Contribution to 3-P Sampling

Abstract

In sample surveys, use of information on as a auxiliary character highly correlated with the character under study is a very common practice for increasing the efficiency of the estimate of the population character either at the stage of stratification or selection of the sampling units or at the stage of estimation. While selecting the units to form a sample, the units are assigned probabilities of selection in proportion to the value of the auxiliary character, X, for each of the units in the population. It is supposed that this auxiliary information is available for all the units in the population at the time of planning the design of the survey. But in some situations, like forest inventory surveys, it may not be possible to record information on X for all or some of the units in the population in advance of selection of units for recording information on Y, the character under study. Also the cost of relocating and reobserving usually makes it inefficient to visit a unit more than once. In such a situation, 3-P sampling has been advocated. The details on the work so far done on 3-P sampling procedure are discussed in Chapter-2. In Chapter-3, comparisons are made of 3-P sampling with some other well-known sampling procedures. Comparing 3-P sampling with PPS sampling (without replacement), It was observed that in most of the situations PPS would prove to be more efficient than 3-P sampling. However, due to operational difficulties and lack of information on all X’s before the commencement of the survey, 3-P sampling is to be preferred in spite of its lack of superiority over PPS. While comparison was made of 3-P estimate with SRS (without replacement) estimate, it was observed that 3-P sampling would be more efficient than SRS (without replacement). If C.V. of X is greater than or equal to 1. The unadjusted and adjusted estimates are derived along with their variances and estimates of variances for double-sampling procedure with 3-P sampling being adopted at the second phase. Variance is minimized for fixed cost for this procedure (using the unadjusted estimate) and it is compared with the minimum variance due to double-sampling where PPS sampling is adopted at the second phase. Again, it was observed that PPS would prove to be more efficient than 3-P sampling at the second phase. For these two procedures of sampling, minimum cost is worked out for fixed variance and they are compared with each other. In Chapter-4, a class of estimators has been developed, similar to the one suggested by Das Raj (1956). Taking into account the order in which the units are drawn. Here it is assumed that it is possible to identify and locate specific units in the population and also that another duplicate sample. In addition to the sample obtained through 3-P sampling, could be drawn during the course of the survey. This scheme is recommended when no list of XI is available in advance of sampling and thus the other procedures for sampling with PPS such as Lahiri‘s method cannot be used. As estimate of the variance of the sample mean obtained through this procedure is developed. For a comparable sample size, this procedure inevitably reduces the cost as compared to PPS.