$ U $-statistics represent a fundamental class of statistics used to model quantities derived from responses of multiple subjects. These statistics extend the concept of the empirical mean of a $ d $-variate random variable $ X $ by considering sums over all distinct $ m $-tuples of observations of $ X $. Within this realm, W. Stute [
Citation: Salim Bouzebda, Amel Nezzal, Issam Elhattab. Limit theorems for nonparametric conditional U-statistics smoothed by asymmetric kernels[J]. AIMS Mathematics, 2024, 9(9): 26195-26282. doi: 10.3934/math.20241280
$ U $-statistics represent a fundamental class of statistics used to model quantities derived from responses of multiple subjects. These statistics extend the concept of the empirical mean of a $ d $-variate random variable $ X $ by considering sums over all distinct $ m $-tuples of observations of $ X $. Within this realm, W. Stute [
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