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.