ESTIMATION OF POPULATION MEAN THROUGH IMPROVED RATIO AND PRODUCT TYPE ESTIMATORS USING AUXILIARY INFORMATION
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Date
2017
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Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu
Abstract
The auxiliary information can be efficiently used in survey sampling at pre-selection stage, selection stage and estimation stage. The study entitled “Estimation of Population Mean through Improved Ratio and Product Type Estimators using Auxiliary Information” has been conducted in order to develop improved ratio and product type estimators when auxiliary information is available for the estimation of population mean. It is a well established fact that if the auxiliary information is used at estimation stage, the estimates of the population mean of characteristic under study can be obtained with greater precision. In sampling theory and statistical inference, there is variety of procedures which can led to development of improved estimators for estimation the population mean under study. In this study, an attempt has been made to develop a general class of improved ratio and product type estimators (may be biased or unbiased) for estimation of population mean by modifying conventional estimators whose large sample properties are compared with the conventional estimator and some existing estimators. The expressions for the relative bias and relative mean squared error of the proposed estimators have been derived up to first order and second order approximation respectively. The theoretical and empirical comparisons of efficiency of the proposed estimators have been done with existing estimators. It has been observed that the proposed class of ratio type estimators performed better than conventional ratio estimator and estimators proposed by Sharma et al. (2010) on the basis of mean squared error criterion. Likewise, general improved class of product type estimators have performed better than conventional product type estimators and estimators proposed by Robson (1957), Singh (1989), Dubey (1993) and Sharma et al. (2007) on the basis of relative mean squared error criterion. The empirical study has been done through simulation data by using R and SAS softwares. Two populations /datasets have been generated for ratio and product type estimators each i.e., populations P1 and P2 for ratio estimators and population P3 and P4 for product type estimators. The empirical comparisons showed that the proposed estimators were more efficient than the conventional and existing estimators. In this regard, five types of general class of ratio type estimators have been developed. Further, by setting different values of scalars p and q, various estimators have been proposed. The proposed biased ratio estimators i.e., t_(1(-3,1)), t_(2(-3,1)), t_(3(-3,1)), t_(4(-3,1)) and t_(5(-3,1)) and proposed unbiased ratio estimators t_(1(-1,-1)), t_(2(-1,-1)), t_(3(-1,-1)) and t_(4(-1,-1)) were more efficient than the conventional ratio type estimators and the estimators proposed by Sharma et al. (2010) which is empirically analyzed as per population datasets P1 and P2. The proposed ratio estimator t_(1(-3,1)) was the best among all other proposed ratio type estimators for small sample sizes. In case of product type estimator, five types of general class of product type estimators have been developed. The proposed product type estimators t_(1(1))^p, t_(2(3))^p, t_(3(2))^p¸〖 t〗_(4(-2,1))^p and t_(5(3,1))^p were found to be more efficient than the conventional product type estimator and the estimators proposed by Robson (1957), Singh (1989), Dubey (1993) and Sharma et al. (2007) in both the populations i.e., P3 and P4. The proposed product estimator 〖 t〗_2(3)^p was the best among all other proposed product type estimators for small sample sizes.
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No. of references 165