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.

Inhalt
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 alternatives.- § 10. Limit distributions under alternatives.- § 11. Rank tests under almost regular models.- IV. Tests based on minimum ranks.- § 12. The minimum rank test (finite sample results).- § 13. The minimum rank test (asymptotic results).- V. Parametric results for almost regular models.- § 14. Local asymptotic normality under almost regular assumptions.- VI. Semiparametric models and Monte Carlo results.- § 15. Adaptive tests for semiparametric regression alternatives.- § 16. A comparison of rank tests and parametric tests: the Monte Carlo approach.- Statistical experiments with non-regular densities.- § A1. Introduction.- § A2. Preliminaries.- § A3. Convergence of triangular arrays to Gaussian experiments.- § A4. Convergence of non-regular experiments to Gaussian experiments.- § A5. Convergence to Poisson experiments.- § A6. A representation for certain stable Poisson experiments.- § A7. Applications for one-sided test problems.- References.- List of symbols.- Author index.