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670B Final Flashcards | StudBud
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670B Final
670B Final
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Answers
1
Let F\left(t|\theta\right) be the cdf of a continuous random variable T, then F\left(T|\theta\right) is a pivot
True
False
2
\hat{\theta}_1 (biased)and \hat{\theta}_2 (unbiased)are two estimators of \theta, then
False
True
3
Suppose \left[L\left(X\right),U\left(X\right)\right] is 1-\alpha confidence interval estimator for \theta,
True
False
4
A UMP level \alpha test has the smallest Type I error probability among all level \alpha tests.
True
False
5
Sufficient statistic is unique.
False
True
6
In frequentist statistics, a parameter is a fixed unknown value.
True
False
7
If X_i are iid Poisson(\lambda), then Var\left(\overline{X}\right)=n\lambda
True
False
8
The variance of an UMVUE must achieve the CR lower bound.
True
False
9
If \hat{\theta} is the MLE of \theta, then \hat{\theta}^2 is a consistent estimator of \theta^2 under some conditions.
True
False
10
Using derivatives can always find the MLE
True
False
11
\hat{\theta} is the MLE of \theta, \frac{1}{\theta^2} is the fisher information, which of the following is not true?
\frac{\hat{\theta}-\theta}{\sqrt{\frac{\theta^2}{n}}}→N(0,1) in dist
Var\left(\hat{\theta}^2\right)\approx\frac{4\theta^4}{n}
Var\left(\hat{\theta}^2\right)\approx\frac{^{2\theta^2}}{n}
\sqrt{n}(\hat{\theta}-\theta)→N(0,\theta^2) in distribution.
12
Uniform\left(0,\theta\right) belongs to an exponential family.
True
False
13
TRUE or FALSE?
True
False
14
TRUE or FALSE?
False
True
15
If \hat{\theta} is the MLE of \theta, then \log\hat{\theta} is the MLE of \log\theta. (all functions are well defined.)
False
True
16
Which is a sufficient statistic for \theta?
\sum_{_{i=1}}^nX_i
\left(\sum_{_{i=1}}^nX_i,\sum_{_{i=1}}^nX_i^2\right)
\sum_{_{i=1}^{ }}^nX_i^2
17
The distribution of a pivotal quantity does not depend on parameters.
True
False
18
Consider testing H_0:\theta\le\theta_0vs \theta>\theta_0, power function is a function of \theta.
False
True
19
Minimal sufficient statistic is unique.
False
True
20
Consider the following pdf of N\left(\theta,\theta^2\right), then it belongs to an exponential family.
True
False
21
If (2,4) is a 95% CI for \theta, then the probability of \theta within (2,4) is 0.95.
True
False
22
If \hat{\theta} is an unbiased estimator of \theta, then \hat{\theta}^2 is unbiased estimator of \theta^2.
True
False
23
If \hat{\theta} is the MLE of \theta, I\left(\theta\right) is the fisher information, then
False
True
24
\left(\sum _{_{i=1}}^nX_i,\sum _{_{i=1}}^nX_i^2\right) is complete.
True
False
