Effect of Correlation Level on the Use of Auxiliary Variable in Double Sampling for Regression Estimation

While an auxiliary information in double sampling increases the precision of an estimate and solves the problem of bias caused by non-response in sample survey, the question is that, does the level of correlation between the auxiliary information x and the study variable y ease in the accomplishment of the objectives of using double sampling? In this research, investigation was conducted through empirical study to ascertain the importance of correlation level between the auxiliary variable and the study variable to maximally accomplish the importance of auxiliary variable(s) in double sampling. Based on the Statistics criteria employed, which are minimum variance, coefficient of variation and relative efficiency, it was established that the higher the correlation level between the study and auxiliary variable(s) is, the better the estimator is.

Efficiency of the Adaptive Cluster Sampling Designs in Estimation of Rare Populations

Adaptive cluster sampling (ACS) has been a very important tool in estimation of population parameters of rare and clustered population. The fundamental idea behind this sampling plan is to decide on an initial sample from a defined population and to keep on sampling within the vicinity of the units that satisfy the condition that at least one characteristic of interest exists in a unit selected in the initial sample. Despite being an important tool for sampling rare and clustered population, adaptive cluster sampling design is unable to control the final sample size when no prior knowledge of the population is available. Thus adaptive cluster sampling with data-driven stopping rule (ACS’) was proposed to control the final sample size when prior knowledge of population structure is not available. This study examined the behavior of the HT, and HH estimator under the ACS design and ACS’ design using artificial population that is designed to have all the characteristics of a rare and clustered population. The efficiencies of the HT and HH estimator were used to determine the most efficient design in estimation of population mean in rare and clustered population. Results of both the simulated data and the real data show that the adaptive cluster sampling with stopping rule is more efficient for estimation of rare and clustered population than ordinary adaptive cluster sampling.

Estimation of Population Variance Using the Coefficient of Kurtosis and Median of an Auxiliary Variable under Simple Random Sampling

In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order of Taylor’s series expansion. The efficiency conditions derived theoretically under which the proposed estimator performs better than existing estimators. Empirical studies have been done using real populations to demonstrate the performance of the developed estimator in comparison with the existing estimators. The proposed estimator as illustrated by the empirical studies performs better than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared Error and the highest Percentage Relative Efficiency. The developed estimator therefore is suitable to be applied to situations in which the variable of interest has a positive correlation with the auxiliary variable.

An Efficient Scrambled Estimator of Population Mean of Quantitative Sensitive Variable Using General Linear Transformation of Non-sensitive Auxiliary Variable

In the present paper,we propose an efficient scrambled estimator of population mean of quantitative sensitive study variable,using general linear transformation of nonsensitive auxiliary variable.Efficiency comparisons with the existing estimators have been carried out both theoretically and numerically.It has been found that our optimal scrambled estimator is always more efficient than most of the existing scrambled estimators and also it is more efficient than few other scrambled estimators under some conditions.