Estimation of Simple Linear Regression Model Parameters Using Double Ranked Set Sampling

Abstract

The notion of ranked set sampling (RSS) for estimating the mean of a population and its advantage over the use of a simple random sampling for the same aim is well known and established in the literature. Furthermore, the double ranked set sampling (DRSS), a two-stage RSS, has proven that it is even more efficient than RSS when estimating the mean. In this article, we review the use of the DRSS to estimate the intercept, the slope, and the standard deviation of the error terms as parameters of a simple linear regression model, when replications exist at each value of the predictor. We derive the best linear unbiased estimators of simple linear regression model parameters using the DRSS. Finally, we illustrate the proposed procedure by applying it when the underlying distribution of the error terms is normal or Laplace. Regardless of the assumed number of replications in the experiment, we observe a substantial gain in relative precision while using DRSS procedure over using RSS technique.