Subsampling

The goal of this book is to provide a rigorous foundation for the theory and practice of subsampling. The asymptotic consistency of subsampling distribution estimation is shown under extremely weak conditions, including cases where the bootstrap fails. Consistent estimation of the sampling distribution of a statistic allows for the construction of asymptotically valid inferential procedures, such as confidence intervals and hypothesis tests. The crux of the method relies on recomputing a statistic over appropriate subsamples of the data, and using these recomputed values to build up a sampling distribution.
Readers are assumed to have a background roughly equivalent to a first-year graduate course in theoretical statistics. A large number of examples should make the book of interest to graduate students, researchers, and practitioners alike.

Dimitris N. Politis is Associate Professor of Mathematics at the University of California, San Diego.