1 The Glivenko - Cantelli Theorem

  • Published 2009


a.s (in order to apply the strong law of large numbers we only need to show that E[|I{Xi ≤ x}|] <∞, which in this case is trivial because |I{Xi ≤ x}| ≤ 1). In this sense, F̂n(x) is a reasonable estimate of F (x) for a given x ∈ R. But is F̂n(x) a reasonable estimate of the F (x) when both are viewed as functions of x? The Glivenko-Cantelli Thoerem provides an answer to this question. It asserts the following:

Cite this paper

@inproceedings{20091TG, title={1 The Glivenko - Cantelli Theorem}, author={}, year={2009} }