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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

3 votes
1 answer
682 views

Asymptotic bound on the total variation distance between a standard multivariate normal and ...

Let $P = N(\vec{0}, I^d)$ be a standard multivariate Gaussian distribution in $d$ dimensions. Let $Q$ be distributed the same as $P$, except that samples from $Q$ have one of their coordinates, chosen …
Florian Tramèr's user avatar
2 votes
1 answer
245 views

Asymptotic rate for the expected value of the square root of sample average

I have iid random variables $X_1, \dots, X_n$ with $X_i \geq 0$, $E[X_i]=1$ and $V[X_i] = \sigma^2$. Let $S_n = \frac{\sum_{i=1}^n X_i}{n}$. I'd like to say that $E[\sqrt{S_n}] = 1-O(1/n)$. My first …
Florian Tramèr's user avatar
6 votes
3 answers
2k views

Estimating the variance of a discrete normal distribution

Let $f(x; \sigma) = \frac{1}{\sigma\sqrt{2\pi}}\cdot e^{-\frac{x^2}{2\sigma^2}}$ be the probability density function of a normal distribution $\mathcal{N}(0, \sigma^2)$. We consider a discrete normal …
Florian Tramèr's user avatar