A Flexible Framework for Hypothesis Testing in High-Dimensions
Talkat Robust and High-Dimensional Statistics (Simons Institute workshop, 2018) · 2018-10-29..11-02·
summary
Framework projects the high dimensional null onto a chosen K‑dimensional subspace then constructs a de‑biased estimator of U^T theta via a rotated debiasing step whose columns G are chosen by a quadratic program balancing bias and variance. Calibration uses sample splitting to pick U from a LASSO pilot and then tests by an L∞ projection onto Ω. Theory controls Type I error under sub‑Gaussian rows when S log p / sqrt n → 0 and shows convex Ω reduces to K = 1 with orthogonal projection, with project onto subspace U, de‑bias in rotated basis, data splitting to choose U.
AI-written summary · about
chapters (20)
- 0:00Intro
- 0:28Statistical model
- 1:28Linear Models and Lasso Estimator
- 2:22Statistical Inference on model parameters
- 3:22Testing individual parameters
- 5:49Example 2 (Inference on Quadratic Forms)
- 7:02Testing minimum signal strength)
- 7:45Testing over Convex Cones)
- 8:37Testing arbitrary functionals of 8)
- 9:07Outline
- 10:55Debiasing (in rotated basis)
- 12:50How should we choose G?
- 17:25Step 3: Los projection and test statistic
- 18:46Summary
- 19:55Controlling false positive rate
- 21:20How should we choose basis U?
- 25:02Data splitting
- 29:32Examples
- 30:18Experiment 1
- 32:21Experiment 3: Inference on predictions Confidence intervals for ET
related talks
01h 02mTheory and Big Data
45mHigh Dimensional Robust Sparse Regression
01h 07mRecent Progress in High-Dimensional Learning
01h 30mHigh-Dimensional Statistics I
01h 12mRecent Progress in High-Dimensional Learning
29mHigh Dimensional Calibration for Rational Decision Making
01h 00mAlgorithmic High Dimensional Robust Statistics I
01h 03mSampling for Linear Algebra, Statistics, and Optimization I