Abstract:
In this thesis, attempt to study the e ects of extreme observations on one ap-
proximator of nite population total is made. We are particularly approximating
the nite population totals using the Lagrange polynomial of nite population
totals given di erent nite populations. The study revealed that both the clas-
sical and the non parametric estimator based on the local linear polynomial give
good outcomes when the auxiliary and the study variables are highly correlated.
It is however realized that in the presence of outliers the local linear polynomial
performs better with respect to design mean square error. However, this approach
relies entirely on the bandwidth selection in order to attain a better precision.
The Lagrange polynomial has been proposed which does not put emphasis on
choice of bandwidth selection. The study developed a Lagrange polynomial and
showed how to obtain the error term. However, the asymptotic properties are also
determined with the use of the Karl Weierstrass theorem. This revealed that, the
linear polynomial is the best approximating polynomial which can converge faster
than other higher degree polynomials with high precision. Finally, the empirical
analysis showed a good outcome which is in conformity with what the theorem
revealed and gave a good projection of the population total for the coming census
in Kenya in 2019.
