Effect of Varying Correlation Values on the Efficiency of some Selected Population Variance Estimator using known Values of an Auxiliary Variable

Abstract:

The use of Auxiliary variable in estimating the parameters of a study variable has been on the increase. Several authors have worked on some estimator combining various population values of the auxiliary variable and the study variable. There is need to compared some of these estimators under varying correlation values. Twelve estimators were considered. Two distributions were used to do the comparison. Three correlation levels were considered. The performance criteria used is the Mean Square Error (MSE). A sample of size 30 was simulated. The results showed that estimator T4 is the best under Geometric distribution but the worst under the uniform distribution. Estimator T12 is the best under the Uniform while it took 7th in Geometric distribution. Estimators T1, T3, T4, T8, T9, T10 and T12 under the Geometric distribution are not affected by correlation while T2, T5, T6 and T7 were affected by correlation. Under the Uniform distribution, only estimator T3 and T11 had a little effect at high correlation. All other estimators are not affected by correlation. Almost all the estimators are affected by distribution except T1.