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# Bootstrap08 - Bootstrap resampling ESM 206C Here's some...

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Bootstrap resampling May 13, 2008 ESM 206C

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Here’s some data μ g of mercury in one gram soil samples 0.853511661, 0.391905707, 0.143344303, 0.198267857, 0.266572367, 0.327306702, 0.834747834, 5.322618220, 0.817037696, 0.157247167, 0.328456677, 3.793153524, 0.513433215, 0.502938253, 0.733454663, 0.279345254, 0.952473470, 0.742740502, 0.178309271, 0.469049646, 0.764546106, 1.819858816, 0.830187557, 0.369993886, 0.644729374, 0.841576129, 0.734056277, 0.773035692, 0.810722543, 0.357449318
Soil mercury at a mine site 2 0.858; 1.166; 30. x x s n = = =

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How well does the sample statistic estimate the population parameter ? Accuracy: bias and precision Thought experiment: imagine repeating the sampling procedure many times, and each time calculating a sample mean Bias is the difference between average sample mean and population mean Precision is the standard deviation of the sample means
Take some more samples Sample.1 Sample.2 Sample.3 Sample.4 Sample.5 0 2 4 6 8 10 12 Sample Mercury.concentration

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Some statistical theory If the population is normally distributed: The sample mean is a normally distributed random variable with mean μ and variance σ 2 / n The sample mean and variance are unbiased estimates of the population mean and variance The standard error of the mean is an unbiased estimate of the precision of the sample mean, and can be used to construct confidence intervals The above are also true even if the population is not normally distributed, as long as the sample size is large enough
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## This note was uploaded on 08/06/2008 for the course ESM 206 taught by Professor Kendall,berkley during the Spring '08 term at UCSB.

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Bootstrap08 - Bootstrap resampling ESM 206C Here's some...

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