Chapter 14 - Bootstrap Methods and Permutation Tests - WH Freeman

More documents

Recommendations

Info

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

Population distribution Sampling distribution Population median = M Sample median = m –4 M 10 –4 M 10 Sample 1 Bootstrap distribution for Sample 1 Bootstrap distribution 2 for Sample 1 –4 m 10 –4 m 10 –4 m 10 Sample 2 Bootstrap distribution for Sample 2 Bootstrap distribution 3 for Sample 1 –4 m 10 –4 m 10 –4 m 10 Sample 3 Bootstrap distribution for Sample 3 Bootstrap distribution 4 for Sample 1 –4 m 10 –4 m 10 –4 m 10 Sample 4 Bootstrap distribution for Sample 4 Bootstrap distribution 5 for Sample 1 –4 m 10 –4 m 10 –4 m 10 Sample 5 Bootstrap distribution for Sample 5 Bootstrap distribution 6 for Sample 1 –4 m 10 –4 m 10 –4 m 10 FIGURE 14.14 Five random samples (n = 15) from the same population, with a bootstrap distribution for the sample median formed by resampling from each of the five samples. At the right are five more bootstrap distributions from the first sample. 14-32
Section 14.3 Exercises 14-33 CAUTION There are more advanced variations of the bootstrap idea that improve performance for small samples and for statistics such as the median and quartiles. Unless you have expert advice or undertake further study, avoid bootstrapping the median and quartiles unless your sample is rather large. SECTION 14.3 Summary Almost all of the variation among bootstrap distributions for a statistic is due to the selection of the original random sample from the population. Resampling introduces little additional variation. Bootstrap distributions based on small samples can be quite variable. Their shape and spread reflect the characteristics of the sample and may not accurately estimate the shape and spread of the sampling distribution. Bootstrap inference from a small sample may therefore be unreliable. Bootstrap inference based on samples of moderate size is unreliable for statistics like the median and quartiles that are calculated from just a few of the sample observations. SECTION 14.3 Exercises 14.23 Most statistical software includes a function to generate samples from normal distributions. Set the mean to 8.4 and the standard deviation to 14.7. You can think of all the numbers that would be produced by this function if it ran forever as a population that has the N(8.4, 14.7) distribution. Samples produced by the function are samples from this population. (a) What is the exact sampling distribution of the sample mean x for a sample of size n from this population? (b) Draw an SRS of size n = 10 from this population. Bootstrap the sample mean x using 1000 resamples from your sample. Give a histogram of the bootstrap distribution and the bootstrap standard error. (c) Repeat the same process for samples of sizes n = 40 and n = 160. (d) Write a careful description comparing the three bootstrap distributions and also comparing them with the exact sampling distribution. What are the effects of increasing the sample size? 14.24 The data for Example 14.1 are 1664 repair times for customers of Verizon, the local telephone company in their area. In that example, these observations formed a sample. Now we will treat these 1664 observations as a population. The population distribution is pictured in Figures 14.1 and 14.8. It is very nonnormal. The population mean is µ = 8.4, and the population standard deviation is σ = 14.7. (a) Although we don’t know the shape of the sampling distribution of the sample mean x forasampleofsizen from this population, we do know the mean and standard deviation of this distribution. What are they?
Page 1 and 2: CHAPTER 14 Bootstrap Methods and Pe
Page 3 and 4: 14.1 The Bootstrap Idea 14-3 are su
Page 5 and 6: 14.1 The Bootstrap Idea 14-5 The bi
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 29 and 30: 14.3 How Accurate Is a Bootstrap Di
Page 31: 14.3 How Accurate Is a Bootstrap Di
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 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 (

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?