An Efficient Estimation Procedure for the Population Mean under Non-Response


  • Shashi Bhushan Dr. Shakuntal Misra National Rehabilitation University
  • Abhay Pratap Pandey Ramanujan College University of Delhi



Auxiliary information, Non-response, Mean square error


This paper introduces an efficient estimation procedure for the population mean in the presence of non-response. The proposed estimators of population mean provides an improvement over the corresponding conventional estimators proposed by Cochran (1977), Rao (1983, 1986) and Singh and Kumar (2008, 2010) under the deterministic non-response in terms of efficiency. A comparative study has been performed and it has been shown that the proposed estimators perform better in comparison to the conventional estimators. The theoretical findings are supported by an empirical study.


S. BAHL, R. K. TUTEJA (1991). Ratio and product type exponential estimators. Information and Optimization Sciences, 12, no. 1, pp. 159–163.

S. BHUSHAN, R. GUPTA (2015). Some log type classes of estimators using auxiliary. International Journal of Agricultural and Statistical Sciences, 2, no. 2, pp. 487–491.

W. G. COCHRAN (1977). Sampling Techniques. JohnWiley & Sons, New York, 3rd ed.

G. DIANA, P. F. PERRI (2013). A class of estimators in two-phase sampling with subsampling the non-respondents. Applied Mathematics and Computation, 219, pp. 10033–10043.

G. DIANA, C. TOMASI (2003). Optimal estimation for finite population mean in two phase sampling. Statistical Methods and Applications, 12, pp. 41–48.

M. H.HANSEN,W.N.HURWITZ (1946). The problem of non-response in sample surveys. Journal of American Statistical Association, 41, pp. 517–529.

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

B. B. KHARE, S. SRIVASTAVA (1993). Estimation of population mean using auxiliary character in presence of non-response. National Academy Science Letters - India, 16, pp. 111–114.

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

B. B. KHARE, S. SRIVASTAVA (1997). Transformed ratio type estimators for the population mean in the presence of non-response. Communication in Statistics - Theory and Methods, 26, pp. 1779–1791.

S. L. LOHR (1999). Sampling-Design & Analysis. Duxbury Press, New York.

F. C. OKAFOR, H. LEE (2000). Double sampling for ratio and regression estimation with sub sampling the non respondents. Survey Methodology, 26, no. 2, pp. 183–188.

P. S. R. S. RAO (1983). Randomization approach. In W. G. MADOW, I. OLKIN, D. B. RUBIN (eds.), Incomplete Data in Sample Surveys, Academic Press, New York, vol. 2, pp. 33–44.

P. S. R. S. RAO (1986). Ratio estimation with sub sampling the non-respondents. Survey Methodology, 12, pp. 217–230.

S. K. RAY, R. K. SINGH (1981). Difference-cum-ration type estimators. Journal of the Indian Statistical Association, 19, pp. 147–151.

D. T. SEARLS (1964). The utilization of a known coefficient of variation in the estimation procedure. Journal of the American Statistical Association, 59, pp. 1225–1226.

G. K. SHUKLA (1966). An alternative multivariate ratio estimate for finite population. Calcutta Statistical Association Bulletin, 15, pp. 127–134.

H. P. SINGH, S. KUMAR (2008). A regression approach to the estimation of the finite population mean in the presence of non-response. Australian & New Zealand Journal of Statistics, 50, no. 4, pp. 395–408.

H. P. SINGH, S. KUMAR (2010). Estimation of mean in presence of non-response using two phase sampling scheme. Statistical Papers, 51, pp. 559–582.

H. P. SINGH, S. KUMAR, M. KOZAK (2010). Improved estimation of finite population mean using sub sampling to deal with non-response in two phase sampling scheme. Communication in Statistics, Theory and Methods, 39, no. 5, pp. 791–802.

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

M. P. SINGH (1967). Ratio cum product method of estimation. Metrika, 112, no. 1, pp. 34–43.

R. K. SINGH, S. BHUSHAN (2012). Generalized classes of two phase sampling estimators of population mean in presence of non-response. In Proceeding of VII ISOS Aligarh Muslim University. Aligarh Muslim University, Aligarh.

V. K. SINGH, H. P. SINGH, H. P. SINGH, D. SHUKLA (1994). A general class of chain estimator for ratio and product of two means of a finite population. Communication in Statistics - Theory and Methods, 23, no. 5, pp. 1341–1365.

S. SRIVASTAVA (1993). Some problems on the estimation of population mean using auxiliary character in presence of non-response in sample survey. Ph.D. thesis, Banaras Hindu University, Varanasi, India.

S. K. SRIVASTAVA, H. S. JHAJJ (1981). A class of estimators of the population mean in survey sampling using auxiliary information. Biometrika, 68, pp. 341–343.




How to Cite

Bhushan, S., & Pandey, A. P. (2019). An Efficient Estimation Procedure for the Population Mean under Non-Response. Statistica, 79(4), 363–378.