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In this paper, we study Kaplan-Meier V- and U-statistics respectively defined as $theta(widehat{F}_n)=sum_{i,j}K(X_{[i:n]},X_{[j:n]})W_iW_j$ and $theta_U(widehat{F}_n)=sum_{i eq j}K(X_{[i:n]},X_{[j:n]})W_iW_j/sum_{i eq j}W_iW_j$, where $widehat{F}_n$ is the Kaplan-Meier estimator, ${W_1,ldots,W_n}$ are the Kaplan-Meier weights and $K:(0,infty)^2tomathbb R$ is a symmetric kernel. As in the canonical setting of uncensored data, we differentiate between two asymptotic behaviours for $theta(widehat{F}_n)$ and $theta_U(widehat{F}_n)$. Additionally, we derive an asymptotic canonical V-statistic representation of the Kaplan-Meier V- and U-statistics. By using this representation we study properties of the asymptotic distribution. Applications to hypothesis testing are given.
We study the problem of distributional approximations to high-dimensional non-degenerate $U$-statistics with random kernels of diverging orders. Infinite-order $U$-statistics (IOUS) are a useful tool for constructing simultaneous prediction intervals
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A novel sequential change detection problem is proposed, in which the change should be not only detected but also accelerated. Specifically, it is assumed that the sequentially collected observations are responses to treatments selected in real time.