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.

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.

In this article, ratio estimators for the population mean have suggested using the robust covariance estimation under the simple random scheme. Zaman and Bulut have developed a class of ratio-type estimators for the mean estimation by utilizing robust regression coefficients. In this paper, we extend the estimators presented in Zaman and Bulut by using minimum covariance determinant (MCD) robust covariance estimation. The mean square error (MSE) equation for the new estimators is obtained. These theoretical results are supported with the aid of numerical example and simulation based on dataset that include outliers.

Estimating the population mean is of prime concern in many studies, and calibrations are popular choices. A robust calibration estimator estimates the mean using the minimum covariance determinant (MCD) and the minimum volume ellipsoid (MVE) estimations under stratified random sampling. Efficiency comparisons have been made between the robust calibration estimator and classical calibration estimator. Simulations and empirical results show that the proposed robust calibration estimator has a lower mean square error than the calibration estimators. When the relative efficiency and computation times are considered together, it is seen that the proposed robust calibration estimators based on MCD estimates are more efficient.

Outlier detection is an extensively studied issue in robust literature. The most popular and traditional approach using to detect outliers is to calculate the Mahalanobis distance. However, conventional Mahalanobis distances may fail to detect outliers because they base on the classical sample mean vector and covariance matrix, which are sensitive to outliers. To solve this problem, the Minimum Covariance Determinant (MCD) estimators are used instead of classical estimators. However, the MCD estimators cannot be calculated in high dimensional data sets, which variable number p is higher than the sample size n. To detect outliers in high dimensional data, we propose Mahalanobis distance based on the Minimum Regularized Covariance Determinants (MRCD) estimators, which can be calculated in high dimensional data sets. We have shown that this distance is successful for outlier detection in high dimensional data sets with the simulation study and real data sets.