V. Koltchinskii

activity

20042024

most cited2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization

379 citations · 1.2k across the 30 of their papers we have counts for

collaborators

39 papers

math.ST2024

Estimation of trace functionals and spectral measures of covariance operators in Gaussian models

Vladimir Koltchinskii

Let $f : R_{+} \mapsto R$ be a smooth function with $f (0) = 0.$ A problem of estimation of a functional $τ_{f} (Σ) := tr (f (Σ))$ of unknown covariance operator $Σ$ in…

math.ST2023

Functional estimation in high-dimensional and infinite-dimensional models

Vladimir Koltchinskii, Minghao Li

Let $P$ be a family of probability measures on a measurable space $(S, A) .$ Given a Banach space $E,$ a functional $f : E \mapsto R$ and a mapping $θ: {…

math.ST2022★ 1 cited

Estimation of smooth functionals of covariance operators: jackknife bias reduction and bounds in terms of effective rank

Vladimir Koltchinskii

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 $Σ: E…

math.ST2021

Functional estimation in log-concave location families

Vladimir Koltchinskii, Martin Wahl

Let ${P_{θ} : θ \in R^{d}}$ be a log-concave location family with $P_{θ} (d x) = e^{- V (x - θ)} d x,$ where $V : R^{d} \mapsto R$ is a known convex function and let $X_1,\…

math.ST2020

Estimation of smooth functionals in high-dimensional models: bootstrap chains and Gaussian approximation

Vladimir Koltchinskii

Let $X^{(n)}$ be an observation sampled from a distribution $P_{θ}^{(n)}$ with an unknown parameter $θ,$ $θ$ being a vector in a Banach space $E$ (most often, a high-dimensional spac…

math.ST2019

Estimation of Smooth Functionals in Normal Models: Bias Reduction and Asymptotic Efficiency

Vladimir Koltchinskii, Mayya Zhilova

Let $X_{1}, \dots, X_{n}$ be i.i.d. random variables sampled from a normal distribution $N (μ, Σ)$ in $R^{d}$ with unknown parameter $θ=(μ,Σ)\in Θ:={\mathbb R}^d\times {\mathcal C…