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This paper considers in the high dimensional setting a canonical testing problem in multivariate analysis, namely testing the equality of two mean vectors. We introduce a new test statistic that is based on a linear transformation of the data by the precision matrix which incorporates the correlations among the variables. Limiting null distribution of the(More)
This supplement provides theoretical and numerical comparisons of the three oracle tests and presents more extensive simulation results comparing the numerical performance of the proposed test with that of other tests in the non-sparse cases as well as for non-Gaussian distributions. We also prove Propositions 1-3 and the technical results, Lemmas 3 and 4,(More)
Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in terms of an analytic quantity , the local modulus of continuity. This bound depends not only on the function but also(More)
Alternative land use zoning scenarios provide guidance for sustainable land use controls. This study focused on an ecologically vulnerable catchment on the Loess Plateau in China, proposed a novel land use zoning model, and generated alternative zoning solutions to satisfy the various requirements of land use stakeholders and managers. This model combined(More)
In this supplement we prove Proposition 1-3 and the technical results, Lemmas 3, 4 and 5, which are used in the proofs of the main results. We also present more extensive simulation results comparing the numerical performance of the proposed test with that of other tests. According to the proof of Theorem 1 and letting d = 1 in (29), we have P H 0 (M ij ≥ q(More)
This paper proposes a new test for testing the equality of two covariance matrices Σ 1 and Σ 2 in the high-dimensional setting and investigates its theoretical and numerical properties. The limiting null distribution of the test statistic is derived. The test is shown to enjoy certain optimality and to be especially powerful against sparse alternatives. The(More)
Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical dependence that is often encoded in terms of partial correlation. Such a graph is inferred from the matrix-valued(More)
Acknowledgments It has been a great honor for me to be associated to so many great people in my past six years at UPenn. It fills me with great joy to look back and think about all the help, guidance and encouragement I found here. Now I would like to take this great opportunity to express my sincere thankfulness to them. First of all, I owe my deepest(More)
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