Abstract
The use of auxiliary information in survey sampling to enhance the efficiency of the estimators of population parameters is a common phenomenon. Generally, the ratio and regression estimators are developed by using the known information on conventional parameters of the auxiliary variables, such as variance, coefficient of variation, coefficient of skewness, coefficient of kurtosis, or correlation between the study and auxiliary variable. The efficiency of these estimators is dubious in the presence of outliers in the data and a nonsymmetrical population. This study presents improved variance estimators under simple random sampling without replacement with the assumption that the information on some nonconventional dispersion measures of the auxiliary variable is readily available. These auxiliary variables can be the inter-decile range, sample inter-quartile range, probability-weighted moment estimator, Gini mean difference estimator, Downton’s estimator, median absolute deviation from the median, and so forth. The algebraic expressions for the bias and mean square error of the proposed estimators are obtained and the efficiency conditions are derived to compare with the existing estimators. The percentage relative efficiencies are used to numerically compare the results of the proposed estimators with the existing estimators by using real datasets, indicating the supremacy of the suggested estimators.
Highlights
IntroductionEstimation of population variance is dealt with in the context of augmenting the conventional parameters of the auxiliary variable through a ratio or regression method of estimation to achieve greater efficiency
Suppose a finite population W = {W1, W2, . . . , WN } consists of N different and identifiable units.Let Y be a measurable variable of interest with values Yi being ascertained on Wi ; i = 1, 2, . . . , N resulting in a set of observations Y = {Y1, Y2, . . . , YN }
These measures are resistant to outliers and used in a linear combination with the other conventional measures to improve the efficiency of the variance estimator under simple random sampling without replacement (SRSWOR) in the presence of outliers in the target population
Summary
Estimation of population variance is dealt with in the context of augmenting the conventional parameters of the auxiliary variable through a ratio or regression method of estimation to achieve greater efficiency. The present study is focused on estimation of population variance by incorporating information on nonconventional dispersion parameters (detailed in Section 3) of the auxiliary variable. These measures are resistant to outliers and used in a linear combination with the other conventional measures to improve the efficiency of the variance estimator under simple random sampling without replacement (SRSWOR) in the presence of outliers in the target population.
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