A more accurate title for this book might be: An Exposition of Selected Parts of Empirical Process Theory, With Related Interesting Facts About Weak Convergence, and Applications to Mathematical Statistics. The high points are Chapters II and VII, which describe some of the developments inspired by Richard Dudley's 1978 paper. There I explain the combinatorial ideas and approximation methods that are needed to prove maximal inequalities for empirical processes indexed by classes of sets or classes of functions. The material ...
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A more accurate title for this book might be: An Exposition of Selected Parts of Empirical Process Theory, With Related Interesting Facts About Weak Convergence, and Applications to Mathematical Statistics. The high points are Chapters II and VII, which describe some of the developments inspired by Richard Dudley's 1978 paper. There I explain the combinatorial ideas and approximation methods that are needed to prove maximal inequalities for empirical processes indexed by classes of sets or classes of functions. The material is somewhat arbitrarily divided into results used to prove consistency theorems and results used to prove central limit theorems. This has allowed me to put the easier material in Chapter II, with the hope of enticing the casual reader to delve deeper. Chapters III through VI deal with more classical material, as seen from a different perspective. The novelties are: convergence for measures that don't live on borel a-fields; the joys of working with the uniform metric on D[O, IJ; and finite-dimensional approximation as the unifying idea behind weak convergence. Uniform tightness reappears in disguise as a condition that justifies the finite-dimensional approximation. Only later is it exploited as a method for proving the existence of limit distributions. The last chapter has a heuristic flavor. I didn't want to confuse the martingale issues with the martingale facts.
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Good. No jacket. Ex library with typical labeling on cover, spine, and inside front cover. Main text unmarked. Good binding, some cosmetic wear on edges and corners.
Add this copy of Convergence of Stochastic Processes (Springer Series in to cart. $116.59, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 1984 by Springer.
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Very Good in None Issued jacket. Text is unmarked; pages are bright, though the top edge of the pages is foxed. Previous owner's signature in pen on the first free end page. Binding is sturdy. Covers are worn around the edges, especially at the corners and at the head and base of the spine. No dust jacket, as issued.
