Chapter 14 - Bootstrap Methods and Permutation Tests - WH Freeman

More documents

Recommendations

Info

$Design and analysis of a fractional 413125 split-plot ... - ResearchGate$

14-4 CHAPTER 14 Bootstrap Methods and Permutation Tests 600 500 400 300 200 100 0 0 50 100 150 Repair times (in hours) (a) Repair times (in hours) 150 100 50 0 –2 0 2 z-score (b) FIGURE 14.1 (a) The distribution of 1664 repair times for Verizon customers. (b) Normal quantile plot of the repair times. The distribution is strongly right-skewed.
14.1 The Bootstrap Idea 14-5 The big idea: resampling and the bootstrap distribution Statistical inference is based on the sampling distributions of sample statistics. The bootstrap is first of all a way of finding the sampling distribution, at least approximately, from just one sample. Here is the procedure: resamples Step 1: Resampling. A sampling distribution is based on many random samples from the population. In Example 14.1, we have just one random sample. In place of many samples from the population, create many resamples by repeatedly sampling with replacement from this one random sample. Each resample is the same size as the original random sample. Sampling with replacement means that after we randomly draw an observation from the original sample we put it back before drawing the next observation. Think of drawing a number from a hat, then putting it back before drawing again. As a result, any number can be drawn more than once, or not at all. If we sampled without replacement, we’d get the same set of numbers we started with, though in a different order. Figure 14.2 illustrates three resamples from a sample of six observations. In practice, we draw hundreds or thousands of resamples, not just three. sampling with replacement Step 2: Bootstrap distribution. The sampling distribution of a statistic collects the values of the statistic from many samples. The bootstrap distribution of a statistic collects its values from many resamples. The bootstrap distribution gives information about the sampling distribution. bootstrap distribution THE BOOTSTRAP IDEA The original sample represents the population from which it was drawn. So resamples from this sample represent what we would get if we took many samples from the population. The bootstrap distribution of a statistic, based on many resamples, represents the sampling distribution of the statistic, based on many samples. 3.12 0.00 1.57 19.67 0.22 2.20 mean = 4.46 1.57 0.22 19.67 0.00 0.22 3.12 mean = 4.13 0.00 2.20 2.20 2.20 19.67 1.57 mean = 4.64 0.22 3.12 1.57 3.12 2.20 0.22 mean = 1.74 FIGURE 14.2 The resampling idea. The top box is a sample of size n = 6 from the Verizon data. The three lower boxes are three resamples from this original sample. Some values from the original are repeated in the resamples because each resample is formed by sampling with replacement. We calculate the statistic of interest—the sample mean in this example—for the original sample and each resample.
Page 1 and 2: CHAPTER 14 Bootstrap Methods and Pe
Page 3: 14.1 The Bootstrap Idea 14-3 are su
Page 7 and 8: 14.1 The Bootstrap Idea 14-7 Observ
Page 9 and 10: SRS of size n x - x - x - SRS of si
Page 11 and 12: Section 14.1 Summary 14-11 Number o
Page 13 and 14: 14.2 First Steps in Using the Boots
Page 23 and 24: Section 14.2 Exercises 14-23 800 Or
Page 25 and 26: Section 14.2 Exercises 14-25 (b) In
Page 27 and 28: 14.3 How Accurate Is a Bootstrap Di
Page 33 and 34: Section 14.3 Exercises 14-33 CAUTIO
Page 35 and 36: 14.4 Bootstrap Confidence Intervals
Page 43 and 44: Section 14.4 Exercises 14-43 (a) Ex
Page 45 and 46: Section 14.4 Exercises 14-45 (a) De
Page 47 and 48: 14.5 Significance Testing Using Per
Page 55 and 56:
14.5 Significance Testing Using Per
Page 57 and 58:
Section 14.5 Exercises 14-57 SECTIO
Page 59 and 60:
Section 14.5 Exercises 14-59 that p
Page 61 and 62:
Section 14.5 Exercises 14-61 14.56
Page 63 and 64:
Chapter 14 Exercises 14-63 TABLE 14
Page 65 and 66:
Chapter 14 Exercises 14-65 areas kn
Page 67 and 68:
Chapter 14 Exercises 14-67 (b) Do a
Page 69 and 70:
Chapter 14 Notes 14-69 CHAPTER 14 (
show all

Chapter 14 - Bootstrap Methods and Permutation Tests - WH Freeman

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?