Sampling properties of the Bayesian posterior mean with an application to WALS estimation

Giuseppe De Luca (), Jan Magnus () and Franco Peracchi

No 20-015/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these learning methods in repeated samples is assessed using the variance of the posterior distribution of the parameters of interest given the data. This may be permissible when the sample size is large because, under the conditions of the Bernstein--von Mises theorem, the posterior variance agrees asymptotically with the frequentist variance. In finite samples, however, things are less clear. In this paper we explore this issue by first considering the frequentist properties (bias and variance) of the posterior mean in the important case of the normal location model, which consists of a single observation on a univariate Gaussian distribution with unknown mean and known variance. Based on these results, we derive new estimators of the frequentist bias and variance of the WALS estimator in finite samples. We then study the finite-sample performance of the proposed estimators by a Monte Carlo experiment with design derived from a real data application about the effect of abortion on crime rates.

Keywords: Normal location model; posterior moments and cumulants; higher-order delta method approximations; double-shrinkage estimators; WALS (search for similar items in EconPapers)
JEL-codes: C11 C13 C15 C52 I21 (search for similar items in EconPapers)
Date: 2020-03-09
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Sampling properties of the Bayesian posterior mean with an application to WALS estimation (2022)
Working Paper: Sampling properties of the Bayesian posterior mean with anapplication to WALS estimation (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20200015

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