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Two-sample tests utilizing a similarity graph on observations are useful for high-dimensional data and non-Euclidean data due to their flexibility and good performance under a wide range of alternatives. Existing works mainly focused on sparse graphs, such as graphs with the number of edges in the order of the number of observations. However, the tests have better performance with denser graphs under many settings. In this work, we establish the theoretical ground for graph-based tests with graphs that are much denser than those in existing works.
In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently estimate,
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 $widehat{F}_n$
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null hypothesi
Over the last two decades, many exciting variable selection methods have been developed for finding a small group of covariates that are associated with the response from a large pool. Can the discoveries from these data mining approaches be spurious
We consider testing the equality of two high-dimensional covariance matrices by carrying out a multi-level thresholding procedure, which is designed to detect sparse and faint differences between the covariances. A novel U-statistic composition is de