Robust M-Estimators of the Population Mean.
Loading...
Date
2018-07
Authors
Mutuguta, Bernard Githui
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
Abstract
Valuable information may be contained in outliers. Data collected from many medical
equipment such as the ECG time-series may result in unusual patterns, a situation
that may represent disease conditions. Some outliers may therefore provide an insight
into crucial information that may lead to the discovery of new knowledge.Due to
the di culties involved in the study of outliers, majority of current research works
have chosen not to out-rightly reject the outliers but have adopted methods that
accommodates them but have their in
uence reduced to some degree. This has
resulted in the development of estimation and testing techniques that have yielded
robust estimation. Three robust M-estimators (the Huber, the Hampel and the
Tukey's biweight) were adopted in this paper with an aim of comparing their e ciency
in the estimation of population mean in an asymmetrical distribution. Simulation
was used to generate a normal population which was then contaminated with a few
outlying observations. A simple example illustrated how the comparison of the M-
estimators was carried out on real data. On the basis of the ndings from this research,
the M-estimator that turned out to be the best, was the Tukey's biweight followed
by the Hampel's and the Huber's was the weakest of the three. However all the three
M-estimators yielded unbiased estimates of the population mean.
Description
A Research Project Submitted in Partial FullLlment of the Requirement for the Award of Degree Master of Science (Statistics) in the School of Pure and Applied Sciences of Kenyatta University, July 2018