Invariant Conclusions in Statistics

The book is based on a course of lectures delivered by the author (professor of the Department of Applied Mathematics and Computer Modeling of the Gubkin Russian State University of Oil and Gas) at the Faculty of Computational Mathematics and Cybernetics of Moscow State University, at universities and research centers in Warsaw, Berlin, Liege, Brussels, and the US. The book deals with statistical problems that are invariant under a suitable group of transformations of observed and estimated quantities, for example, the choice of the coordinate system in which these quantities are measured. For such problems, the choice of the optimal solution in the class of invariant statistical solutions is simplified. For frequently used invariant statistical models, such solutions are explicitly defined. The book gives many examples as well as some commentary on the problem of reconstructing a multidimensional function from observations.

For students and postgraduate students of universities and institutes, as well as for reference and for individuals who study or use applied mathematics in their studies.