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Bootstrap Methods
Bootstrap Methods
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The bootstrap estimates the sampling distribution of a statistic by resampling with replacement from the observed data. Why does resampling with replacement work as an approximation to drawing new samples from the true population?
Hide and think first
A.
The bootstrap method is valid only when the underlying population follows a normal distribution, since normality ensures the sampling distribution is well-behaved
B.
Drawing with replacement creates mutually independent samples from the original data, which satisfies the independence requirement of the central limit theorem
C.
F
^
n
converges to the true
F
(Glivenko-Cantelli), so resampling from
F
^
n
approximates sampling from
F
D.
The bootstrap works because any resampling scheme produces the same distribution
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