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Lecture 8

ECON 2500 Lecture 8: Chapter 16 Bootstrap Methods and Permutation Tests Lecture 8

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ECON 2500
Andrei Semenov

Chapter 16 Bootstrap Methods and Permutation Tests Lecture 8 Thinking about the bootstrap idea • It might appear that resampling creates new data out of nothing. This seems suspicious. Even the name “bootstrap” comes from the impossible image of “pulling yourself up by your own bootstraps.”3 But the resampled observations are not used as if they were new data. • The bootstrap distribution of the resample means is used only to estimate how the sample mean of one actual sample of size 1664 would vary because of random sampling. • Using the same data for two purposes—to estimate a parameter and also to estimate the variability of the estimate—is perfectly legitimate. • We do exactly this when we calculate x to estimate μ and then calculate s/√n from the same data to estimate the variability of x. What is new? First of all, we don’t rely on the formula s/√n to estimate the standard deviation of x. • Instead, we use the ordinary standard deviation of the many x-values from our many resamples.4 Suppose that we take B resamples. • Call the means of these resamples x∗ to distinguish them from the mean x of the original sample. Find the mean and standard deviation of the x∗’s in the usual way. • To make clear that these are the mean and standard deviation of the means of the B resamples rather than the mean x and standard deviation s of the original sample, we use a distinct notation: • These formulas go all the way back to Chapter 1. Once we have the values x∗, LOOK BACK describing distributions with numbers, page 30 we just ask our software for their mean and standard deviation. • We will often apply the boots trap to statistics other than the sample mean. Here is the general definition. • Another thing that is new is that we don’t appeal to the central limit theorem or other theory to tell us that a sampling distributio
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