Effective estimation of population mean, ratio and product in two-phase sampling in presence of random non-response

Year 2018, Volume: 47 Issue: 1, 279 - 295, 01.02.2018

G. N. Singh , A. K. Sharma A. Bandyopadhyay , C. Paul

Abstract

This paper presents some eective estimation strategies of population mean, ratio and product of two population means in two-phase (double) sampling when random non-response observed in the sample data. Proposed estimators are dened using a random imputation method which is capable in reducing the negative impact of random non-response in two-phase (double) sampling setup. Properties of proposed estimators have been examined and their performances are compared with sample mean, ratio and product estimators under the similar situations while the complete response was observed in the sample data. Empirical studies are carried out to validate the theoretical results, which are subsequently well interpreted followed by suitable recommendations.

Keywords

Two-phase sampling , random non-response , imputation , auxiliary variable , bias , mean square error

References

• Bandyopadhyay, A. and Singh, G. N. Estimation of ratio of population means in two- occasion successive sampling. Communications in Statistics-Theory and Methods, DOI:10.1080/03610926.2014.917185, ISSN: 0361-0926, 2014. (Article in Press)
• Chand, L. Some ratio-type estimators based on two or more auxiliary variables. Ph. D. dissertation, Iowa State University, Ames, Iowa, 1975.
• Diana, G. and Perri, P. F. Improved estimators of the population mean for missing data. Communications in Statistics-Theory and Methods, 39, 3245-3251, 2010.
• Kiregyera, B. A chain ratio-type estimator in nite population double sampling using two auxiliary variables. Metrika, 27, 217-223, 1980.
• Kiregyera, B. Regression-type estimators using the two auxiliary variables and the model of double sampling from nite population. Metrika, 31(3-4), 215-226, 1984.
• Lee, H., Rancourt, E. and Sarndall, C. E. Experiments with Variance Estimation from Survey Data with Imputed Values. Journal of Ocial Statistics, 10(3), 231-243. 1994.
• Mukherjee, R., Rao, T. J. and Vijayan, K. Regression type estimators using multiple auxil- iary information. Australian & New Zealand Journal of Statistics, 29, 244-254, 1987.
• Pradhan, B. K. A chain regression estimator in two-phase sampling using multi-auxiliary information. Bulletin of the malaysian mathematical sciences society, 28(1), 81-86, 2005.
• Rubin, D. B. Inference and Missing Data. Biometrika, 63(3), 581-592, 1976.
• Sande, I. G. A personal view of hot-deck imputation procedures. Survey Methodology, 5, 238-247, 1979.
• SanaullahA, Ali, H.A., Noor ul Amin, M., and Hanif, M. Generalized Exponential Chain Ratio Estimators Under Stratied Two-Phase Random Sampling. Applied Mathematics and Computation, 226 (2014) 541547, 2014.
• Senapati, S. C. and Sahoo, L. N. An alternative class of estimators in double sampling. Bulletin Malaysian Mathematical Sciences Society, (2) 29(1), 89-94, 2006.
• Singh, G. N. On the use of transformed auxiliary variable in the estimation of population mean in two-phase sampling. Statistics in Transition, 5(3), 405-416, 2001.
• Singh, S. A new method of imputation in survey sampling. Statistics, 43(5), 499-511, 2009.
• Singh, G. N and Upadhyaya, L. N. A class of modied chain type estimators using two auxiliary variables in two-phase sampling. Metron, LIII, 117-125, 1995.
• Sing, G. N and Sharma, A. K. An improved estimation procedure of population mean in two phase sampling, Journal of International Academy of Physical Sciences, 18(1), 1-10, 2014.
• Singh, G. N and Sharma, A. K. Some improved estimators for population mean in double sampling. International Journal of Mathematics & ComputationTM, 26(3), 36-45, 2015.
• Singh, H. P., Chandra, P., Joarder, A. H. and Singh, S. Family of estimators of mean, ratio and product of a nite population using random non-response. TEST, 16(3), 565-597, 2007.
• Singh, H. P. and Kumar, S. A general family of estimators of nite population ratio, product and mean using two phase sampling scheme in the presence of non-response. Journal of Statistical Theory and Practise, 2(4), 677-692, 2008.
• Singh, S. and Deo, B. Imputation by power transformation. Statistical Papers, 4, 555-579, 2003.
• Singh, S., Joarder, A. H. and Tracy, D. S. Median estimation using double sampling. Aus- tralian & New Zealand Journal of Statistics, 43(1), 33-46, 2001.
• Singh, S. and Joarder, A. H. Estimation of nite population variance using random non- response in survey sampling. Metrika, 47, 241-249, 1998.
• Singh, V.K. and Singh, G.N. Chain type regression estimators with two auxiliary variables under double sampling scheme. Metron, XLIX, No. 1-4, 279-289, 1991.
• Singh, V. K., Singh, H. P. and Singh, H. P. A general class of chain estimators for ratio and product of two means of a nite population. Communications in Statistics-Theory and Methods, 23, 1341-1355, 1994.
• Singh, H. P. and Vishwakarma, G. K. Modied exponential ratio and product estimators for nite population mean in double Sampling. Austrian Journal of Statistics, 36, 3, 217-225, 2007.
• Srivastava, S. R., Srivastava, S. P. and Khare, B. B. Chain ratio type estimators for ratio of two population means using auxiliary characters. Communications in Statistics-Theory and Methods, 18, 3917-3926, 1989.
• Upadhyaya, L. N. and Singh, G. N. Chain type estimators using transformed auxiliary variable in two-phase sampling. Advances in Modeling and analysis, 38, (1-2), (1-10), 2001.
• Ministry of Statistics & Programme Implementation, Chapter-2(2.1), 2013. http://mospi.nic.in/Mospi_New/upload/SYB2013/ch2.html