Geodesic
Limit joint distribution of $U$-statistics, $M$-estimates, and sample quantiles
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2023), pp. 9-16

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Let $X_1, X_2, \ldots, X_n$ be independent identically distributed random vectors. Consider a vector $V(X_1, X_2, \ldots, X_n)$ whose each component is either a $U$-statistic or an $M$-estimator. Sufficient conditions for asymptotic normality of the vector $V(X_1, X_2, \ldots, X_n)$ are obtained. In the case when $X_1, X_2, \ldots$ are one-dimensional sufficient conditions for asymptotic normality are obtained for a vector, each component of which is either a $U$-statistic, or an $M$-estimator, or a sample quantile. 
@article{VMUMM_2023_6_a1,
     author = {M. P. Savelov},
     title = {Limit joint distribution of $U$-statistics, $M$-estimates, and sample quantiles},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {9--16},
     publisher = {mathdoc},
     number = {6},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a1/}
}
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M. P. Savelov. Limit joint distribution of $U$-statistics, $M$-estimates, and sample quantiles. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2023), pp. 9-16. http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a1/