Estimation of mean under imputation of missing data using factor-type estimator in two-phase sampling

Diwakar Shukla; Narendra Singh Thakur; Sharad Pathak; Dilip Singh Rajput

doi:https://doi.org/10.59170/stattrans-2009-030

Estimation of mean under imputation of missing data using factor-type estimator in two-phase sampling

Diwakar Shukla Deptt. of Mathematics and Statistics, H.S. Gour University of Sagar, Sagar,(M.P.) INDIA, Pin-470003 , Narendra Singh Thakur Deptt. of Mathematics and Statistics, H.S. Gour University of Sagar, Sagar,(M.P.) INDIA, Pin-470003 , Sharad Pathak Deptt. of Mathematics and Statistics, H.S. Gour University of Sagar, Sagar,(M.P.) INDIA, Pin-470003. , Dilip Singh Rajput Dilip Singh Rajput, Govt. College, Rehli, Sagar (M.P.), INDIA Statistics in Transition new series, vol. 10, 2009, 3, pages: 397-414 Published online: 1 December 2009 https://doi.org/10.59170/stattrans-2009-030

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ABSTRACT

In sample surveys, the problem of non-response is one of the most frequent and widely appearing, whose solution is required to obtain using relevant statistical techniques. The imputation is one such methodology, which uses available data as a source for replacement of missing observations. Two-phase sampling is useful when population parameter of auxiliary information is unknown. This paper presents the use of imputation for dealing with non-responding units in the setup of two-phase sampling. Two different two-phase sampling strategies (subsample and independent sample) are compared under imputed data setup. Factor- Type (F-T) estimators are used as tools of imputation and simulation study is performed over multiple samples showing the comparative strength of one over other. First imputation strategy is found better than second whereas second sampling design is better than first.

KEYWORDS

Estimation, Missing data, Imputation, Bias, Mean squared error (MSE), Factor Type (F-T) estimator, Two-phase sampling, Simple Random Sampling Without Replacement (SRSWOR), Compromised Imputation (C. I.).

REFERENCES

AHMED, M. S., AL-TITI, O., AL-RAWI, Z. and ABU-DAYYEH, W. (2006): Estimation of a population mean using different imputation methods, Statistics in Transition, 7, 6, 1247–1264.

COCHRAN, W. G. (2005): Sampling Techniques, John Wiley and Sons, Fifth Edition New York.

HEITJAN, D. F. and BASU, S. (1996): Distinguishing ‘Missing at random’ and ‘missing completely at random’, The American Statistician, 50, 207–213.

RAO, J. N. K. and SITTER, R. R. (1995): Variance estimation under two-phase sampling with application to imputation for missing data, Biometrica, 82, 453–460.

RUBIN, D. B. (1976): Inference and missing data, Biometrica, 63, 581–593.

SHUKLA, D. (2002): F-T estimator under two-phase sampling, Metron, 59, 1–2, 253–263.

SHUKLA, D., SINGH, V. K. and SINGH, G. N. (1991): On the use of transformation in factor type estimator, Metron, 49 (1–4), 359–361.

SINGH, S. and HORN, S. (2000): Compromised imputation in survey sampling, Metrika, 51, 266–276.

SINGH, V. K. and SHUKLA, D. (1987): One parameter family of factor type ratio estimator, Metron, 45, 1–2, 273–283.

SINGH, V. K. and SHUKLA, D. (1993): An efficient one parameter family of factor - type estimator in sample survey, Metron, 51, 1–2, 139–159.

SINGH, V. K. and SINGH, G. N. (1991): Chain type estimator with two auxiliary variables under double sampling scheme, Metron, 49, 279–289.

REDDY, V. N. (1978): A study on the use of prior knowledge on certain population parameters in estimation, Sankhya, C, 40, 29–37.