Some limit theorems

Some Limit Theorems

Some Converse Limit Theorems for Exchangeable Bootstraps

The bootstrap Glivenko-Cantelli and bootstrap Donsker theorems of Giné and Zinn (1990) contain both necessary and sufficient conditions for the asymptotic validity of Efron’s nonparametric bootstrap. In the more general case of exchangeably weighted bootstraps, Praestgaard and Wellner (1993) and Van der Vaart and Wellner (1996) give analogues of the sufficiency half of the Theorems of Giné and ...

Some Useful Functions for Functional Limit Theorems

Many useftil descriptions of stochastic models can be obtained from functional limit theorems (invariance principles or weak convergence theorems for probability meastires on function ŝpaces). These descriptions typically come from standard functional limit theorems via the o^ntinuous mapping theorem. This paper facilitates applications of the continuous mapping theorem by determining when seve...

Central Limit Theorems for Some Graphs in Computational Geometry

Let Bn be an increasing sequence of regions in d-dimensional space with volume n and with union d. We prove a general central limit theorem for functionals of point sets, obtained either by restricting a homogeneous Poisson process to Bn, or by by taking n uniformly distributed points in Bn. The sets Bn could be all cubes but a more general class of regions Bn is considered. Using this general ...

Some Exact Limit Theorems for Negatively Associated Sequences

Using the probability inequalities and the weak invariance principles, the limit behavior of the complete moment convergence for negatively associated (NA) random variables is investigated. Namely, it is shown how fast the series generated by the moments of the sums for NA sequences tends to infinity as goes to zero.