Random Permutation Model Incorporating Auxiliary Information and Response Error for Finite Populations

We derive optimal estimators of a linear combination of the responses, under the random permutation model, incorporating auxiliary information and response error. In particular, we propose estimators of a measure of association, that is named B and defined farther in (1), between a response and an explanatory variable based on a simple random sample obtained without replacement from a finite population. We illustrate the method with numerical examples. We also obtain the variance of the estimators and show that they have a smaller mean square error than the ordinary least squares estimator via a simulation study.