## Bootstrap Methods and Their ApplicationThis book gives a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis. Applications include stratified data; finite populations; censored and missing data; linear, nonlinear, and smooth regression models; classification; time series and spatial problems. Special features of the book include: extensive discussion of significance tests and confidence intervals; material on various diagnostic methods; and methods for efficient computation, including improved Monte Carlo simulation. Each chapter includes both practical and theoretical exercises. Included with the book is a disk of purpose-written S-Plus programs for implementing the methods described in the text. Computer algorithms are clearly described, and computer code is included on a 3-inch, 1.4M disk for use with IBM computers and compatible machines. Users must have the S-Plus computer application. Author resource page: http://statwww.epfl.ch/davison/BMA/ |

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### Contents

Introduction | ix |

The Basic Bootstraps | 9 |

22 Parametric Simulation | 13 |

23 Nonparametric Simulation | 20 |

24 Simple Confidence Intervals | 25 |

25 Reducing Error | 29 |

26 Statistical Issues | 35 |

27 Nonparametric Approximations for Variance and Bias | 43 |

64 Aggregate Prediction Error and Variable Selection | 288 |

65 Robust Regression | 305 |

66 Bibliographic Notes | 313 |

67 Problems | 314 |

68 Practicals | 319 |

Further Topics in Regression | 324 |

72 Generalized Linear Models | 325 |

73 Survival Data | 344 |

28 Subsampling Methods | 53 |

29 Bibliographic Notes | 57 |

210 Problems | 58 |

211 Practicals | 64 |

Further Ideas | 68 |

32 Several Samples | 69 |

33 Semiparametric Models | 75 |

34 Smooth Estimates of F | 77 |

35 Censoring | 80 |

36 Missing Data | 86 |

37 Finite Population Sampling | 90 |

38 Hierarchical Data | 98 |

39 Bootstrapping the Bootstrap | 101 |

310 Bootstrap Diagnostics | 111 |

311 Choice of Estimator from the Data | 118 |

312 Bibliographic Notes | 121 |

313 Problems | 124 |

314 Practicals | 129 |

Tests | 134 |

42 Resampling for Parametric Tests | 138 |

43 Nonparametric Permutation Tests | 154 |

44 Nonparametric Bootstrap Tests | 159 |

45 Adjusted Pvalues | 173 |

46 Estimating Properties of Tests | 178 |

47 Bibliographic Notes | 181 |

48 Problems | 182 |

49 Practicals | 185 |

Confidence Intervals | 189 |

52 Basic Confidence Limit Methods | 191 |

53 Percentile Methods | 200 |

54 Theoretical Comparison of Methods | 209 |

55 Inversion of Significance Tests | 218 |

56 Double Bootstrap Methods | 221 |

57 Empirical Comparison of Bootstrap Methods | 228 |

58 Multiparameter Methods | 229 |

59 Conditional Confidence Regions | 236 |

510 Prediction | 241 |

511 Bibliographic Notes | 244 |

512 Problems | 245 |

513 Practicals | 249 |

Linear Regression | 254 |

62 Least Squares Linear Regression | 255 |

63 Multiple Linear Regression | 271 |

74 Other Nonlinear Models | 351 |

75 Misclassification Error | 356 |

76 Nonparametric Regression | 360 |

77 Bibliographic Notes | 372 |

78 Problems | 374 |

79 Practicals | 376 |

Complex Dependence | 383 |

83 Point Processes | 411 |

84 Bibliographic Notes | 422 |

85 Problems | 424 |

86 Practicals | 428 |

Improved Calculation | 433 |

92 Balanced Bootstraps | 434 |

93 Control Methods | 442 |

94 Importance Resampling | 446 |

95 Saddlepoint Approximation | 460 |

96 Bibliographic Notes | 479 |

97 Problems | 480 |

98 Practicals | 486 |

Semiparametric Likelihood Inference | 491 |

102 MultinomialBased Likelihoods | 492 |

103 Bootstrap Likelihood | 499 |

104 Likelihood Based on Confidence Sets | 501 |

105 Bayesian Bootstraps | 504 |

106 Bibliographic Notes | 506 |

107 Problems | 508 |

108 Practicals | 511 |

Computer Implementation | 514 |

112 Basic Bootstraps | 517 |

113 Further Ideas | 523 |

114 Tests | 526 |

115 Confidence Intervals | 528 |

116 Linear Regression | 529 |

117 Further Topics in Regression | 532 |

118 Time Series | 535 |

119 Improved Simulation | 537 |

1110 Semiparametric Likelihoods | 541 |

Cumulant Calculations | 543 |

Bibliography | 547 |

560 | |

562 | |

565 | |

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### Common terms and phrases

adjusted algorithm analysis apply approach appropriate approximation assume average balanced basic bias block boot bootstrap bootstrap samples calculate Chapter choice conditional confidence intervals confidence limits correlation corresponding covariates defined denote density depend described discussed distribution effect empirical equal error estimate exact Example exponential Figure fitted follows function given gives hypothesis idea importance independent influence values interest least squares left panel likelihood mean method nonparametric normal Note null observed obtained original P-value panel of Figure panel shows parameter permutation plot population possible practice probability Problem properties quantiles random ratio replacement resampling residuals response right panel sample scale scheme Section shows similar simple simulation smoothing standard statistic suggests Suppose Table theoretical transformation true usual values variables variance vector weighted zero