A novel family of variance estimators based on L-moments and calibration approach under stratified random sampling

• Published in: Communications in statistics. Simulation and computation Vol. 52; no. 8; pp. 3782 - 3795
• Main Authors: Shahzad, Usman, Ahmad, Ishfaq, Almanjahie, Ibrahim M., Al-Noor, Nadia H., Hanif, Muhammad
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03.08.2023; Taylor & Francis Ltd
• Subjects: Calibration; Calibration approach; Estimators; Extreme values; L-moments; Random sampling; Robustness; Stratified random sampling; Variance; Variance estimation
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2021.1945629

Estimation of the population variance is of major concern in numerous examinations and ratio estimators are mainstream choices for it. It is a typical practice to utilize conventional central moments to construct variance estimators utilizing auxiliary information. However, conventional central moments give equal weight to each observation and hence highly affected by extreme values. For solving this issue, some recent developments are available in literature based on non-conventional/robust characteristics (inter-decile range, mid-range, etc.) of an auxiliary variable with conventional central moments under a simple random sampling scheme. This article initially, defines a family of ratio type variance estimators based on an adaptation of existing estimators with conventional central moments and non-conventional/robust characteristics of the auxiliary variable under a stratified random sampling scheme. After that, a novel family of variance estimators is proposed, in the presence of extreme values. The novel family of variance estimators is based on L-moments and calibration approach with some suitable constraints which can provide enhance the estimation of the population variance. We utilize L-moments characteristics (L-location, L-scale, and L-CV) for the purposes of the article. The variance expression of the novel family is also provided. Empirical illustrations are done using real and artificial data sets. The percentage relative efficiency is used for assessing the performances of adapted and novel families of estimators.