Robust regression type estimators to determine the population mean under simple and two-stage random sampling techniques

Abstract

For the estimation of population mean, there are several ratio and regression type estimators available in literature. However, they can be misleading
to contain the desired results when data are contaminated by outliers. In
recent past, Zaman and Bulut (2019a) provided the solution of this issue
by utilizing some robust regression tools and develop a class of ratio type
estimators under simple random sampling scheme. To extending their work,
Zaman (2019) has suggested another class of estimators but this time using
ratio technique. In this paper, we proposed a new class of robust regression type estimators with utilizing LAD, LMS, LTS, Huber-M, Hampel-M,
Tukey-M, Huber-MM as robust regression tools. The desired class is subsequently extended for two stage sampling, where mean of the study variable
is not available at first stage. Also, we have developed some reviewed and
proposed estimators under above mentioned sampling technique. Further,
we have divided our supposition into two cases as: (i)- when drawn a second stage sample depends upon first stage sample and, (ii)- when drawn a
second stage sample is independent of first stage sample. The mean square
expressions of the proposed estimators have been determined through Taylor series expansion. A real life application and the simulation study are also
provided to assess existing and proposed estimators. In the light of numerical
illustration, we see that our proposed estimators give more efficient results
than the reviewed ones.