Ratio and Regression Methods of Estimation

4.1 INTRODUCTION In sampling theory the auxiliary information is being utilized in following ways:  Utilization of information at pre-selection stage i.e. for stratifying the population.  Utilization of information at selection stage i.e. in selecting the units with probabilities proportional to some suitable measure of size (size being based on some auxiliary variables).  Utilization of information at estimation stage i.e. in formulation of the ratio-type, regression, difference and product estimators etc.  Auxiliary information may also be utilized in mixed ways. Usually the information available is in the form that:  The values of the auxiliary character(s) are known in advance for each and every sampling unit of the population.  The population total(s) or mean(s) of auxiliary character(s) are known in advance.  If it is desired to stratify the population according to the values of some variate x, their frequency distribution must be known. The use of auxiliary information at estimation stage in the formation of ratio-type and regression estimators and sampling scheme providing unbiased regression estimator has been discussed in the following sections. In sample surveys, many a time the characteristic y under study is closely related to an auxiliary characteristic x, and data on x are either readily available or can be easily collected for all the units in the population. In such situations, it is customary to consider estimators of population mean N Y of survey variable y that use the data on x and are more efficient than the estimators which use data on the characteristic y alone. The fact that the data on the auxiliary variable can be used even at a later stage after selecting the sample, encourages such procedures. Two types of these commonly used methods are as follows:  the ratio-type method of estimation  the regression method of estimation 4