2020/07/22 by Erez Buchweitz, Buchweitz, Erez, Shlomo Ahal +5
Economics, Econometrics and Finance · Mathematics · #62J07 #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Monetary Policy and Economic Impact #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2007.11306
openalex publication_date 2020/07/22 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
Estimators derived from score functions that are not the likelihood are in wide use in practical and modern applications. Their regularization is often carried by pseudo-posterior estimation, equivalently by adding penalty to the score function. We argue that this approach is suboptimal, and propose a two-staged alternative involving estimation of a new score function which better approximates the true likelihood for the purpose of regularization. Our approach typically identifies with maximum a-posteriori estimation if the original score function is in fact the likelihood. We apply our theory to fitting ordinary least squares (OLS) under contemporaneous exogeneity, a setting appearing often in time series and in which OLS is the estimator of choice by practitioners.