An efficient Hartley–Ross type estimators of nonsensitive and sensitive variables using robust regression methods in sample surveys

In sample surveys, the problem of outliers is one of the most frequent and widest, whose solution is required to be obtained using statistical techniques. To overcome this problem, various robust regression methods are being developed such as LTS, LMS, LAD, Huber-M, Hample-M, Tukey-M and Huber-MM methods. This article presents the modified Hartley–Ross type ratio estimators to estimate the population mean in sample surveys. The proposed design is taken into account under the two suppositions one is that the study variable is a non-sensitive variable, which means that measurements on it do not embarrass participants in personal interviews and other is the sensitive variable, which means that measurement errors are introduced as a result of a few dishonest responses. The use of scrambling response models helps to reduce these measurement errors to some extent. The proposed estimator is found to be more efficient than the existing classical estimators. A Numerical illustration was performed on a real data set in R-Program Software to support of our findings.