APPROXIMATION OF FINITE POPULATION TOTALS USING LAGRANGE POLYNOMIAL

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.