Subsampling [Paperback]

Since Efron's profound paper on the bootstrap, an enormous amount of effort has been spent on the development of bootstrap, jacknife, and other resampling methods. The primary goal of these computer-intensive methods has been to provide statistical tools that work in complex situations without imposing unrealistic or unverifiable assumptions about the data generating mechanism. This book sets out to lay some of the foundations for subsampling methodology and related methods.Since Efron's profound paper on the bootstrap, an enormous amount of effort has been spent on the development of bootstrap, jacknife, and other resampling methods. The primary goal of these computer-intensive methods has been to provide statistical tools that work in complex situations without imposing unrealistic or unverifiable assumptions about the data generating mechanism. The primary goal of this book is to lay some of the foundation for subsampling methodology and related methods.I Basic Theory.- 1 Bootstrap Sampling Distributions.- 1.1 Introduction.- 1.1.1 Pivotal Method.- 1.1.2 Asymptotic Pivotal Method.- 1.1.3 Asymptotic Approximation.- 1.1.4 Bootstrap Approximation.- 1.2 Consistency.- 1.3 Case of the Nonparametric Mean.- 1.4 Generalizations to Mean-like Statistics.- 1.5 Bootstrapping the Empirical Process.- 1.6 Differentiability and the Bootstrap.- 1.7 Further Examples.- 1.8 Hypothesis Testing.- 1.9 Conclusions.- 2 Subsampling in the I.I.D. Case.- 2.1 Introduction.- 2.2 The Basic Theorem.- 2.3 Comparison with the Bootstrap.- 2.4 Stochastic Approximation.- 2.5 General Parameters and Other Choices of Root.- 2.5.1 Studentized Roots.- 2.5.2 General Parameter Space.- 2.6 Hypothesis Testing.- 2.7 Data-Dependent Choice of Block Size.- 2.8 Variance Estimation: The Delete-d Jackknife.- 2.9 Conclusions.- 3 Subsampling for Stationary Time Series.- 3.1 Introduction.- 3.2 Univariate Parameter Case.- 3.2.1 Some Motivation: The Simplest Example.- 3.2.2 Theory and Methods for the General Univariate Palƒ)