# Questions tagged [moments]

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### Convergence in probability of sample covariance for permutation invariant triangular arrays

Take two triangular arrays $X_{N,i}$ and $Y_{N,i}$ of random variables where $1 \le i \le N$. Suppose that the families $\{X_{N,i}\}$ and $\{Y_{N,i}\}$ are independent, and that the following ...
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### Finding $\sum_i x_i$ given $\{\sum_i x_i^{2n}\}_{n\in \mathbb{N}}$

Can we find $\sum_i x_i$ given $\{\sum_i x_i^{2n}\}_{n\in \mathbb{N}}$, assuming $\{x_i\}_{i\in\mathbb{N}}$ is a set of positive real numbers? Perhaps an easier question is, can we find $\sum_i x_i$ ...
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### Under what conditions is the least-squares approximation bounded with the same Lipschitz gradient constants?

Let $f(x):\mathbb{R}^K\Longrightarrow \mathbb{R}^L$ denote a multivariate continuously differentiable function. All the partial derivatives of $f$ (all its Jacobian elements) are bounded from above ...
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### Comparison of Rademacher and Gaussian moments under linear transformations

Let $X$ be an $n$ dimensional standard Gaussian and let $U$ be an $n \times n$ orthogonal matrix. Then, the random vector $Z = U^\top X$ is also distributed as a standard Gaussian in $R^n$ and we have ...
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### Stochastic dominance using moment-generating function

Traditionally, stochastic dominance is defined using the cumulative distribution function(CDF). But sometimes, the CDF is not easily to be obtained. For example, the generalized noncentral Chi-square ...
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### Uniqueness of a moment style problem

This is a leftover from this question (and I've modified slightly to make the question more natural in the new setting). It's maybe not a very fascinating question by itself, but it seems this is what ...
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### Tail bounds via moments

Suppose X is a discrete random variable with $\mathbb{E}[X] = \mu$, such that $\mathbb{E}[(X - \mu)^k] = \Theta(\mu^{k-1})$ for every $k \geq 2$. What (if anything) can be said about the concentration ...
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### Moments of Dirichlet $L$-functions on the critical line

I'm looking for a reference for some questions related to the moments of Dirichlet characters on the critical line, $$M_k(T;\chi) = \int_T^{2T} |L(1/2+it,\chi)|^{2k}\,dt,$$ where $\chi$ is a ...
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