Multivariate analysis of longitudinal surveys for population median

Abstract

This article explores the analysis of longitudinal surveys in which same units are investigated on several occasions. Multivariate exponential ratio type estimator has been proposed for the estimation of the finite population median at the current occasion in two occasion longitudinal surveys. Information on several additional auxiliary variables, which are stable over time and readily available on both the occasions, has been utilized. Properties of the proposed multivariate estimator, including the optimum replacement strategy, are presented. The proposed multivariate estimator is compared with the sample median estimator when there is no matching from a previous occasion and with the exponential ratio type estimator in successive sampling when information is available on only one additional auxiliary variable. The merits of the proposed estimator are justified by empirical interpretations and validated by a simulation study with the help of some natural populations.

Surface Roughness in Ultra-High Precision Diamond Turning of Silicone Hydrogel Contact Lenses

“…There is a huge potential market for high quality optical elements made by ultra-high precision single-point diamond turning. The optical element market was estimated at $3.6 billion in 2012 and is expected to reach $12.3 billion by 2019 [1].…”