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Let $f:\mathbb R^d \to \mathbb R$ be a "sufficiently smooth" function. For simplicity, we may consider $f$ to be an affine function, i.e $f(x) \equiv b-x^\top w$, for some $(w,b) \in \mathbb ...

Let $X = (X_1, X_2, \ldots , X_n)$ be an $n$-dimensional random variable, where each $X_i$ is a random variable on finite discrete set $S$. In addition, $X_i$ are independent of each other (but not ...

I'm trying to familiarize myself with the latest results in finite sample statistics. It seems to me that these results can be classified into two categories: Unsurprising results confirm that the ...

In the literature the multivariate Bernstein polynomial of a function $f:[0,1]^m\rightarrow\mathbb{R}$ is often defined as the following: $$B_{f,n}(x_1,\dots,x_m)=\sum_{\mathbf{k}\in \{0,\dots,n\}^m}...

The title says it all! When using orthogonal series expansions like the Gram-Charlier expansion to approximate probability density function, a big problem (making this approach less usefull and less ...