Zobrazeno 1 - 10
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pro vyhledávání: '"Koltchinskii, Vladimir"'
Autor:
Koltchinskii, Vladimir
Let $f:{\mathbb R}_+\mapsto {\mathbb R}$ be a smooth function with $f(0)=0.$ A problem of estimation of a functional $\tau_f(\Sigma):= {\rm tr}(f(\Sigma))$ of unknown covariance operator $\Sigma$ in a separable Hilbert space ${\mathbb H}$ based on i.
Externí odkaz:
http://arxiv.org/abs/2402.11321
Autor:
Koltchinskii, Vladimir, Li, Minghao
Let ${\mathcal P}$ be a family of probability measures on a measurable space $(S,{\mathcal A}).$ Given a Banach space $E,$ a functional $f:E\mapsto {\mathbb R}$ and a mapping $\theta: {\mathcal P}\mapsto E,$ our goal is to estimate $f(\theta(P))$ bas
Externí odkaz:
http://arxiv.org/abs/2310.16129
Autor:
Koltchinskii, Vladimir
Let $E$ be a separable Banach space and let $X, X_1,\dots, X_n, \dots$ be i.i.d. Gaussian random variables taking values in $E$ with mean zero and unknown covariance operator $\Sigma: E^{\ast}\mapsto E.$ The complexity of estimation of $\Sigma$ based
Externí odkaz:
http://arxiv.org/abs/2205.10280
Autor:
Koltchinskii, Vladimir, Wahl, Martin
Let $\{P_{\theta}:\theta \in {\mathbb R}^d\}$ be a log-concave location family with $P_{\theta}(dx)=e^{-V(x-\theta)}dx,$ where $V:{\mathbb R}^d\mapsto {\mathbb R}$ is a known convex function and let $X_1,\dots, X_n$ be i.i.d. r.v. sampled from distri
Externí odkaz:
http://arxiv.org/abs/2108.00263
Autor:
Koltchinskii, Vladimir
Let $X^{(n)}$ be an observation sampled from a distribution $P_{\theta}^{(n)}$ with an unknown parameter $\theta,$ $\theta$ being a vector in a Banach space $E$ (most often, a high-dimensional space of dimension $d$). We study the problem of estimati
Externí odkaz:
http://arxiv.org/abs/2011.03789
Autor:
Koltchinskii, Vladimir, Zhilova, Mayya
Let $X_1,\dots, X_n$ be i.i.d. random variables sampled from a normal distribution $N(\mu,\Sigma)$ in ${\mathbb R}^d$ with unknown parameter $\theta=(\mu,\Sigma)\in \Theta:={\mathbb R}^d\times {\mathcal C}_+^d,$ where ${\mathcal C}_+^d$ is the cone o
Externí odkaz:
http://arxiv.org/abs/1912.08877
Autor:
Koltchinskii, Vladimir, Zhilova, Mayya
We study a problem of estimation of smooth functionals of parameter $\theta $ of Gaussian shift model $$ X=\theta +\xi,\ \theta \in E, $$ where $E$ is a separable Banach space and $X$ is an observation of unknown vector $\theta$ in Gaussian noise $\x
Externí odkaz:
http://arxiv.org/abs/1810.02767
Autor:
Koltchinskii, Vladimir
Let $X$ be a centered Gaussian random variable in a separable Hilbert space ${\mathbb H}$ with covariance operator $\Sigma.$ We study a problem of estimation of a smooth functional of $\Sigma$ based on a sample $X_1,\dots ,X_n$ of $n$ independent obs
Externí odkaz:
http://arxiv.org/abs/1710.09072
We study principal component analysis (PCA) for mean zero i.i.d. Gaussian observations $X_1,\dots, X_n$ in a separable Hilbert space $\mathbb{H}$ with unknown covariance operator $\Sigma.$ The complexity of the problem is characterized by its effecti
Externí odkaz:
http://arxiv.org/abs/1708.07642
Autor:
Xia, Dong, Koltchinskii, Vladimir
Let ${\mathcal S}_m$ be the set of all $m\times m$ density matrices (Hermitian positively semi-definite matrices of unit trace). Consider a problem of estimation of an unknown density matrix $\rho\in {\mathcal S}_m$ based on outcomes of $n$ measureme
Externí odkaz:
http://arxiv.org/abs/1604.04600