6 papers · 1 filter
First-order asymptotic expansions for spectral convergence of compact self-adjoint operators on general spectral subsets, with application to kernel Gram matrices
Eunseong Bae, Wolfgang Polonik
We study the spectral convergence of compact, self-adjoint operators on a separable Hilbert space, and derive the first-order asymptotic expansions for their eigenvalues, eigenvect…
Kernel smoothing on manifolds
Eunseong Bae, Wolfgang Polonik
Under the assumption that data lie on a compact (unknown) manifold without boundary, we derive finite sample bounds for kernel smoothing and its (first and second) derivatives, and…
Nonsmooth Nonparametric Regression via Fractional Laplacian Eigenmaps
Zhaoyang Shi, Krishnakumar Balasubramanian, Wolfgang Polonik
We develop nonparametric regression methods for the case when the true regression function is not necessarily smooth. More specifically, our approach is using the fractional Laplac…
Multivariate Gaussian Approximation for Random Forest via Region-based Stabilization
Zhaoyang Shi, Chinmoy Bhattacharjee, Krishnakumar Balasubramanian +1
We derive Gaussian approximation bounds for -Potential Nearest Neighbor (-PNN) based random forest predictions based on a set of training points given by a Poisson process un…
Common Drivers in Sparsely Interacting Hawkes Processes
Alexander Kreiss, Enno Mammen, Wolfgang Polonik
We study a multivariate Hawkes process as a model for time-continuous relational event networks. The model does not assume the network to be known, it includes covariates, and it a…
Gaussian and Bootstrap Approximation for Matching-based Average Treatment Effect Estimators
Zhaoyang Shi, Chinmoy Bhattacharjee, Krishnakumar Balasubramanian +1
We establish Gaussian approximation bounds for covariate and rank-matching-based Average Treatment Effect (ATE) estimators. By analyzing these estimators through the lens of stabil…