A proper circular-arc (PCA) model is a pairM = (C,A) where C is a circle and A is a family of inclusion-free arcs on C in which no two arcs of A cover C. A PCA model U is a (c, `, d, ds)-CA model when C has circumference c, all the arcs in A have length `, all the extremes of the arcs in A are at a distance at least d, and all the beginning points of the arcs in A are at a distance at least d+ ...

Algorithm 1 Suggesting Compatible Colors 1: procedure COMPATIBLECOLORS(palette t, index k, #cands Ncand, #samples Nsample, threshold (τ, κ)) 2: . Sampling candidate’s HSVs 3: f ← COMPUTEHUEPROBABILITY(t, k) . Eq. 3 or Eq. 4 4: hi← SAMPLINGFROMHUEPROB( f , Nsample) 5: si ∼N (μs,σs) . §4.2 6: vi ∼N (μv,σv) . §4.2 7: . Compute rating 8: for i = 1→ m do 9: ci← (hi, si,vi) 10: Ccand i ← COMPATIBLECA...

Mahalanobis distance of covariate means between treatment and control groups is often adopted as a balance criterion when implementing rerandomization strategy. However, this may not work well for high-dimensional cases because it balances all orthogonalized covariates equally. We propose using principal component analysis (PCA) to identify proper subspaces in which should be calculated. Not on...

We study the problem of estimating the leading eigenvectors of a highdimensional population covariance matrix based on independent Gaussian observations. We establish a lower bound on the minimax risk of estimators under the l2 loss, in the joint limit as dimension and sample size increase to infinity, under various models of sparsity for the population eigenvectors. The lower bound on the risk...