Bootstrapping: An Integrated Approach with Python and Stata

by Felix Bittmann

Overview

Bootstrapping is a conceptually simple statistical technique to increase the quality of estimates, conduct robustness checks and compute standard errors for virtually any statistic. This book provides an intelligible and compact introduction for students, scientists and practitioners. It not only gives a clear explanation of the underlying concepts but also demonstrates the application of bootstrapping using Python and Stata.

Product Details

ISBN-13:	9783110693379
Publisher:	De Gruyter
Publication date:	04/19/2021
Sold by:	Barnes & Noble
Format:	eBook
Pages:	128
File size:	8 MB
Age Range:	18 Years

About the Author

Felix Bittmann is a research assistant and PhD candidate at the Leibniz Institute for Educational Trajectories (Bamberg). He studied sociology and history in Freiburg (Breisgau) and Bamberg. His research interests are social inequality, education, quantitative methods and philosophy of science.

Table of Contents

Introduction vii

1 Basic statistical concepts 1

1.1 Arithmetic mean 1

1.2 Standard deviation 1

1.3 Standard error 2

1.4 Confidence intervals 3

1.5 Applied example 4

1.6 P-values 5

1.7 Testing for normality 8

1.8 Probability density functions 10

1.9 Bias and variance 13

1.10 Normality and confidence intervals revisited 14

2 Bootstrapping 17

2.1 Working example 17

2.2 Requirements 19

2.3 Diagnostics 21

2.3.1 Unique values 22

2.3.2 Distribution of bootstrap-results 23

2.3.3 Rate of convergence 25

2.4 The logic of bootstrapping 26

2.5 Failures of the bootstrap 29

3 Confidence intervals 32

3.1 Normal intervals 32

3.2 Percentile intervals 33

3.3 Bias corrected intervals (BC) 34

3.4 Bias corrected and accelerated intervals (BCa) 37

3.5 Double bootstrap 39

3.6 Transformations 42

3.7 Summary and simulation 44

4 Hypothesis testing 49

4.1 The logic of hypothesis tests 49

4.2 Confidence intervals 51

4.3 Sampling in accordance with the null 53

4.4 Permutation tests 54

4.4.1 Paired permutation tests 59

4.4.2 Boot or permute? 61

4.5 Power calculations 63

5 Regression models 66

5.1 Sampling observations 66

5.2 Sampling residuals 70

5.3 Dealing with outliers 71

5.4 Predicting outcomes and bagging 75

6 Applied programming examples 78

6.1 Python 78

6.1.1 Basics 78

6.1.2 All confidence intervals 80

6.1.3 Permutation tests 85

6.1.4 Multithreading 89

6.1.5 Importing data 90

6.1.6 Appendix 92

6.2 Stata 94

6.2.1 Descriptive statistics 95

6.2.2 Estimating models 97

6.2.3 Writing own programs 99

6.2.4 Permutation tests 106

6.2.5 Longitudinal and cluster analyses 108

6.3 Computational speed 114

6.4 Further reading 117

Bibliography 119