Traditional ordinary least square (OLS) regression is commonly utilized to develop regression-ratiotype estimators with traditional measures of location. Abid et al. [1] extended this idea and developed regression-ratio-type estimators with traditional and non-traditional measures of location. In this article, the quantile regression with traditional and non-traditional measures of location is utilized and a class of ratio type mean estimators are proposed. The theoretical mean square error (MSE) expressions are also derived. The work is also extended for two phase sampling (partial information). The pertinence of the proposed and existing group of estimators is shown by considering real data collections originating from different sources. The discoveries are empowering and prevalent execution of the proposed group of estimators is witnessed and documented throughout the article.
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.
Robust regression tools are commonly used to develop regression-type ratio estimators with traditional measures of location whenever data are contaminated with outliers. Recently, the researchers extended this idea and developed regression-type ratio estimators through robust minimum covariance determinant (MCD) estimation. In this study, the quantile regression with MCD-based measures of location is utilized and a class of quantile regression-type mean estimators is proposed. The mean squared errors (MSEs) of the proposed estimators are also obtained. The proposed estimators are compared with the reviewed class of estimators through a simulation study. We also incorporated two real-life applications. To assess the presence of outliers in these real-life applications, the Dixon chi-squared test is used. It is found that the quantile regression estimators are performing better as compared to some existing estimators.
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