Mean Estimators Using Robust Quantile Regression and L-Moments’ Characteristics for Complete and Partial Auxiliary Information

Abstract

Ratio type regression estimator is a prevalent and readily implemented heuristic under simple random sampling (SRS) and two-stage sampling for the estimation of population. But this existing method is based on the ordinary least square (OLS) regression coefficient which is not an effective approach in the presence outliers in the data. In this article, we proposed a class of estimators firstly for complete auxiliary information and, later on, for partial auxiliary information for the presence of outliers in the data. To address this problem, initially we presented a distinct class of estimators by introducing the characteristics of L-moments in the existing estimators. Later on, quantile regression estimators are defined as more robust in the presence of outliers. These techniques empowered the proposed estimators to handle the problem of outliers. To prove the better performance of the proposed estimators, numerical studies are carried out using R language. To calculate the mean square error (MSE), hypothetical equations are expressed for adapted and proposed estimators. Percentage Relative Efficiencies (PRE) are compared to justify the proposed estimators.

An efficient class of estimators for finite population mean in the presence of non-response under ranked set sampling (RSS)

“…Computation of the first few sample L-moments and their ratios provides a useful review of the location, shape, and dispersion of the population from which the sample was drawn. In this regard, the work of [1][2][3][4] can be seen. Another efficient and alternative approach of estimating population parameters is ranked set sampling (RSS) procedure, which is determined by ranking a greater number of sampling units based on their relative sizes, then picking a smaller number of units from each ranked group under observation.…”

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

“…These authors introduced a collection of quantile regression based estimators specifically tailored for non-normally distributed data with outliers, with the goal of estimating the population mean. In a related context, Anas et al [15] defined a similar category of estimators that leverage Linear-moments for estimating the mean parameter in non-normally distributed datasets with outliers under simple random sampling. Shahzad et al [16] presented a resilient category of quantile based estimators explicitly crafted for estimating population means within the context of stratified random sampling.…”

Estimation of population mean under probability proportional to size sampling with and without measurement errors

“…Using the method of pps sampling, many authors like Rao, 1 Tripathi, 2 Anita and Bahl, 3,22 Patel and Bhatt, 4 Ahmad and Shabbir 5 and Singh et al 6 have suggested improved estimators for estimating different population parameters while Anas et al 7,8 and Shahzad et al 9,10 have proposed calibration based mean and variance estimators using $$$ L $$$‐moments. In order to examine the properties and efficiency of the proposed estimators in terms of mean square error, some of the well‐established forms of suggested estimators under pps sampling have been adopted in this section and their properties have been studied.…”