Statistical tests of nonparametric hypotheses. Asymptotic theory (Q2853434)

At first I must say that this is a very nice book which will soon become one of the basic references in the field of statistical testing of hypotheses in nonparametric statistics. The author collected a lot of key results spread out in the rather vast literature and described them in a uniform manner.NEWLINENEWLINE The main subject of the book are tests of hypotheses in regular nonparametric models, including tests based on empirical processes and smooth estimators of density functions, regression functions and regular functions defining the distributions of point processes and Gaussian diffusion processes. The asymptotic behavior of the statistics and the asymptotic properties of the tests are detailed. The last par of the book generalizes tests built for samples to sequential tests, especially tests for processes observed continuously in time. Because there is no unified theory of sequential tests, several approaches are considered.NEWLINENEWLINE This monograph is not exhaustive, its emphasis is on systematically optimal nonparametric tests originated in the empirical processes theory and in a nonparametric version of Lecam's asymptotic theory of testing statistical hypotheses which are presented and generalized in this book.