A Unified Framework for Estimation in Lognormal Models

Abstract

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.

Keywords:

• Cobb–Douglas function model
• Logarithmic transformation
• Lognormal regression

Acknowledgments

The authors thank to editor, associate editor, and two anonymous reviewers for their comments which helped to substantially improve the article.

Supplementary Material

Appendix: This supplementary file contains derivations and proofs. (appendix_lognormal_jbes.pdf) R-package fuel: This supplementary file is the R package fuel (framework for unified estimation in lognormal models), which implements the existing and new lognormal estimators in this article and is available on CRAN. (fuel_1.2.0.tar.gz)