ARTICLE
ABSTRACT
In this paper, a class of two phase sampling estimators for estimating the ratio of two population means using multi-auxiliary characters with unknown population means has been proposed in presence of non-response. The asymptotic bias, mean square error and minimum mean square error of the proposed class of estimators have been obtained. The optimum values of the sample at the first and the second phases along with the sub-sampling fraction of the non-responding group have been determined for the fixed cost and for the specified precision. The efficiency of the proposed class of estimators has also been shown through the theoretical and empirical studies
KEYWORDS
two phase sampling, ratio of two means, bias, mean square error, auxiliary characters.
REFERENCES
HANSEN, M. H., HURWITZ, W. N., (1946). The problem of nonresponse in sample surveys, Jour. Amer. Statist. Assoc., 41, 517–529.
HARTLEY, H. O., ROSS, A., (1954). Unbiased ratio estimators, Nature, 174, 270–271.
KHARE, B. B., (1983). Some problems of estimation using auxiliary character, Ph.D. Thesis submitted to B.H.U., Varanasi, India.
KHARE, B. B., (1991). Determination of sample sizes for a class of two phase sampling estimators for ratio and product of two population means using auxiliary character, Metron, 49(1-4), 185–197.
KHARE, B. B., (1993). On a class of two phase sampling estimators for ratio of two population means using multi-auxiliary characters, Proc. Nat. Acad. Sci. India, 63(A) III, 513–519.
KHARE, B. B., SINHA, R. R., (2002). Estimation of the ratio of two population means using auxiliary character with unknown population mean in presence of non-response, Progress of Mathematic, 36, 337–348.
KHARE, B. B., SINHA, R. R., (2004). Estimation of finite population ratio using two phase sampling scheme in the presence of non-response, Aligarh J. Stat, 2004, 24, 43–56.
KHARE, B. B., SINHA, R. R., (2012). Improved classes of estimators for ratio of two means with double sampling the non respondents, Statistika, 49(3), 75–83.
REDDY, V. N., (1978). A study of use of prior knowledge on certain population parameters in estimation, Sankhaya, C, 40, 29–37.
RAO, P. S. R. S., (1986). Ratio estimation with subsampling the nonrespondents, Survey Methodology, 12(2), 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, (1990), 191–208.
SINGH, M. P., (1965). On the estimation of ratio and product of population parameters, Sankhya, Ser.C, 27, 321–328.
SINGH, R. K., (1982). Generalized double sampling estimators for the ratio and product of population parameters, Jour. Ind. Statist. Assoc., 20, 39–49.
SRIVASTAVA, S. R., 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, 21–29.
SRIVASTAVA, S. K., JHAJJ, H. S., (1983). A class of estimators of the population mean using multi-auxiliary information, Cal. Stat. Assoc. Bull., 32, 47–56.
TRIPATHI, T. P., (1970). Contribution to the sampling theory using multivariate information, Ph.D. Thesis submitted to Punjabi University, Patiyala, India.
TRIPATHI, T. P., CHATURVEDI, D. K., (1979). Use of multivariate auxiliary information in estimating the population ratio, Stat-Math. Tech. Report No. 24/79, I.S.I., Calcutta, India, Abs. J. Indian Soc. Agricultural Statist., bf 31.
TRIPATHI, T. P., SINHA, S. K. P., (1976). Estimation of ratio on successive occasions, Proceedings of Symposium on Recent Developments in Survey Methodology, held at I.S.I., Calcutta, March 1976.
