Outlier Resistant Alternatives to the Ratio Estimator

原文摘要

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 between bias and variance. Often, some bias is the price paid to reduce the variance. A mean squared error estimator is proposed. A model-based estimator proposed by Chambers, reducing the weights given to extreme observations to 1, is also studied. A conditional investigation of the bias, given the proportion of outliers in the sample, is carried out. It reveals that the unconditional unbiasedness of the ratio estimator is, in the presence of outliers, deceptive. Its conditional bias varies substantially with the difference between the sample proportion and the population proportion of outliers. It can be severe if the proportion of outliers in the sample is much larger than in the population. The conditional bias of resistant estimators is, on the other hand, more stable. It does not depend as much on the proportion of outliers in the sample. Monte Carlo comparisons of the ratio estimator with resistant alternatives are presented for two populations. These similations show that in the presence of outliers, the mean squared error of resistant estimators can be substantially smaller than that of the ratio estimator. They also show that resistant confidence intervals are interesting alternatives to intervals based on the ratio estimator.

摘要来源：OpenAlex 索引摘要（稿件版本未注明）