Abstract:
In sample survey, estimation of different finite population parameters like, mean,
median, variance, coefficient of variation, correlation and regression coefficients, interquartile
range, measure of skewness, etc. was considered extensively in the past.
However, comparison of different estimators of the same parameters has been limited.
Also, asymptotic theory for several estimators has not been adequately developed.
One of the main objectives of this Ph.D. thesis is to compare various
well-known estimators of finite population parameters under different sampling designs
based on their asymptotic distributions. Another objective of this thesis is
to understand the role of auxiliary information in the implementation of different
sampling designs and in the construction of different estimators. Four different
chapters in this thesis focus on four major topics. In the second chapter, several
well-known estimators of the finite population mean and its functions are compared
under some commonly used sampling designs. A similar comparison is carried out
in the third chapter for the case of mean, when the data are infinite dimensional in
nature. In the fourth chapter, the weak convergence of different quantile processes
are shown under several sampling designs and superpopulation distributions, and
these results are used to study asymptotic properties of estimators of various finite
population parameters. Finally, in the fifth chapter, the asymptotic behaviour of
the estimators obtained from different regression methods are studied in the context
of sample survey.
