Bootstrap Methods and Permutation Tests
• • Spread: The bootstrap standard error of a statistic is the standard deviation of its boots trap
• The boots trap standard foretime test he standard deviation of the sampling distribution of the
• Bootstrap t conﬁdence intervals If the boots trap distribution of astatistics how sa Normal shape
and small bias, we can get a conﬁdence interval for the parameter by using the bootstrap
standard rora nd the familiar distribution. An example will show how this works.
• Selling prices of residential real estate. We are interested in the selling prices of residential real
estate in Seattle, Washington.
• Table 16.1 displays the selling prices of a random sample of 50 pieces of real estate sold in
Seattle during 2002, as recorded by the county assessor.6 Unfortunately, the data do not
distinguish residential property from commercial property.
• Most sales are residential, but a few large commercial sales in a sample can greatly increase the
sample mean selling price. Figure16.6 shows the distribution of the sample prices.
• The distribution is far from Normal, with a few high outliers that may be commercial sales. The
sample is small, and the distribution is highly skewed and “contaminated” by an unknown
number of commercial sales.
• How can we estimate the center of the distribution despite these difﬁculties?
• The ﬁrst step is to abandon the mean as a measure of center in favor of a statistic that is more
resistant to outliers.
• We might choose the median, but in this case we will use the 25% trimmed mean, the mean of
them idle 50% of the trimmed mean, page 53 observations. The median is the middle or mean
of the 2 middle observations.
• The trimmed mean of tendoes a better job of representing the average of typical observations