From Gauss to Kolmogorov: localized measures of complexity for ellipses
From MaRDI portal
Publication:2199701
DOI10.1214/20-EJS1739zbMath1448.62023arXiv1803.07763OpenAlexW3049028083MaRDI QIDQ2199701
Billy Fang, Yuting Wei, Martin J. Wainwright
Publication date: 14 September 2020
Published in: Electronic Journal of Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1803.07763
least squaresadaptive estimationKolmogorov widthcomplexity measurelocal metric entropyellipse constraint
Algorithmic information theory (Kolmogorov complexity, etc.) (68Q30) Probabilistic measure theory (60A10) Statistical aspects of information-theoretic topics (62B10) Information geometry (statistical aspects) (62B11)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A new perspective on least squares under convex constraint
- The geometry of hypothesis testing over convex cones: generalized likelihood ratio tests and minimax radii
- Minimax risk over hyperrectangles, and implications
- On density estimation in the view of Kolmogorov's ideas in approximation theory
- Optimal filtering of square-integrable signals in Gaussian noise
- Chaining, interpolation and convexity II: the contraction principle
- On the degrees of freedom in shape-restricted regression.
- Risk bounds in isotonic regression
- Weak convergence and empirical processes. With applications to statistics
- Chaining, interpolation, and convexity
- Randomized sketches for kernels: fast and optimal nonparametric regression
- Hypothesis testing for densities and high-dimensional multinomials: sharp local minimax rates
- Local Rademacher complexities and oracle inequalities in risk minimization. (2004 IMS Medallion Lecture). (With discussions and rejoinder)
- Near-optimality of linear recovery in Gaussian observation scheme under \(\| \cdot \|_{2}^{2}\)-loss
- On risk bounds in isotonic and other shape restricted regression problems
- The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
- Some results on Tchebycheffian spline functions and stochastic processes
- Majorizing measures: The generic chaining
- Local Rademacher complexities
- An Automatic Inequality Prover and Instance Optimal Identity Testing
- Adapting to Unknown Smoothness via Wavelet Shrinkage
- Ideal spatial adaptation by wavelet shrinkage
- Rademacher penalties and structural risk minimization
- High-Dimensional Statistics
- The Local Geometry of Testing in Ellipses: Tight Control via Localized Kolmogorov Widths
- Upper and Lower Bounds for Stochastic Processes
- Theory of Reproducing Kernels
- Introduction to nonparametric estimation
- Compressed sensing
- Smoothing spline ANOVA models
