Increased Statistical Efficiency in a Lognormal Mean Model

Author:

Skrepnek Grant H.1,Sahai Ashok2

Affiliation:

1. College of Pharmacy & Peggy and Charles Stephenson Cancer Center, The University of Oklahoma Health Sciences Center, 1110 North Stonewall Avenue, Oklahoma City, OK 73126-0901, USA

2. Department of Mathematics & Statistics, Faculty of Science and Technology, The University of the West Indies, St. Augustine Campus, Debe, Trinidad and Tobago

Abstract

Within the context of clinical and other scientific research, a substantial need exists for an accurate determination of the point estimate in a lognormal mean model, given that highly skewed data are often present. As such, logarithmic transformations are often advocated to achieve the assumptions of parametric statistical inference. Despite this, existing approaches that utilize only a sample’s mean and variance may not necessarily yield the most efficient estimator. The current investigation developed and tested an improved efficient point estimator for a lognormal mean by capturing more complete information via the sample’s coefficient of variation. Results of an empirical simulation study across varying sample sizes and population standard deviations indicated relative improvements in efficiency of up to 129.47 percent compared to the usual maximum likelihood estimator and up to 21.33 absolute percentage points above the efficient estimator presented by Shen and colleagues (2006). The relative efficiency of the proposed estimator increased particularly as a function of decreasing sample size and increasing population standard deviation.

Publisher

Hindawi Limited

Subject

Statistics and Probability

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