Index: Ji 2024 - Valid Standard Errors for Bayesian Quantile Regression

Ji 2024 - Valid Standard Errors for Bayesian Quantile Regression

Routing Summary

Captures Ji, Lee and Rabe-Hesketh (2024), Valid standard errors for Bayesian quantile regression with clustered and independent data (arXiv 2407.09772v4, 50 pp.), which reviews and tests the Yang-Wang-He (2016) AL-posterior adjustment and proposes infinitesimal-jackknife SEs. Includes a concept note on Gibbs posteriors and learning-rate calibration. 5 notes plus overview. Motivating PyMC example: E83 (quantile regression, “when it lies”).

• Need the one-page summary and source map? → Ji 2024 - Valid Standard Errors for Bayesian Quantile Regression - Overview
• Need check loss, AL density, scale-mixture, role of $\sigma$? → Ji 2024 - Asymmetric Laplace Working Likelihood
• Need the asymptotic posterior, sandwich, Yang adjustment, Sriram two-step? → Ji 2024 - Yang-Wang-He Sandwich Adjustment
• Need IJ definition, clustered IJ, code? → Ji 2024 - Infinitesimal Jackknife Standard Errors
• Need simulation designs, coverage findings, Engel and Project STAR results? → Ji 2024 - Simulation Results and Applications
• Need Gibbs posterior / learning-rate calibration? → Ji 2024 - Gibbs Posterior and Learning-Rate Calibration

Concept Map

Concept	Note	Type	Depends On	Key Result
Check loss	Ji 2024 - Asymmetric Laplace Working Likelihood	definition	-	${\rho }_{\tau }(u)=u\{\tau -I(u<0)\}$
Asymmetric Laplace	Ji 2024 - Asymmetric Laplace Working Likelihood	definition	check loss	mode = KB estimator; spread $\propto \sigma$
Asymptotic AL posterior	Ji 2024 - Yang-Wang-He Sandwich Adjustment	theorem	AL	$N(\hat{\beta },\sigma D_1^{-1}/n)$
Sandwich covariance	Ji 2024 - Yang-Wang-He Sandwich Adjustment	theorem	quantile regression	$\tau (1-\tau )D_1^{-1}{D}_0{D}_1^{-1}/n$
Yang adjustment	Ji 2024 - Yang-Wang-He Sandwich Adjustment	definition	both	$\tau (1-\tau ){\sigma }^{-2}\hat{\Sigma }{X}^{\prime }X\hat{\Sigma }$
IJ SE	Ji 2024 - Infinitesimal Jackknife Standard Errors	definition	MCMC draws	$I_i=n\mathrm{cov}[\theta ,{\ell }_i]$
Clustered IJ	Ji 2024 - Infinitesimal Jackknife Standard Errors	definition	IJ	sum over cluster
Coverage findings	Ji 2024 - Simulation Results and Applications	example	all	ALD up to 300% off
Gibbs posterior	Ji 2024 - Gibbs Posterior and Learning-Rate Calibration	concept	AL	$\omega =1/\sigma$ calibrated

Notes

• Ji 2024 - Valid Standard Errors for Bayesian Quantile Regression - Overview — CONTAINS: question, contribution, E83 link, source map.
• Ji 2024 - Asymmetric Laplace Working Likelihood — CONTAINS: Defs. check loss, ALD, scale mixture; priors on $\sigma$; units trap; Python.
• Ji 2024 - Yang-Wang-He Sandwich Adjustment — CONTAINS: Thms. Eqs. 1-2; Def. Eq. 3; Sriram two-step; finite-sample caveat; Python.
• Ji 2024 - Infinitesimal Jackknife Standard Errors — CONTAINS: weights, linear approximation theorem, IJ and clustered IJ, Python.
• Ji 2024 - Simulation Results and Applications — CONTAINS: DGPs, metrics, findings, cluster design, Engel, Project STAR.
• Ji 2024 - Gibbs Posterior and Learning-Rate Calibration — CONTAINS: Gibbs posterior definition, calibration algorithm, Python (concept note).

Sources

• Ji 2024 - Valid Standard Errors for Bayesian Quantile Regression — Ji F, Lee J, Rabe-Hesketh S (2024), arXiv:2407.09772v4. Substitute for the paywalled Yang, Wang and He (2016), Int. Stat. Rev.

See Also

• Quantile Regression, Conformalized Quantile Regression, Stasinopoulos 2007 - GAMLSS in R - Overview