The Glivenko Cantelli Theorem and its Generalizations
نویسنده
چکیده
In this note we will study upper bounds of random variables of the type sup A∈A |ν n (A) − ν(A)| , where A is a class of sets that needs to fulll certain assumptions. These bounds are important tools in the analysis of learning processes and probabilistic theories of pattern recognition. The presentation given here is based on [DGL96].
منابع مشابه
Preservation Theorems for Glivenko-cantelli and Uniform Glivenko-cantelli Classes Aad Van Der Vaart and Jon
We show that the P Glivenko property of classes of functions F1; : : : ;Fk is preserved by a continuous function ' from R k to R in the sense that the new class of functions x! '(f1(x); : : : ; fk(x)); fi 2 Fi; i = 1; : : : ; k is again a Glivenko-Cantelli class of functions if it has an integrable envelope. We also prove an analogous result for preservation of the uniform Glivenko-Cantelli pro...
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