Empirical Bayes shrinkage (mostly) does not correct the measurement error in regression
In the value-added literature, it is often claimed that regressing on empirical Bayes shrinkage estimates corrects for the measurement error problem in linear regression. We clarify the conditions needed; we argue that these conditions are stronger than the those needed for classical measurement error correction, which we advocate for instead. Moreover, we show that the classical estimator cannot be improved without stronger assumptions. We extend these results to regressions on nonlinear transformations of the latent attribute and find generically slow minimax estimation rates.
Code (0)
등록된 구현이 없습니다.
Tasks
AttributeSimilar Papers 제목 키워드 기반
PEBS: Per-rater Empirical-Bayes Shrinkage for RLHF Reward-Model Calibration
Reward models for Reinforcement Learning from Human Feedback (RLHF) pool preferences across thousands of annotators and fit one global affine calibrator, collapsing raters with systematically different rating-scale offse…
Reinforcement LearningComparing Stochastic Volatility Specifications for Large Bayesian VARs
Large Bayesian vector autoregressions with various forms of stochastic volatility have become increasingly popular in empirical macroeconomics. One main difficulty for practitioners is to choose the most suitable stochas…
Estimation of growth in fund models
Fund models are statistical descriptions of markets where all asset returns are spanned by the returns of a lower-dimensional collection of funds, modulo orthogonal noise. Equivalently, they may be characterised as model…
Empirical Bayes Matrix Completion
We develop an empirical Bayes (EB) algorithm for the matrix completion problems. The EB algorithm is motivated from the singular value shrinkage estimator for matrix means by Efron and Morris (1972). Since the EB algorit…
Matrix CompletionAutomatic Inference for Value-Added Regressions
It is common to use shrinkage methods such as empirical Bayes to improve estimates of teacher value-added. However, when the goal is to perform inference on coefficients in the regression of long-term outcomes on value-a…
regression