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4 votes
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How well does an estimator perform on another dataset?

Suppose $X \sim N(0, \Sigma)$ is a $d$-dimensional Gaussian random vector. And we have $2n$ $i.i.d$ sample $X_1, \ldots, X_{n}, \ldots, X_{2n}$. Let $\hat{\Sigma}_1 = \frac{1}{n}\sum_{i=1}^nX_i X_i^ …
Wuchen's user avatar
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4 votes
1 answer
341 views

Concentration of functional of Gaussian random variable

Suppose I have two Gaussian distributions $p(x) = \frac{1}{(2\pi)^{d/2}|\Sigma_p|^{1/2}}\exp(-\frac{1}{2}x^\top \Sigma_p^{-1} x)$ and $q(x) = \frac{1}{(2\pi)^{d/2}|\Sigma_q|^{1/2}}\exp(-\frac{1}{2}x^ …
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  • 515
4 votes
1 answer
670 views

Tail bound for product of normal distribution

Let $U, V$ be two standard normal random variables with covariance $cov(U,V) = \beta \in [0,1)$. Let $W = UV$ be the product of two RV's, and $W_1, W_2, \ldots, W_n$ be n i.i.d copies of $W$, what's t …
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