
Explanation:
Bootstrapping is a resampling technique used to estimate the sampling distribution of a statistic by repeatedly resampling with replacement from the original data. "With replacement" is crucial; it means that after a data point is selected for a resampled dataset, it is put back into the original dataset, so it can be selected again. This process creates multiple "alternative" datasets, each of the same size as the original, but with potentially different combinations of the original data points (some may be repeated, others may be absent).
A is incorrect. Bootstrapping doesn't compress the data; it creates datasets of the same size as the original. While there are repeated observations within each resampled dataset, the overall amount of data across all resampled datasets is much larger than the original.
B is incorrect. Bootstrapping doesn't force the most extreme returns into every sample. The selection is random with replacement, so extreme values might appear multiple times in some resampled datasets, not at all in others, or just once.
C is incorrect. Scaling by the sample mean is not part of the bootstrapping process. Bootstrapping is about resampling the original data points, not modifying them.
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Q.6431 Compared to basic (raw) historical simulation, which of the following statements correctly characterizes what occurs during bootstrapping?
A
Bootstrapping compresses the original data, leading to repeated observations.
B
It replicates the most extreme historical returns in every sample.
C
It scales each historical return by a constant factor obtained from the sample’s mean.
D
It resamples (with replacement) many times, creating multiple “alternative” data sets.
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