题目
Assume we conduct a multivariate regression with based on a sample of 32 observations (n=32). The regression produces four regression coefficients, an intercept plus three partial slope coefficients. These OLS estimates are characterized by a student's t distribution with what, respectively, mean, variance, skew and kurtosis?
选项
A.0 (mean), 1.00 (variance), 0 (skew), 3.0 (kurtosis)
B.0, 1.08, 0, 3.0
C.0, 1.00, 0, 3.25
D.0, 1.08, 0, 3.25
答案
D
解析
For any student's t (without location & scale; i.e, one parameter student's t), the mean = 0 and the skew = 0 variance = df/(df-2). In this case, df = 32 - 4 = 28 and variance = 28/(28-2) = 1.077. excess kurtosis = 6/(df-4). In this case, excess kurtosis = 6/24 = 0.25 such that excess kurtosis = 3.25; i.e., student's t always has a heavy tail but it's only a slightly heavy tail. 对于任何学生t分布（没有位置和比例；即一个参数学生的t），均值=0，偏斜=0,方差=df/（df-2）。 在这种情况下，df= 32-4 = 28，方差=28 /（28-2）=1.077。过量峰度=6 /（df-4）。 在这种情况下，过量峰度=6/24 = 0.25，因此过量峰度=3.25；也就是说，学生的尾巴并不总是很厚，仅是微肥尾。