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 paper, we summarize all the existing estimators for lognormal models, which belong to twelve 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 nineteen new estimators based on different optimization criteria. Mostly importantly, we present a unified framework for all the existing and proposed estimators. The estimators are compared by simulations and applied to data from the Economic Research Service in the United States Department of Agriculture are used to demonstrate the application of the various estimators using a lognormal linear regression model. A general recommendation for choosing an estimator in practice is discussed. An R package to implement thirty-nine estimators is made available on CRAN.