CaJoST, 2023, 3, 246-254 © 2023 Faculty of Science, Sokoto State University, Sokoto. |246 ISSN: 2705-313X (PRINT); 2705-3121 (ONLINE) Research Article Open Access Journal available at: https://cajost.com.ng/index.php/files and https://www.ajol.info/index.php/cajost/index This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. DOI: https://dx.doi.org/10.4314/cajost.v5i3.1 Article Info Received: 10 th August 2022 Revised: 22 nd February 2023 Accepted: 24 th February 2023 1,3,5 Department of Statistics, Usmanu Danfodiyo University, Sokoto, Nigeria. 2 Department of Statistics, Ahmadu Bello University, Zaria, Nigeria. 4 Department of Statistics, Kano University of Sci. and Tech, Wudil, Nigeria 6 Department of Statistics, Binyaminu Usman Polytechnic, Hadejia, Nigeria. *Corresponding author’s email: yahzaksta@gmail.com Cite this: CaJoST, 2023, 3, 246-254 Regression-Cum-Ratio Mean Imputation Class of Estimators using Non-Conventional Robust Measures Ahmed Audu 1 , Yahaya Zakari 2* , Mojeed A. Yunusa 3 , Ishaq O. Olawoyin 4 , Faruk Manu 5 , and Isah Muhammad 6 Different imputation strategies have been developed by several authors to take care of missing observations during analyses. Nevertheless, the estimators involved in some of these schemes depend on known parameters of the auxiliary variable which outliers can easily influence. In this study, a new class of ratio-type imputation methods that utilize parameters that are free from outliers has been presented. The estimators of the schemes were obtained and their MSEs were derived up to first-order approximation using the Taylor series approach. Also, conditions for which the new estimators are more efficient than others considered in the study were also established. Numerical examples were conducted and the results revealed that the proposed class of estimators is more efficient. Keywords: Imputation, Non-response, Estimator, Population Mean, Mean Squared Error (MSE). 1. Introduction It is often assumed at the beginning of the survey that information on sampling units drawn from the population is completely available. This assumption is often violated due to non-response due to incomplete information or inaccessibility to respondents or refusal to answer questions, especially surveys in medical and social science, etc. which often involve sensitive questions. In such situations, responses of non-respondents after often imputed or estimated using imputation techniques. Imputation is the process of replacing missing data with substituted values. There are three main problems that missing data due to non-response causes. It can introduce a substantial amount of bias, make the handling and analysis of the data more arduous, and create reductions in efficiency. Missing data due to non-response creates problems of complications during data analysis. The imputation approach provides all cases by replacing missing data with an estimated value based on other available information and auxiliary variable. Once all missing values have been imputed, the data set can then be analyzed using standard techniques for complete data. [1] were the first to consider the problem of non- response. Several authors also proposed imputation methods to deal with non-response or missing values. Among them are [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16] and [17]. Recently, [18] suggested a generalized class of imputation in which they compared the efficiency of the estimators obtained from the scheme with that of the estimators of the schemes by the previous authors and found that their estimators outperformed the estimators of the previous authors. Nonetheless, having studied the estimators by [18], it was observed that the estimators depend on the known parameters of the auxiliary variable which outliers can easily influence. In this study, new classes of ratio-type imputation methods which utilized parameters that are free from outliers have been presented. Notations The following notations have been used as described in [19], [20], [21], [22], [23], and [24]. Y: Study variable. X: Auxiliary variable. , XY : Population mean of the variables X and Y respectively. N: Population Size. n: Size of the sample r: Number of respondents. R: Ratio of the population mean of study variable to the population mean of auxiliary variable. n x : The sample mean for the sample of size n. Caliphate Journal of Science & Technology (CaJoST)