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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning 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Bounds for Early-Stopping in Gaussian Linear Regression Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent Copula-enhanced Vision Transformer for high myopia diagnosis through OU UWF fundus images General Frameworks for Conditional Two-Sample Testing Improved Hardness Results for Learning Intersections of Halfspaces Consistency of Lloyd's Algorithm Under Perturbations Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation Distribution-Free Stochastic Analysis and Robust Multilevel Vector Field Anomaly Detection Efficient Parameter Estimation of Truncated Boolean Product Distributions
Nonparametric Inference via Bootstrapping the Debiased Estimator
Gang Cheng, Yen-Chi Chen · 2017-02-23 · via math.ST updates on arXiv.org

In this paper, we propose to construct confidence bands by bootstrapping the debiased kernel density estimator (for density estimation) and the debiased local polynomial regression estimator (for regression analysis). The idea of using a debiased estimator was recently employed by Calonico et al. (2018b) to construct a confidence interval of the density function (and regression function) at a given point by explicitly estimating stochastic variations. We extend their ideas of using the debiased estimator and further propose a bootstrap approach for constructing simultaneous confidence bands. This modified method has an advantage that we can easily choose the smoothing bandwidth from conventional bandwidth selectors and the confidence band will be asymptotically valid. We prove the validity of the bootstrap confidence band and generalize it to density level sets and inverse regression problems. Simulation studies confirm the validity of the proposed confidence bands/sets. We apply our approach to an Astronomy dataset to show its applicability