經(jīng)濟(jì)管理假設(shè)及財(cái)務(wù)知識分析檢驗(yàn)

1、Chapter 5 雙變量回歸：區(qū)間估計(jì)與假設(shè)檢驗(yàn),主講：彭紅楓 武漢大學(xué)經(jīng)濟(jì)與管理學(xué)院金融系 CopyrightHongfeng Peng 2006 Wuhan University,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,2,5.1 回顧統(tǒng)計(jì)學(xué)相關(guān)內(nèi)容,問題： 如果 ，使得： 則稱,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,3,假設(shè)檢驗(yàn)中的兩類錯(cuò)誤,第一類錯(cuò)誤：拒絕真實(shí)； 第二類錯(cuò)誤：接受錯(cuò)誤。,2020/7/14,H

2、ongfeng Peng Department of Finance, Wuhan University,4,5.2回歸系數(shù)1和2的置信區(qū)間,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,5,回歸系數(shù)1和2的置信區(qū)間,2的顯著水平為的置信區(qū)間為： 同樣，1顯著水平為的置信區(qū)間為：,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,6,5.3 2的置信區(qū)間,2020/7/14,Hongfeng Peng Department of Fin

3、ance, Wuhan University,7,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,8,5.3 假設(shè)檢驗(yàn),2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,9,5.4 假設(shè)檢驗(yàn)：置信區(qū)間方法,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,10,5.5 假設(shè)檢驗(yàn)：顯著性檢驗(yàn)方法,2020/7/14,Hongfeng Peng Department

4、 of Finance, Wuhan University,11,t檢驗(yàn)方法的直接計(jì)算,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,12,置信區(qū)間方法與顯著性檢驗(yàn)方法的關(guān)系,在置信區(qū)間程序中，我們試圖建立一個(gè)以某種概率包含有真實(shí)但未知的 的一個(gè)范圍或區(qū)間； 而在顯著性檢驗(yàn)步驟中，我們假設(shè) 為某值，然后來看所計(jì)算的 是否位于該假設(shè)值周圍的某個(gè)合理(置信)范圍之內(nèi)。,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,13,顯著性t檢驗(yàn)：決

5、策規(guī)則,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,14,2檢驗(yàn)的顯著性（2檢驗(yàn)）,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,15,補(bǔ)充：自由度,模型中樣本值可以自由變動(dòng)的個(gè)數(shù)，稱為自由度 自由度=樣本個(gè)數(shù)- 樣本數(shù)據(jù)受約束條件（方程）的個(gè)數(shù) 例如，樣本數(shù)據(jù)個(gè)數(shù)=n，它們受k+1個(gè)方程的約束（這n個(gè)數(shù)必須滿足這k+1個(gè)方程） 那么，自由度df = n-k-1,2020/7/14,Hongfeng Peng Department

6、 of Finance, Wuhan University,16,數(shù)據(jù)個(gè)數(shù)與約束方程,Y1+Y2+Y3=7 Y1=7 那么Y2、Y3中只有1個(gè)是自由的。 又如： Y1+Y2+Y3+Y4=7 Y1=7 那么，Y2、Y3、Y4中只有2個(gè)是自由的,k元模型中隨機(jī)擾動(dòng)項(xiàng)的自由度為什么=n-k-1?,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,18,5.6 P value,P value 當(dāng)我們對給定的樣本算出一個(gè)檢驗(yàn)統(tǒng)計(jì)量(如t統(tǒng)計(jì)量)的值時(shí)，為什么不干脆查閱適當(dāng)?shù)慕y(tǒng)計(jì)表，看看得到一個(gè)大到和從樣本得到的檢驗(yàn)統(tǒng)計(jì)量那樣大

7、的數(shù)值的確切概率? 這個(gè)概率就叫做P值(P value),2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,19,5.7 回歸分析的應(yīng)用：預(yù)測問題,樣本回歸函數(shù)的一個(gè)用途是“預(yù)測”或“預(yù)報(bào)”對應(yīng)于給定X的未來的Y值。 均值預(yù)測 已知X的值，去預(yù)測Y的條件均值 個(gè)值預(yù)測 已知X的值，去預(yù)測Y的一個(gè)個(gè)別值,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,20,均值預(yù)測(mean prediction),2020/7/14,Hongfeng P

8、eng Department of Finance, Wuhan University,21,個(gè)值預(yù)測(individual prediction),2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,22,均值預(yù)測與各值預(yù)測之比較,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,23,5.8 報(bào)告回歸分析的結(jié)果,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,

9、24,5.9 評價(jià)回歸分析的結(jié)果,一些準(zhǔn)則： 1、所估系數(shù)的符號是否與理論或事前預(yù)期相一致? 2、系數(shù)在統(tǒng)計(jì)上是否顯著？ 3、方程的顯著性（回歸模型在多大程度上解釋了因變量的變異） 4、殘差的正態(tài)性檢驗(yàn),2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,25,正態(tài)性檢驗(yàn),正態(tài)性檢驗(yàn)方法 Chi卡方擬合優(yōu)度檢驗(yàn) 雅克一貝拉（JB）檢驗(yàn),2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,26,補(bǔ)充： Moments of a Random Va

10、riable,The l-th moment of a continuous random variable X is defined as,2020/7/14,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 momen

11、t of X is defined as,2020/7/14,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.,2020/7/14,Hongfeng Peng Department o

12、f Finance, 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 of asymmetry and tail thickness.,2020/7/14,Hongfeng Peng Department of Finance, Wuhan University,30,Specifica