This paper studies the minimax rate of nonparametric conditional density estimation under a weighted absolute value loss function in multivariate setting. We first demonstrate that is impossible if one only requires pX|Z smooth x for all values z. motivates us to consider sub-class absolutely continuous distributions, restricting pX|Z(x|z) not be Hölder x, but also total variation propose corre...

High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other ℓ r norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we ...

Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the highdimensional settings, the leading eigenvector of the sample covariance can be nearly orthogonal to the true eigenvector. A sparse structure is then commonly assumed along with a low rank structure. Recently, minimax estimation rates of sparse PCA w...

We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks. The estimators we minimize sum squared data-fitting errors plus a regularization term proportional to Euclidean norm network weights. This minimization corresponds common approach training with weight decay. quantify performance (mean-squared error) these when data-generating belongs secon...