A Unified Framework for Estimation in Lognormal Models

Lognormal models have broad applications in various research areas such as economics, actuarial science, biology, environmental science and psychology. In this article, we summarize all the existing estimators for lognormal models, which belong to 12 estimator families. As some estimators were only proposed for the independent and identical distribution setting, we further generalize these estimators to accommodate the general loglinear regression setting. Additionally, we propose 19 new estimators based on different optimization criteria. Mostly importantly, we present a unified framework for all the existing and proposed estimators. The application and comparison of the various estimators using a lognormal linear regression model are demonstrated by simulations and data from the Economic Research Service in the United States Department of Agriculture. A general recommendation for choosing an estimator in practice is discussed. An R package to implement 39 estimators is made available on CRAN.对数正态模型（lognormal models）在经济学、精算科学、生物学、环境科学与心理学等诸多研究领域拥有广泛应用。本文系统性梳理了现有所有适用于对数正态模型的估计方法，这些方法共归属于12类估计器家族。鉴于部分估计方法仅针对独立同分布场景提出，本文进一步将此类估计方法推广至通用对数线性回归场景。此外，本文基于不同的优化准则，提出了19种全新的估计方法。尤为重要的是，本文为所有现有及本文提出的估计方法构建了统一的分析框架。本文通过模拟实验与美国农业部经济研究服务局（Economic Research Service, United States Department of Agriculture）的真实数据集，对对数正态线性回归模型下各类估计方法的应用与对比效果进行了演示。本文还探讨了实际应用中选择合适估计方法的通用原则。一款可实现39种估计方法的R包已在CRAN（Comprehensive R Archive Network）平台公开发布。