Physical description 
1 online resource (ix, 554 pages). 
Series 
Mathematics and Its Applications ; 273 

Mathematics and Its Applications ; 273.

Summary 
This monograph contains, for the first time, a systematic presentation of the theory of Ustatistics. On the one hand, this theory is an extension of summation theory onto classes of dependent (in a special manner) random variables. On the other hand, the theory involves various statistical applications. The construction of the theory is concentrated around the main asymptotic problems, namely, around the law of large numbers, the central limit theorem, the convergence of distributions of Ustatistics with degenerate kernels, functional limit theorems, estimates for convergence rates, and asymptotic expansions. Probabilities of large deviations and laws of iterated logarithm are also considered. The connection between the asymptotics of Ustatistics destributions and the convergence of distributions in infinitedimensional spaces are discussed. Various generalizations of Ustatistics for dependent multisample variables and for varying kernels are examined. When proving limit theorems and inequalities for the moments and characteristic functions the martingale structure of Ustatistics and orthogonal decompositions are used. The book has ten chapters and concludes with an extensive reference list. For researchers and students of probability theory and mathematical statistics. 
Other author 
Borovskikh, 뉬U. V. (뉬Uri橠Vasil嶩ch)

Subject 
Statistics.


Statistics. 

Electronic books. 
ISBN 
9789401735155 (electronic bk.) 

9401735158 (electronic bk.) 

9789048143467 

9048143462 

9401735158 
