Rates Of Convergence Of Limit Distributions Of Order Statistics Under Power Normalization

The purpose of this thesis is to study the rates of convergence of limit dis-tributions of order statistics under power normalization, which includes two main parts. In the first part of the thesis, we discuss the rates of convergence of extremes for general error distribution under power normalization. In the second part of the thesis, we derive the necessary and sufficient conditions of Edgeworth expansion for distributions of extreme value.Firstly, we apply the theory of p-max stable laws to study the rates of con-vergence of extremes for general error distribution under power normalization. We derive the exact uniform convergence rate of the distribution of maximum to its ex-treme value limit. Secondly, we study the rates of convergence of limit distribution of order statistics under power normalization by the unified representation of the six power stable limit laws and the regular varying function. By using the theory of regular varying function, we derive the Edgeworth expansion for distributions of extreme values under power normalizationAs a corollary, rate of the uniform convergence for distributions of extreme values is obtained...