Estimation of population parameters in survey sampling and construction of PBIB designs

Abstract

For a phenomenon that varies over a continuous (or even a large finite) spatial domain, it is seldom feasible to observe every potential datum of some study variable associated with that phenomenon. Thus, important parts of statistics are statistical sampling theory as well as design of experiment where inference about the study variable may be made from a subset or sample of the population of potential data. The theory of sampling and design of experiment has its origin way back in the history of mankind. Special sampling refers to the sampling of geo-referenced of spatially labeled phenomena. In the spatial context, interest is usually in the prediction of the study variable at un-sampled sites. For such purpose, it is necessary to collect information regarding the population with respect to some characteristics. For example, in agricultural surveys, to estimate the production of food, the data are collected on some portion of land under different crops. Most of the government and non-government bodies collect information regularly about the total population, its geographical distribution, sex, age, age-sex etc. for future planning. In business, information is also required for the role and character of wholesale, retail and service traders etc. Given some predictand together with its predictor, a best sampling plan or network refers to the choice of locations at which to sample the phenomenon in order to achieve optimally according to a given criterion. In practice, optimal sampling plans may be extremely difficult to achieve, but atleast good sampling plans may be obtained and designed by constructing best sampling frame which can be formed by using appropriate technique of design of experiments. The main objective of the thesis is to construct best design of sample survey and design of experiments for estimating the parameters of interest and testing the hypothesis under study respectively.