Robust and non-robust models in statistics

by L. B. Klebanov

In this book the authors consider so-called ill-posed problems and stability in statistics. Ill-posed problems are certain results where arbitrary small changes in the assumptions lead to unpredictable large changes in the conclusions. In a companion problem published by Nova, the authors explain that ill-posed problems are not a mere curiosity in the field of contemporary probability. The same situation holds in statistics. The objective of the authors of this book is to (1) identify statistical problems of this type, (2) find their stable variant, and (3) propose alternative versions of numerous theorems in mathematical statistics. The layout of the book is as follows. The authors begin by reviewing the central pre-limit theorem, providing a careful definition and characterization of the limiting distributions. Then, They consider pre-limiting behavior of extreme order statistics and the connection of this theory to survival analysis. A study of statistical applications of the pre-li