Use of Nonconventional Dispersion Measures to Improve the Efficiency of Ratio-Type Estimators of Variance in the Presence of Outliers

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.

Dual-type quantile regression approach for mean estimation incorporating sampled and non-sampled data

“…Abid et al [4] , [5] used non-conventional measures of location. For more about efficient estimation of parameter, interested readers may refer to Naz et al [6] . It is worthy to note that many of these mentioned estimators use ordinary least square regression coefficient.…”

Incorporating the neutrosophic framework into kernel regression for predictive mean estimation

“…So, the major goal of the survey statistician is to minimize errors by using a suitable scheme of sampling or presenting an efficient estimator of parameters. Optimal estimates can often be achieved by effectively incorporating additional data related to supplementary variables associated with the main variable, Bhushan et al [ 1 ] and Naz et al [ 2 ]. Auxiliary information, obtained before a survey, is extra data linked to the study's subject, aiming to minimize errors in the primary information by providing context and relevance.…”

Calibration Estimation of Cumulative Distribution Function Using Robust Measures

“…References [16,17] extended the work by utilizing linear moments' characteristics. Reference [18] developed two novel classes of ratio-and regression-type estimation methods of population variation under SRSWOR by integrating knowledge on nonconventional and robust dispersion measures of supplementary data. Reference [19] proposes a new robust calibration estimation method for estimating the population mean under StRS.…”