A New Test on High-Dimensional Mean Vector Without Any Assumption on Population Covariance Matrix

In this paper, a new test for the equality of the mean vectors between a two groups with the same number of the observations in high-dimensional data. The existing tests for this problem require a strong condition on the population covariance matrix. The proposed test in this paper does not require such conditions for it. This test will be obtained in a general model, that is, the data need not be normally distributed.     

Positive-definite modification of a covariance matrix by minimizing the matrix $$\ell_{\infty}$$ ℓ ∞ norm with applications to portfolio optimization

AStA Advances in Statistical Analysis - The covariance matrix, which should be estimated from the data, plays an important role in many multivariate procedures, and its positive definiteness...     

A Faster Algorithm for Computing Minimum 5-Way and 6-Way Cuts in Graphs

For an edge-weighted graph G with n vertices and m edges, the minimum k-way cut problem is to find a partition of the vertex set into k non-empty subsets so that the weight sum of edges between different subsets is minimized. For this problem with k = 5 and 6, we present a deterministic algorithm that runs in O(n^{k – 1}F(n, m)) = O(mn^k log (n²/m)) time, where F(n, m) denotes the time bound required to solve the maximum flow problem in G. The bounds Õ(mn⁵) for k = 5 and Õ(mn⁶) for k = 6 improve the previous best randomized bounds Õ(n⁸) and Õ(n¹⁰), respectively.