﻿ 简单线性EV回归模型中最小二乘估计量的Berry-Esseen估计 A Note on LS Berry-Esseen Estimator in Simple Linear EV Regression Model

Vol.04 No.01(2015), Article ID:14858,7 pages
10.12677/AAM.2015.41004

A Note on LS Berry-Esseen Estimator in Simple Linear EV Regression Model

Jiao Meng, Mingming Yu

Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu

Received: Jan. 26th, 2015; accepted: Feb. 11th, 2015; published: Feb. 17th, 2015

ABSTRACT

In this paper, we study the convergence rate of the central limit theorems for LS estimator in simple linear errors-in-variables (EV) regression model. Further, its application has been introduced detailedly by Miao, Yang and Shen in [1] .

Keywords:Central Limit Theorem, Convergence Rate, EV Regression Model, LS Estimator

1. 介绍

(1)

(1)是未知常数；

(2)是独立同分布随机变量，，且

(3)是可观测值。

(2)

(3)

(4)

(5)

(6)

。因此，根据定理1.1有

(2) 满足定理B的所有假设，我们知道。随即可以得到

(1)

(2)

2. 定理的证明

(7)

(8)

(9)

(10)

(11)

(12)

，结合(9)，(10)，(11)，(12)，我们可以得到引理2.4的证明。

(13)

(14)

(15)

(16)

，结合(13)，(14)，(15)，(16)和的估计，我们可以证明引理2.5。

(17)

A Note on LS Berry-Esseen Estimator in Simple Linear EV Regression Model. 应用数学进展,01,29-36. doi: 10.12677/AAM.2015.41004

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