Limit joint distribution of $U$-statistics, $M$-estimates, and sample quantiles

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.