Uncertainty Quantification In The Bradley-Terry-Luce Model
Talkat Algorithmic Advances for Statistical Inference with Combinatorial Structure · 2021-10-11..10-15·
summary
Provides non-asymptotic expansion formulas for both MLE and spectral estimators under the Bradley–Terry–Luce model, with the leading error term an average of Bernoulli noises of order 1/sqrt(n p L) (L can be 1). Requires NP >> (log n)^302 for proofs (near optimal). Delivers finite-sample asymptotic normality for any fixed coordinates, data-driven standard errors and confidence intervals for individual skills and ranks, shows MLE optimal constant in L2 while spectral suboptimal, and proves spectral vs MLE variance ordering.
AI-written summary · about
chapters (11)
- 0:00Start
- 1:27Ranked Choice Voting
- 7:04Uncertainty Quantification for Mle
- 9:02Existing Results for the Mle
- 11:52Simulation Result
- 12:37Results on the Asymptotic Normality of the Mle
- 33:31Spectrum Method
- 35:00Find the Station Distribution per Head
- 37:20Simulation for the Spectrum Method
- 44:20Main Error Term of the Spectrum Method
- 56:05Proof Strategy
related talks
48mRobust Sparse Covariance Estimation by Thresholding Tyler's M-estimator
27mInformation Measure Estimation and Applications: Boosting the Sample Size from n to n log n
56mSparsifying Generalized Linear Models
44mA Modern Maximum-Likelihood Theory for High-Dimensional Logistic Regression
01h 30mHigh-Dimensional Statistics II
24mRandomized Least Squares Regression: Combining Model- and Algorithm-Induced Uncertainties
53mOptimality in Locally Private Estimation and Learning
45mOrthogonal Statistical Learning