The Bootstrap Method

Abstract

In the foregoing chapters,wediscussed three replication-based methods of variance estimation. Here we close our coverage of replication methods with a presentation of Efron’s (1979) bootstrap method, which has sparked a massive amount and variety of research in the past quarter century. For example, see Bickel and Freedman (1984), Booth, Butler, and Hall (1994), Chao and Lo (1985, 1994), Chernick (1999), Davison and Hinkley (1997), Davison, Hinkley, and Young (2003), Efron (1979, 1994), Efron andTibshirani (1986, 1993, 1997), Gross (1980), Hinkley (1988), Kaufman (1998), Langlet, Faucher, and Lesage (2003), Li, Lynch, Shimizu, and Kaufman (2004), McCarthy and Snowden (1984), Rao,Wu, and Yue (1992), Roy and Safiquzzaman (2003), Saigo, Shao, and Sitter (2001), Shao and Sitter (1996), Shao and Tu (1995), Sitter (1992a, 1992b), and the references cited by these authors.