Lectures on the asymptotic theory of rank tests (Q2865671)

The booklet under review is based on a course of lectures given by the current author at the Scientific and Educational Center of Steklov Mathematical Institute of the Academy of Sciences of Russia in 2005. The course had two objectives: (i) to present the main results related to the properties of rank tests (which primarily are the limit theorems for rank test distributions and, as a consequence, results on asymptotic power and efficiency of these tests) and (ii) to familiarize students with asymptotic methods developed by L. Le Cam in the 1960s (which at that time allowed to build the asymptotic theory of rank tests). The booklet consists of 8 chapters and a bibliography. Below is the list of chapters:NEWLINENEWLINEChapter 1. Introduction.NEWLINENEWLINEChapter 2. Ranks and their properties under the null hypothesis.NEWLINENEWLINEChapter 3. Asymptotic normality of simple linear rank statistics under the null hypothesis.NEWLINENEWLINEChapter 4. Contigual sequences of distributions.NEWLINENEWLINEChapter 5. Local asymptotic normality.NEWLINENEWLINEChapter 6. Asymptotic power and efficiency of parametric and rank tests.NEWLINENEWLINEChapter 7. Local asymptotic normality conditions.NEWLINENEWLINEChapter 8. Applications.