By AAD W VAN DER VAART
This ebook attempts to do 3 issues. the 1st target is to offer an exposition of definite modes of stochastic convergence, specifically convergence in distribution. The classical thought of this topic used to be built in most cases within the Nineteen Fifties and is definitely summarized in Billingsley (1968). over the past 15 years, the necessity for a extra basic concept permitting random components that aren't Borel measurable has develop into good validated, fairly in constructing the idea of empirical methods. half 1 of the ebook, Stochastic Convergence, offers an exposition of one of these concept following the guidelines of J. Hoffmann-J!1Jrgensen and R. M. Dudley. A moment aim is to take advantage of the vulnerable convergence idea heritage devel oped partly 1 to offer an account of significant parts of the fashionable concept of empirical tactics listed through periods of units and features. The susceptible convergence thought constructed partly 1 is necessary for this, just because the empirical techniques studied partially 2, Empirical strategies, are clearly seen as taking values in nonseparable Banach areas, even within the most simple situations, and tend to be no longer Borel measurable. a lot of the idea awarded partly 2 has formerly been scattered within the magazine literature and has, for that reason, been available purely to a comparatively small variety of experts. In view of the significance of this conception for statis tics, we are hoping that the presentation given the following will make this idea extra obtainable to statisticians in addition to to probabilists drawn to statistical applications.