Research Article
Impact of Correlated Measurement Errors on Some Efficient
Classes of Estimators
Anoop Kumar ,
1
Shashi Bhushan ,
2
Shivam Shukla ,
3
Walid Emam ,
4
Yusra Tashkandy ,
4
and Rajesh Gupta
5
1
Department of Statistics, Amity School of Applied Sciences, Amity University Uttar Pradesh, Lucknow 226028, India
2
Department of Statistics, University of Lucknow, Lucknow 226007, India
3
Department of Mathematics & Statistics, Dr. Shakuntala Misra National Rehabilitation University, Lucknow 226017, India
4
Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455,
Riyadh 11451, Saudi Arabia
5
Global Data Insight & Analytics (GDIA), Ford Motor Company, 1 American Rd, Dearborn, MI 48126, USA
Correspondence should be addressed to Shashi Bhushan; bhushan_s@lkouniv.ac.in
Received 7 July 2023; Revised 12 August 2023; Accepted 23 September 2023; Published 18 October 2023
Academic Editor: Ammar Alsinai
Copyright©2023AnoopKumaretal.TisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
It is well-known that the appearance of measurement errors spoils the traditional results in survey sampling. Te concept of
correlated measurement errors (CMEs) is true in various practical situations, but this has been seldom considered by researchers
in survey sampling. In this article, the infuence of the CME under simple random sampling (SRS) has been considered over some
prominent classes of estimators for the population mean. Te frst-order approximated formulae of the mean square error of the
introduced estimators are reported, and a comparative analysis has also been conducted with traditional estimators. Te the-
oretical fndings are extended by a broad spectrum computational study using real and artifcial data.
1. Introduction
In survey research, the primary objective of any surveyor is
to enhance the efciency of the estimation procedures with
the help of information on the auxiliary/supplementary
variables that are usually associated with the research var-
iable. In this context, the literature contains the ratio, re-
gression, product, exponential methods, and their modifed
forms for efciently estimating the parameters of interest.
Tese estimation methods are further extended using two-
or multiauxiliary information under diferent sampling
schemes. Tese estimation methods either consist of a sup-
plementary variable or only on research variable, pre-
supposing that all data are independent from ME, but this
presupposition practically never happen. Te data are
tainted with or have hidden ME due to diferent types of
reasons (readers can refer to Murthy [1] and Cochran [2]).
Te discrepancy between the true and observed values is
known as ME. Many attempts have been made to examine
the impact of ME on various parameters of the population
such as the mean, variance, total, and distribution function.
Te efect of ME has been observed over the efciency of the
estimation methods by many authors. Shalabh [3] examined
the ME’s impact on the classical ratio estimators. Infuenced
by Shalabh [3], Manisha and Singh [4] studied the ME’s
impact using a new class of estimators for the population
mean. Subsequently, Singh and Karpe [5–7] examined the
efect of ME over the parameters of the population using
diferent sampling strategies. Te variance computation in
the existence of ME was provided by Diana and Giordan [8].
Hussain et al. [9] suggested the estimation of a fnite pop-
ulation distribution function with the dual use of supple-
mentary information under nonresponse. Tariq et al. [10]
proposed a supplementary information-based variance es-
timator to tackle the problem of ME. Tariq et al. [11] sug-
gested a generalized variance estimator utilizing
supplementary information in the presence and absence of
ME. Zahid et al. [12] developed a generalized class of
Hindawi
Journal of Mathematics
Volume 2023, Article ID 8140831, 27 pages
https://doi.org/10.1155/2023/8140831