1、Chapter 5 双变量回归：区间估计与假设检验,主讲：彭红枫武汉大学经济与管理学院金融系 CopyrightHongfeng Peng 2006 Wuhan University,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,2,5.1 回顾统计学相关内容,问题： 如果 ，使得：则称,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,3,假设检验中的两类错误,第一类错误：拒绝真实； 第二类错误：接受错误。,2019/6/14,Hon
2、gfeng Peng Department of Finance, Wuhan University,4,5.2回归系数1和2的置信区间,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,5,回归系数1和2的置信区间,2的显著水平为的置信区间为：同样，1显著水平为的置信区间为：,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,6,5.3 2的置信区间,2019/6/14,Hongfeng Peng Department of Financ
3、e, Wuhan University,7,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,8,5.3 假设检验,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,9,5.4 假设检验：置信区间方法,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,10,5.5 假设检验：显著性检验方法,2019/6/14,Hongfeng Peng Department of
4、 Finance, Wuhan University,11,t检验方法的直接计算,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,12,置信区间方法与显著性检验方法的关系,在置信区间程序中，我们试图建立一个以某种概率包含有真实但未知的 的一个范围或区间； 而在显著性检验步骤中，我们假设 为某值，然后来看所计算的 是否位于该假设值周围的某个合理(置信)范围之内。,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,13,显著性t检验：决策规则
5、,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,14,2检验的显著性（2检验）,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,15,补充：自由度,模型中样本值可以自由变动的个数，称为自由度 自由度=样本个数- 样本数据受约束条件（方程）的个数 例如，样本数据个数=n，它们受k+1个方程的约束（这n个数必须满足这k+1个方程） 那么，自由度df = n-k-1,2019/6/14,Hongfeng Peng Department of
6、 Finance, Wuhan University,16,数据个数与约束方程,Y1+Y2+Y3=7Y1=7 那么Y2、Y3中只有1个是自由的。 又如：Y1+Y2+Y3+Y4=7Y1=7 那么，Y2、Y3、Y4中只有2个是自由的,k元模型中随机扰动项的自由度为什么 =n-k-1?,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,18,5.6 P value,P value 当我们对给定的样本算出一个检验统计量(如t统计量)的值时，为什么不干脆查阅适当的统计表，看看得到一个大到和从样本得到的检验统计量那样大的数值的确
7、切概率? 这个概率就叫做P值(P value),2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,19,5.7 回归分析的应用：预测问题,样本回归函数的一个用途是“预测”或“预报”对应于给定X的未来的Y值。 均值预测 已知X的值，去预测Y的条件均值 个值预测 已知X的值，去预测Y的一个个别值,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,20,均值预测(mean prediction),2019/6/14,Hongfeng Peng D
8、epartment of Finance, Wuhan University,21,个值预测 (individual prediction),2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,22,均值预测与各值预测之比较,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,23,5.8 报告回归分析的结果,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,24,5
9、.9 评价回归分析的结果,一些准则： 1、所估系数的符号是否与理论或事前预期相一致? 2、系数在统计上是否显著？ 3、方程的显著性（回归模型在多大程度上解释了因变量的变异） 4、残差的正态性检验,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,25,正态性检验,正态性检验方法 Chi卡方拟合优度检验 雅克一贝拉（JB）检验,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,26,补充： Moments of a Random Variab
10、le,The l-th moment of a continuous random variable X is defined as,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,27,The first moment is called the mean or expectation of X. It measures the central location of the distribution.We denote the mean of X by x. The l-th central moment of
11、 X is defined as,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,28,The second central moment, denoted by , measures the variability of X and is called the variance of X. The positive square root, x ,of variance is the standard deviation of X.,2019/6/14,Hongfeng Peng Department of Fi
12、nance, Wuhan University,29,The third central moment measures the symmetry of X with respect to its mean,whereas the 4th central moment measures the tail behavior of X. In statistics, skewness and kurtosis, which are normalized 3rd and 4th central moments of X, are often used to summarize the extent
13、of asymmetry and tail thickness.,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,30,Specifically, the skewness and kurtosis of X are defined as,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,31,习题,2019/6/14,Hongfeng Peng Department of Finance, Wuhan University,32,作业发送邮箱,,
