Example applications Bootstrapping (statistics)

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smoothed bootstrap

in 1878, simon newcomb took observations on speed of light. data set contains 2 outliers, influence sample mean. (note sample mean need not consistent estimator population mean, because no mean need exist heavy-tailed distribution.) well-defined , robust statistic central tendency sample median, consistent , median-unbiased population median.


the bootstrap distribution newcomb s data appears below. convolution method of regularization reduces discreteness of bootstrap distribution adding small amount of n(0, σ) random noise each bootstrap sample. conventional choice



σ
=
1

/



n




{\displaystyle \sigma =1/{\sqrt {n}}}

sample size n.


histograms of bootstrap distribution , smooth bootstrap distribution appear below. bootstrap distribution of sample-median has small number of values. smoothed bootstrap distribution has richer support.



in example, bootstrapped 95% (percentile) confidence-interval population median (26, 28.5), close interval (25.98, 28.46) smoothed bootstrap.








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