# Questions tagged [uniformity]

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### Supremum of parameterized random variables over compact set

Suppose that we have a parameterized real-valued discrete stochastic process $x(t) :=\{x_k(t)\}_{k=1}^\infty$, such that $t$ assumes values in a compact set $T\subset \mathbb{R}^d$ for some finite ...
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### Indicators of a VC-class of sets are a universal Donsker class of functions, aren't they?

Let us have some Vapnik-Chevonenkis class $C$ of sets in ${\mathbb R}^d$. Let $F$ be the class of indicator functions for the sets $C$. Do the functions $F$ form a universal Donsker class of functions?...
25 views

### A Glivenko-Cantelli theorem for dependent vectors in $\mathbb R^d$

I need a Glivenko-Cantelli theorem for a weakly dependent or stationary sequence of vectors in $\mathbb R^d$ with a bound on the rate of convergence, for instance, {\bf P}\left(\sqrt{n} \sup_{A\in \...
12 views

### Are uniform LLNs preserved under monotone transformations

A simple question that I'm trying to answer is the following if I have a uniform LLN for a sequence of random vector; namely \sup_\beta \left\| \frac{1}{n} \sum_n^NX_n(\beta)\right\| ...
I am having trouble thinking of a function that operates on a set of samples, that is, single-valued random variables between zero and one, $x_i \in (0,1), i\in\{1,2,...I\}$, and provides a measure of ...