Marcello D'Orazio

Marcello D'Orazio

This note investigates the problem of detecting outliers in longitudinal data. It compares well-known methods used in official statistics with proposals from the fields of data mining and machine learning that are based on the distance between observations or binary partitioning trees. This is achieved by applying the methods to panel survey data related to different types of statistical units. Traditional methods are quite simple, enabling the direct identification of potential outliers, but they require specific assumptions. In contrast, recent methods provide only a score whose magnitude is directly related to the likelihood of an outlier being present. All the methods require the user to set a number of tuning parameters. However, the most recent methods are more flexible and sometimes more effective than traditional methods. In addition, these methods can be applied to multidimensional data.

Marcello D'Orazio

Nearest neighbor methods have become popular in official statistics, mainly in imputation or in statistical matching problems; they play a key role in machine learning too, where a high number of variants have been proposed. The choice of the distance function depends mainly on the type of the selected variables. Unfortunately, relatively few options permit to handle mixed type variables, a situation frequently encountered in official statistics. The most popular distance for mixed type variables is derived as the complement of the Gower's similarity coefficient; it is appealing because ranges between 0 and 1 and allows to handle missing values. Unfortunately, the unweighted standard setting the contribution of the single variables to the overall Gower's distance is unbalanced because of the different nature of the variables themselves. This article tries to address the main drawbacks that affect the overall unweighted Gower's distance by suggesting some modifications in calculating the distance on the interval and ratio scaled variables. Simple modifications try to attenuate the impact of outliers on the scaled Manhattan distance; other modifications, relying on the kernel density estimation methods attempt to reduce the unbalanced contribution of the different types of variables. The performance of the proposals is evaluated in simulations mimicking the imputation of missing values through nearest neighbor distance hotdeck method.