Local inference by penalization method for biclustering model (Q1631204)

Suppose we observe a matrix \(X=(X_{ij})\in \mathbb{R}^{\mathbf n}\), \(\mathbf n= (n_1,n_2)\in\mathbb{N}^2\): \(X_{ij}=\theta_{ij}=\sigma \xi_{ij}\), \(i=1,\dots,n_1\), \(j=1,\dots, n_2\), where \(\theta= (\theta_{ij})\in \mathbb{R}^{\mathbf n}\) is an unknown high-dimensional parameter with biclustering structure, \(\xi=(\xi_{ij})\in \mathbb{R}^{\mathbf n}\) is a random matrix with \(E_\theta(\xi_{ij})=0\). The authors study the problem of estimation and uncertainty quantification for the unknown parameter in the biclustering model by using the penalization method. A particular case of the biclustering structure is the stochastic block model used in the network analysis.