How do the percentile method and the pivotal method for computing bootstrapping confidence intervals compare? Choose one

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Question:

How do the percentile method and the pivotal method for computing bootstrapping confidence intervals compare?
Choose one or more answers:
a. The width of the percentile confidence interval and the pivotal confidence interval may differ on the same set of bootstrap samples.
b. The pivotal method recenters and inverts the percentile confidence interval.
c. The percentile method provides symmetric confidence intervals around the estimator for the mean.
d. Both bootstrap confidence intervals computed for the mean always contain the mean of the given data set.

My selection: b, c, d

Question 2:
Which statements about bootstrapping are valid?
Choose one or more answers:
a. Bootstrapping does not use knowledge about the distribution of the estimator and is therefore widely applicable.
b. The bootstrap error and true error follow an increasingly similar distribution if the dataset gets larger.
c. If the pivotal bootstrap confidence interval contains the quantity of interest, then also the percentile bootstrap confidence interval does so.
d. An increasing number of bootstrapping samples lets the bootstrap estimator converge to the real parameter.

My selection: a, b, d

Question 3

How does the Bootstrap react to manipulating a standard gaussian data set?
Choose one or more answers:
a. If we increase the variance of the data points, the bootstrapped confidence interval for the first quartile gets larger.
b. The percentile method for computing the bootstrap mean confidence interval approximates the gaussian confidence interval when b gets large, even if the dataset is only very small.
c. If we take the absolute value of each data point, the width of the respective bootstrap confidence intervals for the mean does not change.
d. The lenght c2-c1 of the 95% percentile bootstrap confidence interval [c1,c2] for the median gets smaller than any constant if b* is sufficiently large.