Empirical processes with applications to statistics

✍ Scribed by Shorack, Galen R.; Wellner, Jon A

Publisher: Society for Industrial and Applied Mathematics
Year: 2009
Tongue: English
Leaves: 1000
Series: Classics in applied mathematics 59
Category: Library

No coin nor oath required. For personal study only.

✦ Table of Contents

Content: Introduction and survey of results --
Foundations, special spaces and special processes --
Convergence and distributions of empirical processes --
Alternatives and processes of residuals --
Integral test of fit and estimated empirical process --
Martingale methods --
Censored data the product-limit estimator --
Poisson and exponential representations --
Some exact distributions --
Linear and nearly linear bounds on the empirical distribution function Gn --
Exponential inequalities and [parallel] ·/q [parallel]-metric convergence of Un and Vn --
The Hungarian Constructions of Kn, Un, and Vn --
Laws of the iterated logarithm associated with Un and Vn --
Oscillations of the empirical process --
The uniform empirical difference process Dn [identically equal] Un + Vn --
The normalized uniform empirical process Zn and the normalized uniform quantile process --
The uniform empirical process indexed by intervals and functions --
The standardized quantile process Qn --
L-statistics --
Rank statistics --
Spacing --
Symmetry --
Further applications --
Large deviations --
Independent but not identically distributed random variable --
Empirical measures and processes for general spaces --
Appendix A: Inequalities and miscellaneous --
Appendix B: Counting processes martingales.

✦ Subjects

Mathematical statistics.;Distribution (Probability theory);Random variables.

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