**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30184

##### Adjusted Ratio and Regression Type Estimators for Estimation of Population Mean when some Observations are missing

**Authors:**
Nuanpan Nangsue

**Abstract:**

Ratio and regression type estimators have been used by previous authors to estimate a population mean for the principal variable from samples in which both auxiliary x and principal y variable data are available. However, missing data are a common problem in statistical analyses with real data. Ratio and regression type estimators have also been used for imputing values of missing y data. In this paper, six new ratio and regression type estimators are proposed for imputing values for any missing y data and estimating a population mean for y from samples with missing x and/or y data. A simulation study has been conducted to compare the six ratio and regression type estimators with a previous estimator of Rueda. Two population sizes N = 1,000 and 5,000 have been considered with sample sizes of 10% and 30% and with correlation coefficients between population variables X and Y of 0.5 and 0.8. In the simulations, 10 and 40 percent of sample y values and 10 and 40 percent of sample x values were randomly designated as missing. The new ratio and regression type estimators give similar mean absolute percentage errors that are smaller than the Rueda estimator for all cases. The new estimators give a large reduction in errors for the case of 40% missing y values and sampling fraction of 30%.

**Keywords:**
Auxiliary variable,
missing data,
ratio and regression
type estimators.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1082821

**References:**

[1] G. Kalton, and D. Kasprzyk, "Imputing for missing survey responses", in Proceedings Section of Survey Research Method. American Statistical Association, 1982, pp. 22-33.

[2] JM. Brick, and G. Kalton, "Handling missing data in survey research, "Statistical Methods in Medical Research, Vol. 5, No. 3, pp. 215- 238, 1996.

[3] D.B. Rubin, Multiple imputation for nonresponse in survey, New York: John Wiley and Sons, 1987.

[4] M. Rueda, S. Gonzalez, A. Arcos, Y. Roman,M.D. Martinez, and J.F. Munoz, "Estimation of the population mean using auxiliary information when some observations are missing," International symposium on applied stochastic models and data analysis, May 17-20, Brest France, 2005.

[5] Abu-Dayyeh, A. Walid, M.S. Ahmed, R.A. Ahmed, and Hassen A. Muttlak, "Some estimators of a finite population mean using auxiliary information," Applied Mathematics and Computation, vol. 139, pp. 287- 298, 2003.

[6] C. Kadilar, and H. Cingi, "A new estimator using two auxiliary variables," Applied Mathematics and Computation, vol. 162, pp. 901- 908, 2005.

[7] C. Kadilar, and H. Cingi, "Improvement in estimating the population mean in simple random sampling," Applied Mathematics Letters, vol. 19, pp. 75-79, 2006.

[8] C. Kadilar, M. Candan, and H. Cingi, "Ratio estimators using robust regression," Journal of Mathematics and Statistics, vol. 36, pp. 181 - 188, 2007.

[9] N. Nangsue, and J. Sappakitkamjorn, "Variance estimation of the ratio estimator of the population mean in simple random sampling," in Proceedings of Third Workshop on Statistics, Mathematics and Computation and First Portuguese-Polish Workshop on Biometry, Lisbon, Portugal, 21 - 22 July, 2008, p. 59.

[10] W.G. Cochran, Sampling Technique, 3rd Ed. New York: John Wiley and Sons, 1977.

[11] D.S. Tracy, and S.S. Osahan, "Random nonresponse on study variable versus on study as well as auxiliary variables," Statistica, vol. 54, pp.163 - 168, 1994.

[12] S. Singh, Advanced sampling theory with applications, vol. II. The Netherlands: Kluwer Academic Press Publishers, 2003.