9. Random Subsampling
Bradley Efron · Society for Industrial and Applied Mathematics eBooks · 1982
Hartigan (1969) introduced another resampling plan which we will call random subsampling. It is designed to give exact confidence intervals, rather than just standard deviations, but in a special class of problems: that of estimating the center of a symmetric distribution on the real line. We begin with a description of the problem and Hartigan's “typical value theorem”, which very neatly gives the desired confidence intervals. Then we go on to show the connection between random subsampling and the bootstrap, in terms of large sample theory. Chapter 10 concerns the important problem of small sample nonparametric confidence intervals for nonsymmetric problems.