Efficient Mean Estimation in Lognormal Linear Models

Lognormal linear models are widely used in applications, and many times it is of interest to predict the response variable at the original scale for a new set of covariate values. In this paper we consider the problem of efficient estimation of the conditional mean of the response variable at the original scale for lognormal linear models. Several existing estimators are reviewed, including the maximum likelihood (ML) estimator, the restricted ML (REML) estimator, the uniformly minimum variance unbiased (UMVU) estimator, and a bias-corrected REML estimator. We propose two estimators that minimize the asymptotic mean squared error (MSE) and the asymptotic bias respectively, as well as a bootstrap method to obtain their corresponding confidence intervals. Comparisons of the estimators using simulation studies demonstrate that even for a small sample size and a moderately large σ, ∗email: [email protected]