B. B. Khare , R. R. Sinha
ARTICLE

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ABSTRACT

This paper considers the problem of estimating the product of two population means using the information on multi-auxiliary characters with double sampling the non-respondents. Classes of estimators are proposed for estimating P under two different situations [discussed by Rao (1986, 90)] using known population mean of multi-auxiliary characters. Further, this problem has been extended to the case when population means of the auxiliary characters are unknown and they are estimated on the basis of a larger first phase sample. In this situation, a class of two phase sampling estimators for estimating P is suggested using multi-auxiliary characters with unknown population means in the presence of non-response. The expressions of bias and mean square error of all the proposed estimators are derived and their properties are studied. An empirical study using real data sets is given to justify the theoretical considerations.

KEYWORDS

product, bias, mean square error, auxiliary characters, non-response

REFERENCES

ABU-DAYYEH, W. A., AHMED, M. S., AHMED, R. A., MUTTLAK, H. A., (2003). Some estimators of finite population mean using auxiliary information, App. Math. Comp., 139, pp. 287–298.

HANSEN, M. H., HURWITZ, W. N., (1946). The problem of non-response in sample surveys, Jour. Amer. Stat. Assoc., 41, pp. 517–529. KADILAR, C., CINGI, H., (2005). A new estimator using two auxiliary variables, App. Math. Comp., 162, pp. 901–908.

KHARE, B. B., (1987). On modified class of estimators of ratio and product of two population means using auxiliary character, Proc. Math. Soc., B.H.U., 3, pp. 131–137.

KHARE, B. B., (1990). A generalized class of estimators for a combination of products and ratio of some population means using multi-auxiliary characters, Jour. Stat. Res., 24(1-2), pp. 1–8.

KHARE, B. B., (1991). On generalized class of estimators for ratio of two population means using multi-auxiliary characters, Ali. Jour. Stat., 11, pp. 81–90.

KHARE, B. B., (1992). On class of estimators for product of two population means using multi-auxiliary characters with known and unknown means, Ind. Jour. Appl. Stat., 1, pp. 56–67.

KHARE, B. B., SINHA, R. R., (2002 a). On the class of two phase sampling estimators for the product of two population means using the auxiliary character in presence of non-response, Proceedings of the 5th International Symposium on Optimization and Statistics, pp. 221–232.

KHARE, B. B., SINHA, R. R., (2002 b). Estimation of the ratio of two population means using auxiliary character with unknown population mean in presence of non-response, Prog. Math., 36, pp. 337–348.

KHARE, B. B., SINHA, R. R., (2004 a). Estimation of finite population ratio using two phase sampling scheme in the presence of non-response, Ali. Jour. Stat., 24, pp. 43–56.

KHARE, B. B., SINHA, R. R., (2004 b). On the general class of two phase sampling estimators for the product of two population means using the auxiliary character in the presence of non-response, Ind. Jour. Appl. Stat., 8, pp. 1–14.

KHARE, B. B., SINHA, R. R., (2007). Estimation of the ratio of the two population means using multi-auxiliary characters in the presence of non-response, Proceedings of Statistical Technique in Life Testing, Reliability, Sampling Theory and Quality Control, pp. 205–213.

KHARE, B. B., SINHA, R. R., (2012 a). Improved classes of estimators for ratio of two means with double sampling the non-respondents, Statistika, 49(3), pp. 75–83.

KHARE, B. B., SINHA, R. R., (2012 b). Combined class of estimators for ratio and product of two population means in presence of non-response, Inter. Jour. Stat. Eco., 8, pp. 86–95.

PERRI, P. F., (2005). Combining two auxiliary variables in ratio-cum-product type estimators, Proceedings of Italian Statistical Society, Intermediate Meeting on Statistics and Environment, Messina, 21-23 Sept. 2005, pp. 193–196.

RAJ, D., (1965). On a method of using multi-auxiliary information in sample surveys, Jour. Amer. Stat. Assoc., 60, pp. 154–165.

RAO, P. S. R. S., (1986). Ratio estimation with subsampling the nonrespondents, Survey Methodology, 12(2), pp. 217–230.

RAO, P. S. R. S., (1990). Regression estimators with subsampling of nonrespondents, In-Data Quality Control, Theory and Pragmatics, (Eds.) Gunar E. Liepins and V.R.R. Uppuluri, Marcel Dekker, New York, pp. 191–208.

RAY, S. K., SINGH, R. K., (1985). Some estimators for the ratio and product of population parameters, Jour. Ind. Soc. Ag. Stat., 37, pp. 1–10.

REDDY, V. N., (1978). A study of use of prior knowledge on certain population parameters in estimation, Sankhaya, C, 40, pp. 29–37.

SHAH, S. M., SHAH, D. N., (1978) Ratio cum product estimator for estimating ratio (product) of two population parameters, Sankhya, C, 40, pp. 156–166.

SINGH, H. P., KUMAR, S., (2008). A general family of estimators of finite Population ratio, product and mean using two phase sampling scheme in the presence of non-response, Jour. Stat. Theory and Practice, 2(4), pp. 677–692.

SINGH, H. P., CHANDRA, P., JOARDER, A. H., SINGH, S., (2007). Family of estimators of mean, ratio and product of a finite population using random non-response, Test, 16(3), pp. 565–597.

SINGH, M. P., (1965). On the estimation of ratio and product of population parameters, Sankhya, C, 27, pp. 321–328.

SINGH, M. P., (1967). Ratio cum product method of estimation, Metrika, 12, pp. 34–43.

SINGH, M. P., (1969). Comparison of some ratio cum product estimators, Sankhya, B, 31, pp. 375–378.

SINGH, R. K., (1982 a). Generalized estimators for the estimation of ratio and product of population parameters, Jour. Stat. Res., 16, pp. 15–23.

SINGH, R. K., (1982 b). On estimating ratio and product of population parameters, Cal. Stat. Asso. Bull., 20, pp. 39–49.

SINGH, R. K., (1982 c) Generalized double sampling estimators for the ratio and product of population parameters, Jour. Ind. Stat. Asso., 20, pp. 39–49.

SRIVASTAVA, S. K., JHAJJ, H. S., (1983). A class of estimators of the population mean using multi-auxiliary information, Cal. Stat. Asso. Bull., 32, pp. 47–56.

SRIVASTAVA, S. RANI, KHARE, B. B., SRIVASTAVA, S. R., (1988). On generalised chain estimator for ratio and product of two population means using auxiliary characters, Assam Stat. Rev., 1, pp. 21–29.

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