**
S. K. Yadav **
Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India.

**
O. P. Yadav **
Department of Industrial and Manufacturing Engineering, North Dakota State University, Fargo, ND 58104, USA.

**
D. K. Yadav **
Department of Commercial Tax, Government of Uttar Pradesh, Lucknow-226010, India.

DOI https://dx.doi.org/10.33889/IJMEMS.2019.4.6-103

**Abstract**

In this scripture, we ponder the problem of efficient estimation of population mean of study variable utilizing information on highly correlated auxiliary variables under the presence of non-response on either of the variables. For this purpose, we suggest, an improved estimator under three different situations of non-response. Under the first situation, estimation of population mean is done with the problem of non-response on both the study and the auxiliary variables with the additional condition that the population means of the auxiliary variables are known. The second situation is to estimate the population mean of primary variable when the problem of non-response is only on the primary variable but the population means of the auxiliary variables are known while under the third situation estimation is performed with the problem of non-response on both the study and the auxiliary variables but population mean of one of the auxiliary variables is unknown. We study the sampling properties of the suggested estimator under above three different situations of non-response. We compare the proposed estimator with the competing estimators of population mean, under three different situations of non-response. The efficiency conditions are obtained for all three situations. A numerical study is also carried out to verify the efficiency conditions.

**Keywords-** Study variable, Auxiliary variable, Non-response, Bias, MSE, PRE.

**Citation**

Yadav, S. K., Yadav, O. P., & Yadav, D. K. (2019). Dexterous Estimation of Population Mean in Survey Sampling Under Non-Response Error. *International Journal of Mathematical, Engineering and Management Sciences*, *4*(6), 1307-1324. https://dx.doi.org/10.33889/IJMEMS.2019.4.6-103.

**Conflict of Interest**

The authors have no conflict of interest regarding the publication of the article.

**Acknowledgements**

The authors sincerely thank anonymous reviewers and the Editor-in-Chief for providing critical comments and suggestions for improving the quality of the paper.

**References**

Agrawal, M.C., & Sthapit, A.B. (1997). Hierarchic predictive ratio-based and product-based estimators and their efficiency. Journal of Applied Statistics, 24(1), 97-104.

Bahl, S., & Tuteja, R. (1991). Ratio and product type exponential estimators. Journal of Information and Optimization Sciences, 12(1), 159-164.

Bii, N.K., Onyango, C.O., & Odhiambo, J. (2018, November). Estimating a finite population mean under random non response in two stage cluster sampling with replacement. In Journal of Physics: Conference Series, 1132(1), p. 012071. IOP Publishing.

Cochran, W.G. (1977). Sampling techniques. New-York, John Wiley and Sons.

El-Badry, M.A. (1956). A sampling procedure for mailed questionnaires. Journal of the American Statistical Association, 51(274), 209-227.

Grover, L.K., & Kaur, P. (2014). A generalized class of ratio type exponential estimators of population mean under linear transformation of auxiliary variable. Communications in Statistics-Simulation and Computation, 43(7), 1552-1574.

Hansen, M.H., & Hurwitz, W.N. (1946). The problem of non-response in sample surveys. Journal of the American Statistical Association, 41(236), 517-529.

Khare, B.B., & Sinha, R.R. (2007). Estimation of the ratio of the two population means using multi auxiliary characteristics in the presence of non-response. In Statistical Techniques in Life Testing, Reliability, Sampling Theory and Quality Control. 1, 63–171.

Khare, B.B., & Sinha, R.R. (2009). On the class of estimators for population mean using multi auxiliary characters in the presence of non-response. Statistics in Transition-New Series, 10(1), 3–14.

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

Khare, B.B., & Srivastava, S. (1995). Study of conventional and alternative two phase sampling ratio, product and regression estimators in presence of nonresponse. Proceedings-National Academy Of Sciences India Section A, 65, 195-204.

Khare, B.B., & Srivastava, S. (1997). Transformed ratio type estimators for the population mean in the presence of nonresponse. Communications in Statistics-Theory and Methods, 26(7), 1779-1791.

Kumar S. (2016). Improved estimation of population mean in presence of nonresponse and measurement error. Journal of Statistical Theory and Practice, 10 (4), 707–720.

Kumar, S., & Bhougal, S. (2011). Estimation of the population mean in presence of non-response. Communications for Statistical Applications and Methods, 18(4), 537-548.

Kumar, S., Bhougal, S., Nataraja, N.S., & Viswanathaiah, M. (2015). Estimation of population mean in the presence of non-response and measurement error. Revista Colombiana de EstadÝstica, 38(1), 145-161.

Muneer, S., Shabbir, J., & Khalil, A. (2018). A generalized exponential type estimator of population mean in the presence of non-response. Statistics in Transition-New Series, 19(2), 259–276.

Rao, P.S.R.S. (1986). Ratio estimation with sub sampling the non-respondents. Survey Methodology, 12(2), 217–230.

Searls, D.T. (1964). The utilization of a known coefficient of variation in the estimation procedure. Journal of the American Statistical Association, 59(308), 1225-1226.

Shabbir, J., & Khan, N.S. (2013). On estimating the finite population mean using two auxiliary variables in two phase sampling in the presence of non response. Communications in Statistics-Theory and Methods, 42(22), 4127-4145.

Sharma, P., & Pal, S.K. (2018). Estimation of population mean in presence of random non-response. Journal of Statistics and Management Systems, 21(6), 1105-1119.

Singh, H.P., & Kumar, S. (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(4), 395-408.

Singh, H.P., & Solanki, R.S. (2011). Estimation of finite population mean using random non-response in survey sampling. Pakistan Journal of Statistics and Operations Research, 7(1), 21-41.

Singh, H.P., Kumar, S., & Kozak, M., (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 Method, 39(5), 791–802.

Singh, P., Singh, R., & Bouza, C.N. (2018). Effect of measurement error and non-response on estimation of population mean. Revista Investigacion Operacional, 39(1), 108-120.

Srinath, K.P. (1971). Multiphase sampling in non-response problems. Journal of American Statistical Association, 66(335), 583–586.

Srivastava, A.K., & Shalabh (2001). Effect of measurement errors on the regression method of estimation in survey sampling. Journal of Statistical Research, 35(2), 35-44.

Steel, R.G.D., & Torrie, J.H. (1960). Principles and procedures of statistics. McGraw-Hill Book Company, Inc., New York, Toronto, London.

Sud, U.C., & Srivastava, S.K. (2000). Estimation of population mean in repeat surveys in the presence of measurement errors. Journal of Indian Society of Agricultural Statistics, 53(2), 125-133.

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

Tailor, R., Chouhan, S., & Kim, J.M. (2014). Ratio and product type exponential estimators of population mean in double sampling for stratification. Communications for Statistical Applications and Methods, 21(1), 1-9.

Toutenburg, H., & Srivastava, V.K. (1998). Estimation of ratio of population means in survey sampling when some observations are missing. Metrika, 48(3), 177-187.

Toutenburg, H., & Srivastava, V.K. (2003). Efficient estimation of population mean using incomplete survey data on study and auxiliary characteristics. Statistica, 63(2), 223-236.

Tracy, D.S., & Osahan, S.S. (1994). Random non-response on study variable versus on study as well as auxiliary variables. Statistica, 54(2), 163-168.

Yadav, D.K., Devi, M., & Yadav, S.K. (2018). Estimation of finite population mean using known coefficient of variation in the simultaneous presence of non-response and measurement errors under double sampling scheme. Journal of Reliability and Statistical Studies, 11(1), 51-66.