Consider the high-dimensional linear regression model y = Xβ∗ +w, where y ∈ R is an observation vector, X ∈ R is a design matrix with d > n, the quantity β∗ ∈ R is an unknown regression vector, and w ∼ N (0, σI) is additive Gaussian noise. This paper studies the minimax rates of convergence for estimating β∗ in either l2-loss and l2-prediction loss, assuming that β∗ belongs to an lq-ball Bq(Rq)...

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In this paper, we prove a CLT for the sample canonical correlation coefficients between two high-dimensional random vectors with finite rank correlations. More precisely, consider x˜=x+Az and y˜=y+Bz, where x∈Rp, y∈Rq z∈Rr are independent i.i.d. entries of mean zero variance one, A∈Rp×r B∈Rq×r arbitrary deterministic matrices. Given n samples x˜ y˜, stack them into matrices X=X+AZ Y=Y+BZ, X∈Rp×...

CNC turning is widely used as a manufacturing process through which unwanted material is removed to get the high degree of surface rough. In this research article, Taguchi technique was coupled with grey relation analysis (GRA) to optimize the turning parameters for simultaneous improvement of productivity, average surface roughness (Ra), and root mean square roughness (Rq).Taguchi technique L2...

In this paper, we investigate the influence of two types isolation on malware propagation within a computer network. Model 1 proposes network quarantine strategy, where infected computers are fully disconnected from As for model 2, control strategy is anti-virus software quarantine, files in contained an folder. Both models consider aspect heterogeneous immunity, that is, weak and strong immuni...