A Regression Type Estimator with Two Auxiliary Variables for Two-Phase Sampling

Naqvi Hamad, Muhammad Hanif, Najeeb Haider

Department of Statistics, Government Postgraduate College, Dera Ghazi Khan, Pakistan.
National College of Business Administration and Economics, Lahore, Pakistan.

DOI: 10.4236/ojs.2013.32010                

Abstract

This paper is an extension of Hanif, Hamad and Shahbaz estimator [1] for two-phase sampling. The aim of this paper is to develop a regression type estimator with two auxiliary variables for two-phase sampling when we don’t have any type of information about auxiliary variables at population level. To avoid multi-collinearity, it is assumed that both auxiliary variables have minimum correlation. Mean square error and bias of proposed estimator in two-phase sampling is derived. Mean square error of proposed estimator shows an improvement over other well known estimators under the same case.

Keywords

Mean Square Error; Precision; Two-Phase Sampling; Auxiliary Variable; Regression Type Estimator; Simple Random Sampling without Replacement

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	M. Hanif, N. Hamad and M. Q. Shahbaz, “A Modified Regression Type Estimator in Survey Sampling,” World Applied Sciences Journal, Vol. 7, No. 12, 2009, pp. 1559-1561.
[2]	J. Neyman, “Contribution to the Theory of Sampling Human Populations,” Journal of the American Statistical Association, Vol. 33, No. 201, 1938, pp. 101-116. doi:10.1080/01621459.1938.10503378
[3]	B. V. Sukhatme, “Some Ratio Type Estimators in Two Phase Sampling,” Journal of the American Statistical Association, Vol. 57, No. 299, 1962, pp. 628-632. doi:10.1080/01621459.1962.10500551
[4]	W. G. Cochran Cochran, “The Estimation of the Yields of the Cereal Experiments by Sampling for the Ratio of Grain to Total Produce,” Journal of Agricultural Science, Vol. 30, No. 2, 1940, pp. 262-275. doi:10.1017/S0021859600048012
[5]	M. H. Hansen and W. N. Hurwitz, “On the Theory of Sampling from Finite Populations,” The Annals of Mathematical Statistics, Vol. 14, No. 4, 1943, pp. 333-362. doi:10.1214/aoms/1177731356
[6]	D. S. Robson, “Application of Multivariate Polykays to the Theory of Unbiased Ratio Type Estimators,” Journal of the American Statistical Association, Vol. 52, No. 280, 1957, pp. 511-522. doi:10.1080/01621459.1957.10501407
[7]	D. Raj, “On a Method of Using Multi-Auxiliary Information in Sample Surveys,” Journal of the American Statis tical Association, Vol. 60, No. 309, 1965, pp. 270-277. doi:10.1080/01621459.1965.10480789
[8]	S. Mohanty, “Combination of Regression and Ratio Estimate,” Journal of Indian Statistical Association, Vol. 5, 1967, pp. 16-19.
[9]	S. K. Srivastava, “A Generalized Estimator for the Mean of a Finite Population Using Multi Auxiliary Information,” Journal of the American Statistical Association, Vol. 66, No. 334, 1971, pp. 404-407. doi:10.1080/01621459.1971.10482277
[10]	R. Mukerjee, T. J. Rao and K. Vijayan, “Regression Type Estimators Using Multiple Auxiliary Information,” Australian Journal of Statistics, Vol. 29, No. 3, 1987, pp. 244-254. doi:10.1111/j.1467-842X.1987.tb00742.x
[11]	M. Samiuddin and M. Hanif, “Estimation of Population Mean in Single Phase and Two-Phase Sampling with or without Additional Information,” Pakistan Journal of Statistics, Vol. 23, No. 2, 2007, pp. 99-118.
[12]	P. V. Sukhatme, B. V. Sukhatme, S. Sukhatme and C. Asok, “Sampling Theory of Surveys with Applications,” Iowa State University Press, Ames, 1984.
[13]	H. P. Singh and M. R. Espejo, “Double Sampling Ratio Product Estimator of a Finite Population Mean in Sample Surveys,” Journal of Applied Statistics, Vol. 34, No. 1, 2007, pp. 71-85. doi:10.1080/02664760600994562
[14]	M. Hanif, N. Hamad and M. Q. Shahbaz, “Some New Regression Type Estimators in Two-Phase Sampling,” World Applied Sciences Journal, Vol. 8, No. 7, 2010, pp. 799-803.