STAT1008 Lecture Notes - Lecture 13: Confidence Interval, Statistic, Standard Deviation
STAT1008 Week 5 Lecture A
● Bootstrap sample:
○ Random sample taken with replacement from the original sample, of the
same size as the original sample
○ In order to construct the interval estimates we need the standard error of
the statistics. The standard error = standard deviation of the standard
distribution
○ Bootstrap statistic is the statistic computed on a bootstrap sample
○ Original Sample -> Sample Statistic. From og sample you get multiple
bootstrap samples (given that it is creating a sample form your original
sample it is easy to calculate how many bootstrap samples you want) and
then get the bootstrap statistic. Combine all the bootstrap statistics ->
bootstrap distribution
● Sampling Distribution:
○ In the beginning there’s a population -> finding the mean height ->
creating random sample -> WE ONLY HAVE ONE SEED and are
centered around the mean
● Bootstrap Distribution:
○ Bootstrap population -> seed = bootstrap sample -> estimates the
distribution and variability (SE) of x bar’s from the bootstrap
● GOLDEN RULE FOR BOOTSTRAP:
○ Bootstrap statistics are to the original sample statistic as the original
sample statistics to the population parameter
● Centre:
○ The sampling distribution is centered around the population parameter
○ The bootstrap distribution is centered around the sample statistic
○ This follows from the golden rule
○ We care about the variability
● Standard error:
○ The variability of the bootstrap statistics is similar to the variability of the
sample statistics
○ The standard error of a statistic can be estimated using the standard
deviation of the bootstrap distribution!
● Confidence Intervals:
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Random sample taken with replacement from the original sample, of the same size as the original sample. In order to construct the interval estimates we need the standard error of the statistics. The standard error = standard deviation of the standard distribution. Bootstrap statistic is the statistic computed on a bootstrap sample. From og sample you get multiple bootstrap samples (given that it is creating a sample form your original sample it is easy to calculate how many bootstrap samples you want) and then get the bootstrap statistic. Combine all the bootstrap statistics -> bootstrap distribution. In the beginning there"s a population -> finding the mean height -> creating random sample -> we only have one seed and are centered around the mean. Bootstrap population -> seed = bootstrap sample -> estimates the distribution and variability (se) of x bar"s from the bootstrap. Bootstrap statistics are to the original sample statistic as the original sample statistics to the population parameter.
