Weak Convergence and Empirical Processes pp 238-268 | Cite as
Tail Bounds
Chapter
Abstract
In this chapter we derive moment and tail bounds for the supremum \( \left\| {{G_n}} \right\|F \) of the empirical process. Throughout this chapter, \( {G_{n = \sqrt n }}({P_n} - P) \) denotes the empirical process of an i.i.d. sample X 1,..., X n ,, from a probability measure P, defined as the coordinate projections of a product probability space (X ∞, A ∞, P ∞).
Keywords
Central Limit Theorem Universal Constant Empirical Process Tail Probability Envelope Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
Copyright information
© Springer Science+Business Media New York 1996