Letfnbeanon-parametrickerneldensityestimatorbasedonakernelfunctionK.andasequenceofindependentandidenticallydistributedrandomvariablestakingvaluesinR.Thegoalofthisarticleistoprovemoderatedeviationsandlargedeviationsforthestatisticsupx∈R|fn(x)-fn(-x)|.