8 problems

Let $\boldsymbol{X}=n^{-1}\beta\boldsymbol{\theta}\boldsymbol{\theta}^\top+\boldsymbol{W}$ be a spiked model, where $\beta$ is the signal strength and $\boldsymbol{\theta}$ is the…

Let $X_1,\ldots,X_n$ be independent Gaussian random vectors in $\mathbb{R}^p$ with distribution $N(0,\Sigma)$, let … and consider the rank-one covariance model…

Let $x\in\{-1,+1\}^d$, let $H$ be a self-adjoint random matrix with variance profile $\boldsymbol{\Delta}$, and define the transformed observation … where all variances…

Let $\bm{u}_1,\ldots,\bm{u}_r$ and $\bm{v}_1,\ldots,\bm{v}_r$ be the signal's left and right singular vectors, and let $\hat{\bm{u}}_1,\ldots,\hat{\bm{u}}_r$ and…

Conjecture on transformed-test optimality. With the entrywise transform, the proposed LSS-based test will be optimal for weak detection.

Let $R$ be the signal matrix, and let $r_0$ denote the number of non-degenerate spikes under consideration. In the degenerate case, suppose that the $(r_0+1)$-th and $(r_0+2)$-th s…

Let $Gamma$ be the set of parameter pairs $(\alpha,\beta)$ for which the replica-symmetric formula vanishes, and let $Gamma'$ be its interior. For the likelihood ratio…

Consider the high-dimensional spiked rectangular model with aspect ratio $\frac{M}{N}\to\alpha$, signal strength $\beta$, and likelihood ratio $L(\bm{Y};\beta)$ against the all-noi…