debiasedInference

Reference R and Python implementations for Gang Cheng and Yen-Chi Chen, “Nonparametric Inference via Bootstrapping the Debiased Estimator”.

The project implements the paper's debiased kernel density estimator and debiased local-linear regression estimator, together with empirical-bootstrap simultaneous confidence bands. The R and Python packages intentionally expose matching function names and defaults.

See the paper analysis, statistical specification, published-simulation validation report, and API guide for the reasoning, implementation conventions, numerical evidence, and complete workflow.

Layout

• python/: installable Python package
• r/: installable R package
• docs/: mathematical and implementation notes
• examples/: reproducible cross-language examples

The paper_density_simulation scripts reproduce the paper's two-component Gaussian-mixture coverage design at configurable Monte Carlo and bootstrap sizes; their headers show the paper-scale settings.

Python quick start

python -m pip install debiased-inference

import numpy as np
from debiased_inference import kde_confidence_band

rng = np.random.default_rng(2026)
x = rng.normal(size=300)
band = kde_confidence_band(x, n_boot=499, random_state=2026)

R quick start

install.packages(
  "https://github.com/mathcg/debiased-inference/releases/download/v0.1.1/debiasedInference_0.1.1.tar.gz",
  repos = NULL,
  type = "source"
)
library(debiasedInference)

set.seed(2026)
x <- rnorm(300)
band <- kde_confidence_band(x, n_boot = 499, random_state = 2026)

Scope

Version 0.1.1 implements the Gaussian-kernel procedures analyzed and used in the paper. Confidence bands are simultaneous over the supplied evaluation grid; the grid is therefore part of the numerical approximation and should cover the scientific domain of interest densely.

Citation

If you use these methods or this software in your work, please cite the paper:

Cheng, G. and Chen, Y.-C. (2019). Nonparametric inference via bootstrapping the debiased estimator. Electronic Journal of Statistics, 13(1). https://doi.org/10.1214/19-EJS1575

The published paper on Project Euclid is the canonical methodological reference for this repository. Citation metadata is also available in CITATION.cff.