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The choice of examples used in this text clearly illustrate its use
for a one-year graduate course. The material to be presented in the
classroom constitutes a little more than half the text, while the
rest of the text provides background, offers different routes that
could be pursued in the classroom, as well as additional material
that is appropriate for self-study. Of particular interest is a
presentation of the major central limit theorems via Steins method
either prior to or alternative to a characteristic function
presentation. Additionally, there is considerable emphasis placed
on the quantile function as well as the distribution function, with
both the bootstrap and trimming presented. The section on
martingales covers censored data martingales.
The choice of examples used in this text clearly illustrate its use for a one-year graduate course. The material to be presented in the classroom constitutes a little more than half the text, while the rest of the text provides background, offers different routes that could be pursued in the classroom, as well as additional material that is appropriate for self-study. Of particular interest is a presentation of the major central limit theorems via Steins method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function, with both the bootstrap and trimming presented. The section on martingales covers censored data martingales.
Originally published in 1986, this valuable reference provides a
detailed treatment of limit theorems and inequalities for empirical
processes of real-valued random variables. It also includes
applications of the theory to censored data, spacings, rank
statistics, quantiles, and many functionals of empirical processes,
including a treatment of bootstrap methods, and a summary of
inequalities that are useful for proving limit theorems. At the end
of the Errata section, the authors have supplied references to
solutions for 11 of the 19 Open Questions provided in the book's
original edition.
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