Outlier Resistant Alternatives to the Ratio Estimator

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Abstract
Many techniques have been suggested to lower the impact of outliers on sample survey estimates. Outliers can be downweighted by winsorization; that is, by replacing extreme data points by a data-dependent or a predetermined value before calculating estimates. Another approach is to reduce the weight of outliers, from the inverse sampling fraction to 1, in the estimation of population characteristics. In this article the problem of estimating the population mean using auxiliary information in the presence of outliers is considered. A resistant version of the ratio estimator is introduced. It is constructed with a M or a GM estimator of the slope of the regression model through the origin, which is implicitly called on when considering the ratio estimator. The asymptotic biases and asymptotic variances of the proposed alternatives to the ratio estimator are calculated with respect to the randomization of the sampling plan. The selection of a resistant estimator is seen to involve a trade-off betwee...

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