Minimum Covariance Determinant-Based Quantile Robust Regression-Type Estimators for Mean Parameter

Abstract

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.

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

“…In a different vein, Rueda and Arcos [17] investigated population quantiles using exponentiation method. Shahzad et al [18] and Shahzad et al [19] introduced a robust estimation approach for the population mean using quantile regression within the framework of systematic sampling and robust covariance matrices, respectively. Lastly, Yadav and Prasad [20] , utilizing robust quantile regression methodologies , examined exponential estimation methods in sampling theory.…”

A New Class of Quantile Regression Ratio-Type Estimators for Finite Population Mean in Stratified Random Sampling

“…Shahzad et al [31] proposed a robust estimation technique for the population mean utilizing quantile regression in the context of systematic sampling. Shahzad et al [32] proposed the utilization of quantile regression with minimum covariance determinant-based measures of the location to derive a class of quantile regression-type mean estimators.…”

Compromised-Imputation and EWMA-Based Memory-Type Mean Estimators Using Quantile Regression

“…Shahzad et al [17,18] proposed a group of robust regression estimators under a stratified and systematic random sampling framework using quantile regression. Taking a step further, Shahzad et al [19] harnessed the potential of quantile regression in conjunction with measures derived from the minimum covariance determinant to establish another group of estimators. By extending Shahzad et al's [17] work, Koc and Koc [20], and Yadav and Prasad [21] also provided regression-and exponential-type mean estimators using quantile regression coefficients.…”

“…Koc et al [40] merged auxiliary information with Poisson regression coefficients. So, taking motivation from relveant studies [15][16][17][18][19][20][21], the EWMA-based adapted quantile regression type mean estimators, i.e., (T zb q (0.25)…”