Related papers: A new approach to locally adaptive polynomial regr…
We study nonparametric regression over Besov spaces from noisy observations under sub-exponential noise, aiming to achieve minimax-optimal guarantees on the integrated squared error that hold with high probability and adapt to the unknown…
We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shape-restricted regression, and…
A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for…
Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of…
This paper investigates the size performance of Wald tests for CAViaR models (Engle and Manganelli, 2004). We find that the usual estimation strategy on test statistics yields inaccuracies. Indeed, we show that existing density estimation…
We study adaptive mesh selection for the solution of systems of initial value problems. The goal is a rigorous theoretical analysis of potential advantages of adaption. For an optimal method in the sense of the speed of convergence, we…
We study online adversarial regression with convex losses against a rich class of continuous yet highly irregular prediction rules, modeled by Besov spaces $B\_{pq}^s$ with general parameters $1 \leq p,q \leq \infty$ and smoothness $s >…
The lack of sufficient flexibility is the key bottleneck of kernel-based learning that relies on manually designed, pre-given, and non-trainable kernels. To enhance kernel flexibility, this paper introduces the concept of…
We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative…
Augmenting a smooth cost function with an $\ell_1$ penalty allows analysts to efficiently conduct estimation and variable selection simultaneously in sophisticated models and can be efficiently implemented using proximal gradient methods.…
Contextual bandits are a central framework for sequential decision-making, with applications ranging from recommendation systems to clinical trials. While nonparametric methods can flexibly model complex reward structures, they suffer from…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…
Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…
We propose a nonparametric quantile regression method using deep neural networks with a rectified linear unit penalty function to avoid quantile crossing. This penalty function is computationally feasible for enforcing non-crossing…
Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific…
Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…
We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. In Johannes and Schenk [2010] it has been shown…
Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much…
This paper presents a new method for spatially adaptive local (constant) likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method…
We consider the nonparametric regression with a random design model, and we are interested in the adaptive estimation of the regression at a point $x\_0$ where the design is degenerate. When the design density is $\beta$-regularly varying…