In this article, we employ a regression formulation to estimate the high dimensional covariance matrix for a given network structure. Using prior information contained in the network relationships, we model the covariance as a polynomial function of the symmetric adjacency matrix. Accordingly,...

In this paper we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy-to-implement, and automatically ensures quantile monotonicity by construction. For inference, we propose to...

This paper develops a general framework for conducting inference on the rank of an unknown matrix \Pi_0. A defining feature of our setup is the null hypothesis of the form H_0: rank(\Pi_0)\leq r. The problem is of first order importance because the previous literature focuses on H_0':...

This paper develops a general framework for conducting inference on the rank of an unknown matrix Π0. A defining feature of our setup is the null hypothesis of the form . The problem is of first‐order importance because the previous literature focuses on by implicitly assuming away , which...

This paper presents a unified framework for inference on parameters of the form $\phi(\theta_0)$, where $\theta_0$ is unknown but can be estimated by $\hat\theta_n$, and $\phi$ is known with null first order derivative at $\theta_0$. We show the ``standard'' bootstrap is consistent if and only...