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)