Before revision:  This new class of risk statistics can be considered as a kind of risk extension of risk statisticsintroduced by Kou, Peng and Heyde (2013), and also data-based versions of cash sub-additive riskmeasures introduced by El Karoui and Ravanelli (2009) and Sun and Hu (2019) .
After revision:  This new class of risk statistics can be considered as a kind of risk statistic can be uesd for the quantification of portfolio risk. By further developing the properties related to cash sub-additive risk statistics, we are able to derive representation results for such risk .