Related papers: Robust Nonparametric Regression under Huber's $\ep…
We develop a finite-sample optimal estimator for regression discontinuity design when the outcomes are bounded, including binary outcomes as the leading case. Our estimator achieves minimax mean squared error among linear shrinkage…
Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…
The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is…
Consider nonparametric function estimation under $L^p$-loss. The minimax rate for estimation of the regression function over a H\"older ball with smoothness index $\beta$ is $n^{-\beta/(2\beta+1)}$ if $1\leq p<\infty$ and $(n/\log…
A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…
We introduce and study a local linear nonparametric regression estimator for censorship model. The main goal of this paper is, to establish the uniform almost sure consistency result with rate over a compact set for the new estimate. To…
We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a…
Deviations from the center within a robust neighborhood of a parametric model distribution may naturally be considered an infinite dimensional nuisance parameter. Thus, the semiparametric method may be tried, which is to compute the scores…
We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of the observations. We focus on the application to bearings-only tracking. We first investigate the least squares estimator and prove…
We consider a robust linear regression model $y=X\beta^* + \eta$, where an adversary oblivious to the design $X\in \mathbb{R}^{n\times d}$ may choose $\eta$ to corrupt all but an $\alpha$ fraction of the observations $y$ in an arbitrary…
It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if…
We study Bayesian inference in statistical linear inverse problems with Gaussian noise and priors in Hilbert space. We focus our interest on the posterior contraction rate in the small noise limit. Existing results suffer from a certain…
We consider the nonparametric regression problem when the covariates are located on an unknown smooth compact submanifold of a Euclidean space. Under defining a random geometric graph structure over the covariates we analyze the asymptotic…
We propose a non-convex training objective for robust binary classification of data sets in which label noise is present. The design is guided by the intention of solving the resulting problem by adiabatic quantum optimization. Two…
Nonparametric kernel density and local polynomial regression estimators are very popular in Statistics, Economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as…
In this paper, we consider the problem of estimating the marginal density in some nonlinear autoregressive time series models for which the conditional mean and variance have a parametric specification. Under some regularity conditions, we…
In machine learning, a critical class of decision-related problems concerns preventing predicted undesirable outcomes, referred to as the \textit{avoiding undesired future} (AUF) problem. To address this, the \textit{rehearsal learning}…
This paper studies the statistical complexity of kernel hyperparameter tuning in the setting of active regression under adversarial noise. We consider the problem of finding the best interpolant from a class of kernels with unknown…
Data-driven computing in applied mechanics utilizes the material data set directly, and hence is free from errors and uncertainties stemming from the conventional material modeling. This paper presents a data-driven approach that is robust…
This paper deals with the robust estimation problem of a signal given noisy observations. We assume that the actual statistics of the signal and observations belong to a ball about the nominal statistics. This ball is formed by placing a…