A General Class of Estimators of the Population Mean in Survey Sampling Using Auxiliary Information with Sub Sampling the Non-Respondents

- Journal title : Korean Journal of Applied Statistics
- Volume 22, Issue 2, 2009, pp.387-402
- Publisher : The Korean Statistical Society
- DOI : 10.5351/KJAS.2009.22.2.387

Title & Authors

A General Class of Estimators of the Population Mean in Survey Sampling Using Auxiliary Information with Sub Sampling the Non-Respondents

Singh, Housila P.; Kumar, Sunil;

Singh, Housila P.; Kumar, Sunil;

Abstract

In this paper we have considered the problem of estimating the population mean of the study variable y using auxiliary information in presence of non-response. Classes of estimators for in the presence of non-response on the study variable y only and complete response on the auxiliary variable x is available, have been proposed in different situations viz., (i) population mean is known, (ii) when population mean and variance are known; (iii) when population mean is not known: and (iv) when both population mean and variance are not known: single and two-phase (or double) sampling. It has been shown that various estimators including usual unbiased estimator and the estimators reported by Rao (1986), Khare and Srivastava (1993, 1995) and Tabasum and Khan (2006) are members of the proposed classes of estimators. The optimum values of the first phase sample size n', second phase sample size n and the sub sampling fraction 1/k have been obtained for the fixed cost and the fixed precision. To illustrate foregoing, we have carried out an empirical investigation to reflect the relative performance of all the potentially competing estimators including the one due to Hansen and Hurwitz (1946) estimator, Rao (1986) estimator, Khare and Srivastava (1993, 1995) and Tabasum and Khan (2006) estimator.

Keywords

Asymptotic variance;study variable;auxiliary variable;non-response;double sampling;

Language

English

Cited by

1.

Ratio Cum Regression Estimator for Estimating a Population Mean with a Sub Sampling of Non Respondents,Kumar, Sunil;

2.

Estimation of the Population Mean in Presence of Non-Response,Kumar, Sunil;Bhougal, Sandeep;

3.

Estimation of Mean Using Multi Auxiliary Information in Presence of Non Response,Kumar, Sunil;Singh, Housila P.;

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References

1.

Cochran, W. G. (1977). Sampling Techniques, 3rd ed., John Wiley & Sons, New York

2.

Hansen, M. H. and Hurwitz, W. N. (1946). The problem of non-response in sample surveys, Journal of the American Statistical Association, 41, 517-529

3.

Khare, B. B. and Srivastava, S. (1993). Estimation of population mean using auxiliary character in presence of non-response, National Academic Science and Letters, 16, 111-114

4.

Khare, B. B. and Srivastava, S. (1995). Study of conventional and alternative two-phase sampling ratio, product and regression estimators in presence of non-response, In Proceedings of the Indian National Science Academy, 65(A), 195-203

5.

Rao, P. S. R. S. (1986). Ratio estimation with sub sampling the non-espondents, Survey Methodology, 12, 217-230

6.

Srivastava, S. K. (1967). An estimator using auxiliary information in sample surveys, Bulletin of the Calcutta Statistical Association, 16, 121-132

7.

Srivastava, S. K. (1971). A generalized estimator for the mean of a finite population using multi auxiliary information, Journal of the American Statistical Association, 66, 404-407

8.

Srivastava, S. K. and Jhajj, H. S. (1981). A class of estimators of the population mean in survey sampling using auxiliary information, Biometrika, 68, 341-343

9.

Srivastava, S. K. and Jhajj, H. S. (1987). Improved estimation in two-phase and successive sampling, Journal of Indian Society of Agricultural Statistics, 25, 71-75

10.

Tabasum, R. and Khan, I. A. (2006). Double sampling ratio estimator for the population mean in presence of non-response, Assam Statistical Review, 20, 73-83