Multiple Observers Ranked Set Samples for Shrinkage Estimators

TL;DR

This paper develops and evaluates shrinkage estimators using multiple observer ranked set sampling to improve coefficient estimation efficiency in regression models with costly measurements.

Contribution

It introduces ridge and Liu-type shrinkage estimators under multi-observer RSS, addressing collinearity in various regression models.

Findings

Shrinkage estimators with multi-observer RSS improve estimation efficiency.

Numerical studies confirm the effectiveness of the proposed methods.

Application to bone mineral data demonstrates practical utility.

Abstract

Ranked set sampling (RSS) is used as a powerful data collection technique for situations where measuring the study variable requires a costly and/or tedious process while the sampling units can be ranked easily (e.g., osteoporosis research). In this paper, we develop ridge and Liu-type shrinkage estimators under RSS data from multiple observers to handle the collinearity problem in estimating coefficients of linear regression, stochastic restricted regression and logistic regression. Through extensive numerical studies, we show that shrinkage methods with the multi-observer RSS result in more efficient coefficient estimates. The developed methods are finally applied to bone mineral data for analysis of bone disorder status of women aged 50 and older.