In this paper, two modified, design-based calibration ratio-type estimators are presented. The suggested estimators were developed under stratified random sampling using information on an auxiliary variable in the form of robust statistical measures, including Gini’s mean difference, Downton’s method and probability weighted moments. The properties (biases and MSEs) of the proposed estimators are studied up to the terms of firstorder approximation by means of Taylor’s Series approximation. The theoretical results were supported by a simulation study conducted on four bivariate populations and generated using normal, chi-square, exponential and gamma populations. The results of the study indicate that the proposed calibration scheme is more precise than any of the others considered in this paper.

calibration, outliers, percentage relative efficiency (PRE), stratified sampling

ADITYA, K., SUD, U., CHANDRA, H., BISWAS, A., (2016). Calibration based regression type estimator of the population total under two stage sampling design. Journal of the Indian Society of Agricultural Statistics, 70, pp.19–24.

BARKTUS, I., PUMPUTIS, D., (2010). Estimation of finite population ratio using calibration of strata weights. In Workshop on survey sampling theory and methodology: August 23–27, 2010, Vilnius, Lithuania, Vilnius.

BREWER, K. R. W., (1995). Combining design based model based inference. Chapter 30 in Business Survey Methods (Eds. B.G. Cox, D.A. Binder, B.N. Chinnapa, A. Christianson, MJ. Colledge and P.S. Kolt). New York:Wiley, 589–606.

BREWER, K. R. W., (1999). Cosmetic calibration with unequal probability sampling. Survey Methodology, 25(2), pp. 205–212.

CLEMENT, E. P., ENANG, E. I., (2016). On the efficiency of ratio estimator over the regression estimator. Communications in Statistics - Theory and Methods, 46(11), pp. 5357–5367.

DEVILLE, J. C., SARNDAL, C. E., (1992). Calibration estimators in survey sampling. Journal of American statistical Association, 87(418), pp. 376–382.

ESTEVAO, V. M., SARNDAL, C. E., (2000). A functional form approach to calibration. Journal of Official Statistics, 16(4), pp. 379–399.

ESTEVAO, V. M., SARNDAL, C. E., (2002). The ten cases of auxiliary information for calibration in two-phase sampling. Journal of Official Statistics, 18(2), pp.233–255.

ESTEVAO, V. M., SARNDAL, C. E., (2006). Survey estimates by calibration on complex auxiliary information. International Statistical Review, 74, pp. 127–147.

HORVITZ, D. G., THOMPSON, D. J., (1952). A generalisation of sampling without replacement from a finite universe. J. Amer. Statist. Assoc., 47, pp. 663–685.

KIM, J. M., SUNGUR, E. A., HEO, T. Y., (2007). Calibration approach estimators in stratified sampling. Statistics & probability letters, 77(1), pp.99–103

NIDHI, SISODIA, B. V. S., SINGH, S., SINGH, S. K., (2017). Calibration approach estimation of the mean in stratified sampling and stratified double sampling. Communications in Statistics - Theory and Methods, 46(10), pp. 4932–4942.

RAO, D. K., TEKABU, T., KHAN, M. G., (2016). New calibration estimators in stratified sampling. Asia-Pacific World Congress on Computer Science and Engineering, pp. 66–69.

SALINAS, V. I., SEDORY, S. A., SINGH, S., (2019). Calibrated estimators in two-stage sampling. Communications in Statistics - Theory and Method, 48(6), pp. 1–21

SARNDAL, C.E., WRIGHT, R. L., (1984). Cosmetic form of estimators in survey sampling. Scand. J. Statist., II, pp. 146–156.

SINGH, S., (2003). Advanced Sampling theory with applications. Dorrdrechi: Kluwer Academic Publisher.

SINGH, A. C., MOHL, C. A., (1996).Understanding Calibration estimators in Survey Sampling. Survey Methodology, 22, pp. 107–111.

SUBZAR, S., MAQBOOL, S., RAJA, T. A., BHAT, M. A., (2018). Estimation of finite population mean in stratified random sampling using non-conventional measures of dispersion. Journal of Reliability and Statistical Studies, 11(1), pp. 83–92.

SUD, U.C., CHANDRA, H., GUPTA, V. K., (2014). Calibration-based product estimator in single- and two-phase sampling. Journal of Statistical theory and Practice, 8(1), pp.1–11.

TRACY, D.S., SINGH, S., ARNAB, R., (2003). Note on calibration in stratified and double sampling. Survey Methodology, 29(1), pp.99–104.