# Questions tagged [empirical-processes]

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### Bracketing entropy for unimodal functions

This is exercise 2.3 from van de Geer's Empirical processes in M-estimation. Let $\mathcal G$ be the class of unimodal functions $g : \mathbb R \rightarrow [0, 1]$. A function $f$ is unimodal if there ...
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### Joint measurability of discrete integral.

I'm currently considering the following map: Let $\mathcal{F}$ be a subset of some $L^2$ space with respect to a probability measure on $\mathbb{R}$ and let $X=(X_1,X_2,\ldots,X_n)$ be points on the ...
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### Translation of box type ball to center it in a convex set but maintaining the covering properties

I have the following problem. Suppose to have a cube $Q$ and a symmetric box type ball $B$ whose center is outside Q, but such that $Q\cap B \ne\emptyset$. Furthermore $B$ is not oriented like $Q$. I ...
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### Multivariate Donsker Theorem

Suppose that $(\Omega,\mathcal F, P)$ is a probability space, and let $Z = (X,Y)$ be a $\mathbb R^2$-valued random variable. Let $F_X$ and $F_Y$ denote the respective marginal distribution function of ...
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### Union Bound of two events?

I am trying to understand the assumption proof of Theorem 2(Page -$7$) in the paper "A Universal Law of Robustness via isoperimetry" by Bubeck and Sellke. Inequality 1 \begin{align} \mathbb{...
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### Understanding how to do an Empirical Mode Decomposition

I am trying to create my own code for Empirical Mode Decomposition and extraction of IMFs. As far as I understand, the first part of the process must be done like this: find local maxima and minima....
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### Why is the subspace of uniformly rho continuous functions separable?

I am reading through the book of Kosorok on Empirical Processes and I got stuck on a statement that seems to be clear to the author. To me, it is not clear at all. In chapter 6.1 page 87 he states ...
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### Understanding a step in a proof involving an empirical process (machine learning)

I am unable to understand the apparently simple step that yield the display appearing before Lemma B.1. in page 12 of this paper by Chernozhukov et al. (2016). In particular I fail to see how (2.1) ...
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I'm going through the proof of the symmetrization lemma (Vershynin), which says  \frac{1}{2} E \left\| \sum_i \epsilon_i X_i \right\| \leq E \left\| \sum_i X_i \right\| \leq 2 E \left\| \sum_i \...