On classes of modified ratio type and regression-cum-ratio type estimators in sample surveys using two auxiliary variables

A. K. P. C. Swain

doi:https://doi.org/10.59170/stattrans-2012-035

On classes of modified ratio type and regression-cum-ratio type estimators in sample surveys using two auxiliary variables

A. K. P. C. Swain Former Professor of Statistics Utkal University, Bhubaneswar-751004, India Statistics in Transition new series, vol. 13, 2012, 3, pages: 473-494 Published online: 3 September 2012 https://doi.org/10.59170/stattrans-2012-035

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ABSTRACT

In this paper generalized classes of modified ratio type and regression-cum-ratio type estimators of the finite population mean of the study variable are suggested in the presence of two auxiliary variables in simple random sampling without replacement when the population means of the auxiliary variables are known in advance. Some special cases of the generalized estimators are compared with respect to their biases and efficiencies both theoretically and with the help of some natural populations

KEYWORDS

ratio type estimators, regression-cum-ratio type estimators, simple random sampling, auxiliary variables, bias, efficiency.

REFERENCES

BOWLEY, A. L. (1926). Measurements of precision attained in sampling. Bull. Inst. Internat. Statist, 22, 1-62.

COCHRAN, W. G. (1940). The estimation of the yields of the cereal experiments by sampling for the ratio of grain to total produce. J. Agricultural Sc., 30, 262-275.

COCHRAN, W. G. (1942). Sampling theory when the sampling units are unequal sizes. J. Amer. Stat. Assoc., 37, 199-212.

COCHRAN, W. G. (1977). Sampling Techniques. John Wiley and Sons, New York.

HANSEN, M. H. and HURWITZ, W. N. (1943). On the theory of sampling from finite populations. Ann. Math. Stat., 14, 333-362.

HANSEN, M. H., HURWITZ, W. N. and MADOW, W. G. (1953). Sample survey methods and theory, Vol. 2, John Wiley and Sons, New York.

HANIF, M., HAMMD, N. and SHAHBAZ, M. Q. (2010). Some new regression type estimators in two phase sampling. World Applied Sc. Journal, 8(7), 799-803.

JOHN, S. (1969). On multivariate ratio and product estimators, Biometrika, 56, 533-536.

KHARE, B. B. and SRIVASTAVA, S. R. (1980). On an efficient estimator of population mean using two auxiliary variables, Proc. National Acad. Sc. India, 50(A), 209-214.

KHARE, B. B. and SRIVASTAVA, S. R. (1981). A generalized regression ratio estimator for the population mean using two auxiliary variables. Aligarh J. Statist, 1, 43-51.

MOHANTY, S. (1967). Combination of regression and ratio estimate. J. Ind. Statist., 5, 16-19.

MURTHY, M. N. (1964). Product method of estimation. Sankhya, Series A, 26, 294-307.

NEYMAN, J. (1934). On the two different aspects of representative method : The method of stratified. Sampling and the method of purposive selection. J. Roy. Statist. Soc., 97, 558-606.

NEYMAN. J. (1938). Contributions to the theory of sampling human populations. J. Amer. Statist. Assoc., 33, 101-116.

OLKIN, I. (1958). Multivariate ratio estimation for finite populations, Biometrika, 45, 154-165.

PERRI, P. F. (2007). Improved ratio-cum-product type estimators. Statistics in Transition (New Series), 8, 1, 51-69.

RAJ, DES (1965). On a method of using multi-auxiliary information in sample surveys. J. Amer Stat. Assoc., 60, 270-277.

RAO, P. S. R. S. and MUDHOLKAR, G. S. (1967). Generalized multivariate estimator for the mean of finite populations. J. Amer. Stat. Assoc., 62, 1009-12.

ROBSON, D. S. (1957). Applications of multivariate polykays to the theory of unbiased ratio type estimators. J. Amer. Stat. Assoc., 52, 511-522.

SAHOO, L. N. (1984). A note on estimation of the population mean using two auxiliary variables. Aligarh. J. Statist., 3 and 4, 63-66.

SHUKLA, G. K. (1965). Multivariate regression estimate. J. Ind. Stat. Assoc., 3, 202-211.

SHUKLA, G. K. (1966). An alternative multivariate ratio estimate for finite population. Bull Cal. Stat. Assoc., 15, 127-134.

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

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

SINGH, M. P. (1967). Multivariate product method of estimation for finite population, J. Ind. Soc. Agri. Statist., 19, 1-10.

SRIVASTAVA, S. K. (1965). An estimate of the mean of a finite population using several auxiliary character, J. Ind. Stat. Assoc., 3, 189-194.

SRIVASTAVA, S. K. (1967). An estimator using auxiliary information in sample surveys. Cal. Stat. Assoc., Bull., 16, 121-132.

SRIVASTAVA, S. K. (1971). Generalized estimator for the mean of a finite population using multi-auxiliary information. J. Amer. Stat. Assoc., 66, 404-407.

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

SWAIN, A. K. P. C. (1973). Some contributions to the theory of sampling, Ph.D. Thesis submitted to the Utkal University, India.

TRIPATHI, T. P. (1970). Contributions to the sampling theory using multivariate information. Ph.D. Thesis submitted to Punjabi University, Patiala, India.

TRIPATHI, T. P. (1980). A general class of estimators of population ratio. Sankhya Series C, 42, 63-75.

TRIPATHI, T. P. (1987). A class of estimators for population means using multivariate auxiliary information under any sampling design. Aligarh. J. Statist., 7, 49-62.

WATSON, D. J. (1937). The estimation of leaf areas. J. Agricultural Sc. 27, 474.