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MS22 Class 38 - Summary Flashcards | StudBud
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MS22 Class 38 - Summary
MS22 Class 38 - Summary
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1
Which of the following statements is not correct of the Cramer-Rao lower bound?
It holds for unbiased estimators.
Larger Fisher info results smaller lower bound.
For iid data of sampe size n we have g'(θ)2/(niθ)
The MLE attains the Cramer-Rao lower bound all the time.
2
What is not true for the correlation R in simple linear regression?
R2 gives the proportion of the variation of Y explained by X.
The squared correlation measures the strength of the linear fit.
The sign of R gives the direction of the linear relationship.
It is not invariant for rescaling (changing the measurements of X and Y).
3
Which of the following is the ellastic net penalty?
L1-norm of the parameter
Combination of L1 and squared L2-norms of the parameter
squared L2-norm of the parameter
L0 norm of the parameter.
4
Which of the following statement is not correct about the likelihood ratio test?
The critical region is of the form {λ(x)<cα}
\lambda (x)=\frac{p_{\hat{θ}}\left(x\right)}{p_{\hat{θ}_0}\left(x\right)}
Under regularity condition 2*log λ(x) converges to a χ2-distribution.
Large λ(x) indicates that H1 is correct.
5
Which of the following statement is not correct about the residual and total sum of squares in multiple regression?
The residuals are nonnegative
SSres ⩽ SStot
Y-X\hat{β} is the vector of the residuals
X\hat{β} is the ortogonal projection of Y to X.
6
Which of the following is not appropriate to check the normality of the sample?
χ2-test
Q-Q plots
Kolmogorov-Smirnov
T-test
7
Which assumption (if any) of the linear regression models is not satisfied about the residuals in this pictures ?
all assumptions are satisfies
Normality
linearity
Homoscedasticity (equal variance)
8
What is not true about the sufficient statistics V=V(X)?
The observation X is a sufficient statistic.
The conditional probability P(X=x|V=v) does not depend on θ.
It contains all relevant information about the data.
There is at most one sufficient statistics for a given model.
9
What can one test with the Wilcoxon signed-rank test?
If two samples have the same variance parameter.
If two samples are generated from the same unknown distribution.
If the sample is normally distributed.
If a sample is generated from a given family of distributions.
10
Which of the following statements is not correct about the BIC and/or AIC?
AIC penalizes larger models more than BIC.
Under regularity conditions BIC gives consistent model selection.
BIC selects smaller models than AIC.
AIC satisfies an oracle estimation bound.
11
What is the main problem with multiple testing?
The power of the test is too small.
In 1 out of 20 cases we falsely reject H0 and find non existing evidence
In 1 out of 20 cases we falsely do not reject H0, missing the correct H1.
Requires too many experiments.
12
Which of the following model is not a linear regression model
Y=β1x12+β2 exp(2x2)+e, e~N(0,1)
Y=β0+ β1x1+β2x12+e, e~N(0,1)
Y=β0+β1x1x2+β2 x2+e, e~N(0,1)
Y=β0β1x1+β2x2+e, e~N(0,1)
