Some Investigations on the Role of Sampling for Prediction

Abstract

Regression relations are of very much use to predicting the value of one variable on the basic of the given values of other variables. Recent literature in sampling theory has gathered around the estimation of mean and total only. The relative efficiencies of various sampling procedures have been very well discussed in relation to estimation of population to mean or total. No effort, however, seems to have been made to investigate the possibility of an optimum sampling design which can be used for prediction purposes. In this investigation problem of determining the regression relation on the basis of a sample from finite population has been considered. The expressions for the variance of prediction have been worked out for the situations when the sample is drawn by simple random sampling, Cluster sampling, two stage sampling and stratified sampling under different situations. It has been observed that the performance of all the procedures mentioned above to approximately the same in respect of the prediction variance. The results thus point out the possibility of analyzing the sample as of it is drawn by simple random sampling over when the procedures like multi-stage stratified sampling etc. are adopted from the administrative and technical conveniences. The problem of determining an optimum sampling design for prediction has been also been considered in this investigation and it has been observed that the solution in general is complex. However, to have some idea for empirical results are discussed to compare three sampling procedures under wide range of population. It has been observed that the performance of equal probability sampling is highly satisfactory in comparison to other sampling procedures considered. The results thus indicate that simple random sampling can safely be used for determining a linear regression relationship to be used for prediction. In the end the application of the suggested procedure has been explained to the data collected under pre-harvest forecasting scheme during 1970-71 to 1973-74 of Jute crop to Bihar State. The solutions of various statistical problems involved in pre-harvest forecasting have also been indicated.