Abstract:
In this thesis, we have considered the inference aspects of sampling from a
finite population. There are significant differences between traditional
statistical inference and finite population sampling inference. In the case of
finite population sampling, the statistician is free to choose his own sampling
design and is not confined to independent and identically distributed
observations as is often the case with traditional statistical inference. We look
at the correspondence between the sampling design and the sampling
scheme. We also look at methods used for drawing samples. The non –
existence theorems (Godambe (1955), Hanurav and Basu (1971)) are also
discussed. Since the minimum variance unbiased estimator does not exist for
infinite populations, a number of estimators need to be considered for
estimating the same parameter. We discuss the admissible properties of
estimators and the use of sufficient statistics and the Rao-Blackwell Theorem
for the improvement of inefficient inadmissible estimators. Sampling
strategies using auxiliary information, relating to the population, need to be
used as no sampling strategy can provide an efficient estimator of the
population parameter in all situations. Finally few well known sampling
strategies are studied and compared under a super population model.
