  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.
