Background: The use of body mass index (BMI) could lead to over/under estimation of fat mass percentage. Systematic sampling is to be applied only if the given population is logically homogeneous, because systematic sample units are uniformly distributed over the population. The method of estimation for mean of the study variable under systematic sampling using auxiliary information has been proposed to estimate the body mass index (BMI).
Methods: The measures of different body parts are taken as auxiliary variables. The observation available on different body parts are assumed to be recorded with observational error. Thus we also propose method of estimation for mean in the presence of observational error. Numerical study has been done to reveal the efficacy of the proposed procedure for estimation of mean. Simulation study has also been done to demonstrate the effect of observational error on the estimation of body mass index.
Results: The properties of the proposed estimation method have been derived under large sampling approximation and obtained the conditions under which proposed method are more efficient.
Conclusions: The study provides an easy approach and simplest way to obtain the BMI estimate with and without observational error. Thus the suggested method may be used by statistician for this problem and for many others similar problem in the estimation of mean.