A.A. Ivanov - Böcker

This volume presents an authoritative collection of major survey papers on algebraic combinatorics which originally appeared in Russian, augmented by four survey papers written specially for this book. The algebraic theory of combinatorial objects is the branch of mathematics that studies the relation between local properties of a combinatorial object and the global properties of its automorphism group. The content is divided into three parts: the first deals with cellular rings; the second deals with distance-regular and distance-transitive graphs; and part 3 contains papers on the relatively new branch of amalgams and geometry. For complex systems theorists; mathematicians interested in group theory and combinatorics.

Presents up-to-date mathematical results in asymptotic theory on nonlinear regression on the basis of various asymptotic expansions of least squares, its characteristics, and its distribution functions of functionals of Least Squares Estimator. The text is divided into four chapters. In Chapter 1 assertions on the probability of large deviation of normal Least Squares Estimator of regression function parameters are made. Chapter 2 indicates conditions for Least Moduli Estimator asymptotic normality. An asymptotic expansion of Least Squares Estimator as well as its distribution function are obtained and two initial terms of these asymptotic expansions are calculated. Separately, the Berry-Esseen inequality for Least Squares Estimator distribution is deduced. In the third chapter asymptotic expansions related to functionals of Least Squares Estimator are dealt with. Lastly, Chapter 4 offers a comparison of the powers of statistical tests based on Least Squares Estimators. The Appendix gives an overview of subsidiary facts and a list of principal notations. Additional background information, grouped per chapter, is presented in the Commentary section.

This volume presents an authoritative collection of major survey papers on algebraic combinatorics which originally appeared in Russian, augmented by four survey papers written specially for this book. The algebraic theory of combinatorial objects is the branch of mathematics that studies the relation between local properties of a combinatorial object and the global properties of its automorphism group. The content is divided into three parts: the first deals with cellular rings; the second deals with distance-regular and distance-transitive graphs; and part 3 contains papers on the relatively new branch of amalgams and geometry. For complex systems theorists; mathematicians interested in group theory and combinatorics.

This book presents up-to-date mathematical results in asymptotic theory on nonlinear regression on the basis of various asymptotic expansions of least squares, its characteristics, and its distribution functions of functionals of Least Squares Estimator. It is divided into four chapters. In Chapter 1 assertions on the probability of large deviation of normal Least Squares Estimator of regression function parameters are made. Chapter 2 indicates conditions for Least Moduli Estimator asymptotic normality. An asymptotic expansion of Least Squares Estimator as well as its distribution function are obtained and two initial terms of these asymptotic expansions are calculated. Separately, the Berry-Esseen inequality for Least Squares Estimator distribution is deduced. In the third chapter asymptotic expansions related to functionals of Least Squares Estimator are dealt with. Lastly, Chapter 4 offers a comparison of the powers of statistical tests based on Least Squares Estimators. The Appendix gives an overview of subsidiary facts and a list of principal notations. Additional background information, grouped per chapter, is presented in the Commentary section.The volume concludes with an extensive Bibliography. Audience: This book will be of interest to mathematicians and statisticians whose work involves stochastic analysis, probability theory, mathematics of engineering, mathematical modelling, systems theory or cybernetics.