Yadav, Vinay Kumar; Bulut, Hasan; Zaman, Tolga

In survey sampling, the calibration approach is among the most widely used techniques to improve estimator efficiency. In this study, we introduced robust regression approaches into calibrated exponential ratio-type estimators for finite population mean, which helps to ensure better estimation precision when outliers are present in the data. In particular, using stratified random sampling, we introduce the first three moments of the origin of an auxiliary variable in the calibration approach. Second-and third-order moments are also considered by using exponential mean-type estimators. This technique is further modified for study involving sensitive variables, especially in research on personal relationships and intimate health where the respondent may under-report because of privacy concerns. Biased answers are often obtained when questions such as “Have you ever engaged in unprotected sex?" or “Have you ever been tested for a sexually transmitted infection?" By reducing these biases, our strong calibration estimators improve the accuracy of the study. In a simulation study, the data is randomly generated for each stratum and outliers are introduced at 5%, 10% and 25% by randomly selecting a specified proportion of the generated data and multiplying those values by a factor of 10. The findings of our suggested robust estimators perform better than those already in use, especially when it comes to managing sensitive data and outliers, which makes them more effective for real-world use.

Zaman, Tolga; Islamoglu, Ebrucan; Bulut, Hasan

This study addresses the challenge of outliers in sample surveys, a common issue that can distort results and lead to inaccurate conclusions. To tackle this problem, researchers have developed various robust regression techniques including least trimmed squares, least median of squares, least absolute deviations, Huber’s, Hample’s and Tukey’s maximum likelihood estimators, and Huber’s maximum likelihood estimator for location and scale estimators. We propose a new approach: minimum covariance determinant-based ratio estimators for estimating the population mean in sample surveys. To assess the performance of the proposed minimum covariance determinant-based estimators, we derive their mean square error expressions and determine the conditions under which they surpass existing estimators in efficiency. To validate our theoretical findings, we conduct a numerical illustration using real-world data and perform simulations with R-Programme software. The results demonstrate that our method effectively handles outliers and improves the overall accuracy of survey-based estimations, making it a valuable tool for researchers working with sample survey data.

Zaman, Tolga; Bulut, Hasan

It is a general practice to use robust estimates to improve ratio estimators using functions of the parameters of an auxiliary variable. In this study, a new class of robust estimators based upon the Minimum Covariance Determinant (MCD) and the Minimum Volume Ellipsoid (MVE) robust covariance estimates have been suggested for estimating population variance in the presence of outlier values in the data set for the simple random sampling. The expression for the Mean Square Error (MSE) of the proposed class of estimators is derived from the first degree of approximation. The efficiency of the proposed class of robust estimators is compared with some competing estimators discussed in the literature, and found that proposed estimators are better than other mentioned estimators here. In addition, real data set and simulation studies are performed to present the efficiencies of the estimators. We demonstrate theoretically and numerically that the proposed class of estimators performs better than all other competitor estimators under all situations.