When there is an outlier in the data set, the efficiency of traditional methods decreases. In order to solve this problem, Kadilar et al. (2007) adapted Huber-M method which is only one of robust regression methods to ratio-type estimators and decreased the effect of outlier problem. In this study, new ratio-type estimators are proposed by considering Tukey-M, Hampel M, Huber MM, LTS, LMS and LAD robust methods based on the Kadilar et al. (2007). Theoretically, we obtain the mean square error (MSE) for these estimators. We compared with MSE values of proposed estimators and MSE values of estimators based on Huber-M and OLS methods. As a result of these comparisons, we observed that our proposed estimators give more efficient results than both Huber M approach which was proposed by Kadilar et al. (2007) and OLS approach. Also, under all conditions, all of the other proposed estimators except Lad method are more efficient than robust estimators proposed by Kadilar et al. (2007). And, these theoretical results are supported with the aid of a numerical example and simulation by basing on data that includes an outlier.

In this study, we propose the robust ratio-type estimator of finite population variance considering the minimum covariance determinant (MCD) and the minimum volume ellipsoid (MVE) robust covariance matrices in simple and stratified random sampling. The mean square errors (MSE) equations are obtained for the robust ratio-type estimator. The conditions for which the proposed robust ratio-type estimator is more efficient as compared to competing estimators have been discussed. The MCD and MVE are robust against outliers. Thus, when there is an outlier in the data, simulations and empirical results show that the proposed robust ratio-type estimators under simple and stratified random sampling have a lower mean square error than the traditional estimators. In addition, we support theoretical results with contaminated real examples and simulation studies.

This article proposes new regression-type estimators by considering Tukey-M, Hampel M, Huber MM, LTS, LMS and LAD robust methods and MCD and MVE robust covariance matrices in stratified sampling. Theoretically, we obtain the mean square error (MSE) for these estimators. We compare the efficiencies based on MSE equations, between the proposed estimators and the traditional combined and separate regression estimators. As a result of these comparisons, we observed that our proposed estimators give more efficient results than traditional approaches. And, these theoretical results are supported with the aid of numerical examples and simulation based on data sets that include outliers.

This paper suggests a new family of exponential estimators in the two-phase sampling using the information of an auxiliary attribute. Theoretically, we obtain the mean square error (MSE) for these estimators. We compare the MSE equations of the proposed exponential ratio families of estimators with the MSE equations of the ratio estimators in literature. As a result of these comparisons, we observe that the proposed families of estimators give more efficient results than the estimators in literature for the determined conditions obtained in theory. In addition, these theoretical results are supported by an application with original data sets.

Stratification of population is a probability sampling design used to increase the precision of estimation. An efficient exponential ratio estimator allows estimating the population mean in stratified random sampling using an auxiliary variable. Its expected bias, expected mean square error, and minimum mean square error are expressed. The conditions for which the estimator is more efficient are obtained. The proposed estimators under stratified random sampling have a lower mean square error than the ratio and the exponential estimators.