COMPUTER-AIDED SIMULATION STUDIES EXPLORING EFFICIENT MIXING-TYPE ESTIMATORS

Abstract

In sample surveys, one area of interest has been to improve the ratio and product methods of estimation. A number of estimators has been proposed by various authors (e.g., Srivenkataramana, T. & Tracy, D.S.(1979,1981-Statistica Neerlandica, Aust. Jr. of Stat.); Sahai, A.(1979-Statistica Neerlandica); Vos, J.W.E. (1980-statistica Neerlandica) and others) which are ratio, product and ratio-cum-product type in nature. These estimators make the use of auxiliary information to estimate the population total/mean. In the present thesis, we have proposed some new estimators as also the efficient mixings of some existing and proposed estimators. The problem with the ratio, product and ratio-cum-product estimators proposed in the thesis as also with the usual ratio estimator is that their mean-square-errors (MSEs) could not be found analytically in a closed form. Hence, only the approximate MSEs could be the basis of comparison in terms of relative efficiencies. If we take a first order (0(n-1); n being the sample size) large sample approximation to the MSEs of these estimators, a comparison is algebraically intricate and the issue depending on many population parameters' values, which are unknown, it is difficult to conclude as to which one of these estimators is more efficient and when. Further, in case the sample size is that large as to justify the first order large sample approximation, regression estimator will be better motivated than the proposed families of estimators. As such, only when the sample is rather fairly large though not very large, we are motivated enough to use the proposed families of estimators and in this case we will have to go for at least a second order (0(n-2)) large sample approximations to the MSEs of the estimators. In this case, the approximations to the MSEs turn out to be still more intractable algebraically and a comparison isl just impossible. So, we have 1 compared the various estimators through the computer-aided empirical-simulation study. In this study, we. generate the random samples of desired size from a hypothetical bivariate normal population. Sisodia & Dwivedi(1981-Jr. Ind. Soc. Agri Stat.) and Singh & Upadhyaya (1986-Proc. Nat. Acad. Sci., INDIA) proposed modified ratio and product estimators, respectively, by making the use of coefficient of variation for the auxiliary variable. Motivated by their, works, we have proposed variants of ratio and product estimators with the use of sample counter part of the coefficient of variation in Chapter-2. We have also proposed a few other estimators using one design-parameter in this chapter. A part of the work in this chapter has been published in Int. Jr. of ii Management and System-Volume 6, No.3 (1990); Allahabad Mathematical Society Bulletin-Second Biennial Conference (April, [990) and The Proc. of 73rd Indian Science Congress. We have also proposed two families of ratio-cum-product estimators which make the use of two design-parameters. Thus, we will be having two degrees of freedom and it enables us to control the first and second order MSEs of ,Ilese estimators. This work has been presented in Chapter-3 of the thesis. A part of this work has been published in Proc. of 47th session of Int. Stat. Inst. (Aug.-Sep., 1989, PARIS). Further, we have proposed some efficient mixings of the already existing estimators and the estimators proposed by us. These mixings are motivated by the work of Vos(1980-Statistica Neerlandica). We have improved the various estimators by mixing them with the usual mean-per-unit estimator. The weights for these Mixings have been ascertained using the relative frequencies of the respective estimators to be winner in the comparison via the empirical-simulation study. Two more types of mixings of the estimators have been dealt with. In the first type of mixing, WE have proposed efficient mixings of the estimators proposed/studiec by us taking two of the winning estimators at a time and in the second type of mixing, we have proposed a few linear combination: of mean-per-unit estimators, ratio estimator and the two winning estimators proposed/studied by us. Again, the weights for these mixings have been ascertained as per the empirical-probabilities of winning of the mixing-estimators estimable from the relevant empirical-simulation study. We have also taken up the fine] iii comparisons of the estimators. For this, we first have picked up various winners from the earlier study and then have compared these with each other to bring forth the various ranges of :;-values and p-values for a particular estimator to be the best. The concluding chapter enlists a brief review of the highlights of the work presented in the thesis. As regards to future possibilities of gainful consequences in this area, it is hoped that the various estimation strategies proposed in the thesis can be the basis of defining multivariate generalised/mixing-type estimator's besides leading to possible discoveries of more gainful mixing-estimators.