in the appendix should also be of separate interest.I. Locally most powerful rank tests  finite sample results.- ? 1. Preliminaries.- ? 2. Locally most powerful rank tests for H0.- ? 3. Locally most powerful rank tests for H1.- ? 4. Locally most powerful rank tests for H2 against dependence.- II. Asymptotic results for locally most powerful rank tests.- ? 5. Approximate rank tests.- ? 6. Asymptotic results for locally most powerful rank tests with respect to H0.- ? 7. Asymptotic results for H1.- ? 8. Asymptotic results for H2.- ? 9. Asymptotic results for locally most powerful rank tests in the case a = 0.- III. Asymptotic results for rank tests under alterl“.