第三章 经典线性回归模型

Quiz 2

1、单选题:

‌The OLS estimator  does NOT exist if 

‍选项:
A:  is singular
B:
C: for some 
D: All of the above
答案: 【  is singular

2、单选题:

‌If Assumption 3.1,3.2 and Assumption 3.3(a) and 3.4 holds, which of the following is NOT true about the OLS estimator  ?

‌选项:
A:
B:
C:
D:
答案: 【 

3、单选题:

‏Which of the following is NOT true about the projection matrix ?

‍选项:
A: P is symmetric
B:

C: is also symmetric
D:
答案: 【 

4、单选题:
​Which of the following is NOT true about Assumption 3.2 ?‎
选项:
A: Assumption 3.2 implies 
B: Assumption 3.2 implies, for t = 1, 2, · · · , n.
C: Assumptions 3.1 and 3.2 ensure correct model specification on  for a linear regression model.
D: Assumptions 3.1 and 3.2 can NOT guarantee correct model specification on  for a linear regression model.
答案: 【 Assumptions 3.1 and 3.2 can NOT guarantee correct model specification on  for a linear regression model.

5、单选题:

‎Which of the following is not true about ?

​选项:
A:   is always between 0 and 1
B:
C: When X contains an intercept term,  is between 0 and 1
D: When X does not contain an intercept term,  might be negative
答案: 【 When X does not contain an intercept term,  might be negative

6、判断题:

‍When X is NOT stochastic,  is equivalent to .

‏选项:
A: 正确
B: 错误
答案: 【 正确

7、判断题:

‍If  is an independent random sample,  is equivalent to  for t = 1, 2, · · · , n.

‌选项:
A: 正确
B: 错误
答案: 【 正确

8、判断题:

‍Assumption 3.4 can be written more compactly as .

​选项:
A: 正确
B: 错误
答案: 【 错误

9、判断题:

‎Let be the estimated residual from the OLS estimation. We
always have .

​选项:
A: 正确
B: 错误
答案: 【 错误

10、判断题:

​Let  be the estimated residual from the OLS estimation. ’s are independent.

​选项:
A: 正确
B: 错误
答案: 【 错误

11、判断题:

‏Let be the estimated residual associated with the OLS estimator . We have  under some assumptions.

‎选项:
A: 正确
B: 错误
答案: 【 正确

12、判断题:

‍In Section 3.7, under and some assumptions, we have .

‏选项:
A: 正确
B: 错误
答案: 【 正确

13、判断题:

‎In Section 3.7, under and some assumptions, we have .

‎选项:
A: 正确
B: 错误
答案: 【 错误

14、判断题:

‏When , where V is some known symmetric and positive definite matrix,  in general.

‏选项:
A: 正确
B: 错误
答案: 【 错误

15、判断题:

‍When , where V is some known symmetric and positive definite matrix, we can still use the T and F test statistics derived in Section 3.7 to conduct hypothesis testing.

‎选项:
A: 正确
B: 错误
答案: 【 错误

第四章 独立同分布样本的线性回归模型

Quiz 3

1、单选题:
‏The asymptotic theory discussed in Chapter 4 is applicable for​
选项:
A: Time series data with serial correlation
B: i.i.d cross-sectional data
C: None of the above
D: All of the above
答案: 【 i.i.d cross-sectional data

2、单选题:
‍Which of the following assumption is dropped in Chapter 4?‎
选项:
A: is an observable i.i.d random sample.
B: Linearity, i.e., for t = 1, 2, · · · , n.
C:
D:
答案: 【 

3、单选题:

‎Which of the following is NOT true about Assumption 4.4, regarding ?

‌选项:
A: The dimension of Q is n × n
B: Q is nonsingular
C: Every element of Q is finite
D: Q contains elements like ’s.
答案: 【 The dimension of Q is n × n

4、单选题:

‎Which of the following is NOT true about Assumption 4.5, regarding ?

‎选项:
A: With
B: The dimension of V is n × n
C: Every element of V is finite
D: V is symmetric
答案: 【 The dimension of V is n × n

5、单选题:
‎Which of the following is NOT true about Assumptions 4.1-4.5?‍
选项:
A: Assumptions 4.1 and 4.3 imply that the strict exogeneity condition (Assumption 3.2) holds
B: When Xt contains the intercept term, Assumption 4.5 implies 
C: in Assumption 4.3 rules out conditional heteroskedasticity
D: When there exits conditional homoskedasticity, Assumption 4.4 can ensure Assumption 4.5
答案: 【 in Assumption 4.3 rules out conditional heteroskedasticity

6、判断题:

‎The correct model specification assumption, i.e.,  ensures consistency of the OLS estimator β

‏选项:
A: 正确
B: 错误
答案: 【 正确

7、判断题:

‏We utilize a univariate Central Limit theorem for i.i.d random sample to establish the asymptotic normality of  in Chapter 4.

‌选项:
A: 正确
B: 错误
答案: 【 错误

8、判断题:

​Under Assumptions 4.1-4.5, we can show that the asymptotic variance of  is 

‌选项:
A: 正确
B: 错误
答案: 【 正确

9、判断题:

‎With , the asymptotic variance of  can be simplified to .

‍选项:
A: 正确
B: 错误
答案: 【 错误

10、判断题:

‍With .

‍选项:
A: 正确
B: 错误
答案: 【 错误

11、判断题:

‌We can use   to consistently estimate Q.

​选项:
A: 正确
B: 错误
答案: 【 正确

12、判断题:

​We can use  to consistently estimate .

‌选项:
A: 正确
B: 错误
答案: 【 正确

13、判断题:

‌In Section 4.6, under and conditional homoskedasticity, we have .

‏选项:
A: 正确
B: 错误
答案: 【 正确

14、判断题:

‌ In Section 4.6, under 

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