Regression-in-Ratio Estimator and Confidence Interval for the Population Mean for Data with Outliers

Abstract

Parameter estimation is a method in statistical inference widely used in several areas of research. However, in a sampling survey, many types of data are obtained. Suitable statistical tools are then necessary in consideration. In this paper, we focus on the data included outliers in the variable of interest. The ratio estimators used information on an auxiliary variable and two robust regression estimators based on the least quantile of squares and bisquare methods are then interested to estimate the population mean in simple random sampling. Novel variance estimation of these estimators derived based on the Fieller method is proposed to construct the confidence intervals. Moreover, simulations in many situations when outliers are available are studied. The results show that the proposed confidence interval using variance estimator derived from the Fieller method provides the coverage probability greater than the confidence interval using the mean square error derived based on the Taylor series expansion in all cases in the study. A real-world dataset on apple products in Turkey is analyzed to confirm the practical application of our estimators.