Compromised imputation based mean estimators using robust quantile regression

• Published in: Communications in statistics. Theory and methods 2022-08, Vol.53 (5), p.1700-1715
• Main Authors: Anas, Malik Muhammad, Huang, Zhensheng, Shahzad, Usman, Zaman, Tolga, Shahzadi, Shabnam
• Format: Article
• Language: English
• Subjects: Estimation; Estimators; Extreme values; imputation methods; Missing information; Population statistics; Quantiles; Random sampling; Regression coefficients; relative mean square error; robust quantile regression; robust variance-covariance matrices; Robustness (mathematics); simple random sampling (SRS); Statistical analysis; Statistical inference
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2022.2108057

Missing information is a typical issue in sampling surveys. The analysts have perceived that statistical inference possibly ruined due to occurrence of non-response. Ratio type regression estimators under simple random sampling (SRS) scheme for estimating the population mean are commonly used when some of the data suffered with the issue of missingness. It is worth noting that this class is based on ordinary least square regression coefficient which is not suitable when extreme values present in the data set. In this research, primarily a modified class of estimators is presented by adapting the idea of Zaman and Bulut. Later on, a class of quantile regression type estimators is defined which is an effective technique in presence of extreme observations. The utilization of quantile regression in the idea of Zaman and Bulut's work empowered the proposed class of estimators for the estimation of population mean especially for missingness in the data. For mean square error (MSE), the hypothetical equations are also formulated for adapted and proposed estimators, on the basis of three possible cases of missingness. To justify the proposed work these hypothetical innovations are illustrated by the numerical demonstrations.