The endpoint theorem *

Bootstrapping Endpoint

It is known that bootstrapping maximum for estimating the endpoint of a distribution function is inconsistent and subsample bootstrap method is needed. Under an extreme value condition, some other estimators for the endpoint have been studied in the literature, which are preferrable to the maximum in regular cases. In this paper, we show that the full sample bootstrap method is consistent for t...

Generation of the Ahlfors Five Islands Theorem

The Basic Theorem and its Consequences

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...