Outliers in official statistics

Abstract

The purpose of this manuscript is to provide a survey on the important methods addressing outliers while producing official statistics. Outliers are often unavoidable in survey statistics. They may reduce the information of survey datasets and distort estimation on each step of the survey statistics production process. This paper defines outliers to be focused on each production step and introduces practical methods to cope with them. The statistical production process is roughly divided into the following three steps. The first step is data cleaning, and outliers to be focused are that may contain mistakes to be corrected. Robust estimators of a mean vector and covariance matrix are introduced for the purpose. The next step is imputation. Among a variety of imputation methods, regression and ratio imputation are the subjects in this paper. Outliers to be focused on in this step are not erroneous but have extreme values that may distort parameter estimation. Robust estimators that are not affected by remaining outliers are introduced. The final step is estimation and formatting. We have to be careful about outliers that have extreme values with large design weights since they have a considerable influence on the final statistics products. Weight calibration methods controlling the influence are discussed based on the robust weights obtained in the previous imputation step. A few examples of practical application are also provided briefly, although multivariate outlier detection methods introduced in this paper are mostly in the research stage in the field of official statistics.