Monika Devi B. V. S. Sisodia


In the present paper, we have considered the problem of estimation of population mean in the presence of non-response under two-stage sampling. Two different models of non-response with deterministic response mechanism have been discussed in the paper. The estimators under two non-response models have been developed by using Hansen and Hurwitz (1946) technique. The expressions for the variances and estimates of variance of these estimators have been derived. The optimum values of sample sizes have been obtained by considering a suitable cost function for a fixed variance. A limited simulation study has been carried out to examine the magnitude of percent relative loss (% RL) in standard error due to non-response. An empirical study with the real populations has also been carried out to assess the % RL in standard error due to non-response.




Population mean, Two-stage sampling, Non-response, Percent relative loss

Al Baghal, T. and Lynn, P. (2015). Using motivational statements in web-instrument design to reduce item-missing rates in a mixed-mode context. Public Opinion Quarterly, 79: 568 -579.
Anderson, Me., Henrikson, N., King, D. and Ulrich, K. (2015). Measuring the effects of operational designs on response rates and nonresponse bias. The American Association for Public Opinion Research, 70th Annual Conference. Retrieved from www.websm.org/db/12/17894/Web_Survey_Bibliography/Measurng_the_Effects_of_Operational_Designs_on_Response_Rates_and_Nonresponse_Bias/menu =1&lst=&q=search_1_111111_-1 & qdb=12 & qsort =1
Anido, C. and Valdes, T. (2000). An Iterative Estimation Procedure for Probit-type Nonresponse Models in Surveys with Call Backs. Sociedad de Estadistica e Invetigacion Operativa, 9(1): 233-253.
Biemer, P., and M. Link (2006). “A Latent Call-Back Model for Nonresponse,” in 17th International Workshop on Household Survey Nonresponse, Omaha, Nebraska, USA.
Burton, J., Jaeckle, A. and Lynn, P. (2015). Going online with a face-to-face household panel: Effects of a mixed mode design on item and unit non-response. Survey Research Methods, 9(1): 57-70.
Chhikara, R. S. and Sud, U. C. (2009). Estimation of population and domain totals under two phase sampling in the presence of non-response. Journal of the Indian Society of Agricultural Statistics, 63(3): 297-304.
Cochran, W.G. (1997). Sampling Techniques, 3rd Edition. John Wiley & Sons, Inc., New York.
Colombo, R. (1992). Using Call-Backs to Adjust for
Non-response Bias. Pages: 269-277. Elsevier, North Holland.
Fahimi, M., F. M. Barlas, R. K. Thomas and N. Buttermore (2015). Scientific Surveys Based on Incomplete
Sampling Frames and High Rates of Nonresponse. Survey Practice, 8(5).
Hansen, M. H. and Hurwitz, W. N. (1946). The problem of nonresponse in sample surveys. Journal of the
American Statistical Association, 41: 517-529.
Khare, B. B. and Srivastava, S. (1993). Estimation of population mean using auxiliary character in presence of non-response. Nat. Acad. Sc. Letters, India, 16(3): 111-114.
Khare, B.B. and Sinha, R.R. (2009). On 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.
Matei, A. and Ranalli, M.G. (2015). Dealing with non-ignorable nonresponse in survey sampling: A latent modeling approach. Survey Methodology, 41(1), 145-164.
Monika, D., Sisodia, B.V.S. and Dube, L.K. (2014). Estimation of finite population mean under non-response using auxiliary information. International Journal of Agricultural and Statistical Sciences. 10(1): 127-131.
Okafor, F. C. and Lee, H. (2000). Double sampling for ratio and regression estimation with sub sampling the non-respondent. Survey Methodology, 26: 183-188.
Okafor, F. C. (2001). Treatment of non-response in successive sampling, Statistica, 61(2):195-204.
Okafor, F. C. (2005). Sub-sampling the non-respondents in two-stage sampling over two successive occasions. Journal of the Indian Statistical Association, 43(1): 33-49.
Rao, P. S. R. S. (1986). Ratio estimation with sub sampling the nonrespondents. Survey Methodology, 12(2): 217–230.
S. Kumar and M. Viswanathaiah (2014). Population mean estimation with sub sampling the non-respondents using two phase sampling. Journal of Modern Applied Statistical Methods, 13(1): 187-198.
Sarndal, C. E., Swensson, B. and Wretman, J. (1992). Model Assisted Survey Sampling, Springer Verlag, New York.
Singh, H. P. and Kumar, S. (2011). Combination of regression and ratio estimate in presence of nonresponse. Braz. J. Probab. Stat., 25(2): 205-217.
Sodipo, A.A. (2010). Difference- type and regression- type estimators for the population mean based on post stratification and subsampling of the non-respondents. European Journal of Scientific Research. 43(4): 445-451.
Sud, U. C., Aditya, Kaustav, Chandra H. and Parsad, Rajender (2012). Two stage sampling for estimation of population mean with sub-sampling of non-respondents, Journal of the Indian Society of Agricultural Statistics, 66(3): 447-457.
Tripathi, T. P. and Khare, B. B. (1997). Estimation of mean vector in presence of nonresponse. Communications in Statistics-Theory and Methods, 26(9): 2255 - 2269.
Research Articles

How to Cite

Estimation of population mean in two– stage sampling under a deterministic response mechanism in the presence of non-response. (2017). Journal of Applied and Natural Science, 9(3), 1666-1675. https://doi.org/10.31018/jans.v9i3.1419