Nonparametric goodness-of-fit testing under Gaussian models

the long version

This book presents the modern theory of nonparametric goodness-of-fit testing. The study is based on an asymptotic version of the minimax approach. The methods for the construction of asymptotically optimal, rate optimal, and optimal adaptive test procedures are developed. The authors present many new results that demonstrate the principal differences between nonparametric goodness-of-fit testing problems with parametric goodness-of-fit testing problems and with non-parametric estimation problems. This book fills the gap in modern nonparametric statistical theory by discussing hypothesis testing. The book is addressed to mathematical statisticians who are interesting in the theory of non-parametric statistical inference. It will be of interest to specialists who are dealing with applied non-parametric statistical problems that are relevant in signal detection and transmission and in technical and medical diagnostics among others.