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rbbnp

Overview

The rbbnp package implements the bias-bound approach of Schennach 2020: it bounds the estimation bias via Fourier analysis, giving valid confidence intervals for kernel density and conditional-expectation estimators at optimal, MSE-minimizing bandwidths without undersmoothing.

Installation 

# Install from CRAN
install.packages("rbbnp")

# Or install development version from GitHub
# install.packages("devtools")
devtools::install_github("xinyu-daidai/rbbnp-dev")

Key Functions

Function Purpose
biasBound_density() Density estimation with bias-aware confidence intervals
biasBound_condExpectation() Regression with bias-aware confidence intervals
select_bandwidth() Cross-validation or Silverman bandwidth selection

Usage

Density Estimation 

library(rbbnp)

# Generate sample data
X <- gen_sample_data(size = 500, dgp = "2_fold_uniform", seed = 123)

# Estimate density with bias-aware confidence intervals
fit <- biasBound_density(X, h = 0.1, kernel.fun = "Schennach2004")

# View results
fit
#> Bias-Bound Density Estimation
#> ==============================
#> Observations: 500 | Bandwidth: 0.100 | Kernel: Schennach2004
#> Smoothness: A = 4.30, r = 2.00

# Visualize
plot(fit)

Conditional Expectation (Regression) 

# Generate regression data
Y <- -X^2 + 3*X + rnorm(500) * X

# Estimate E[Y|X]
fit_reg <- biasBound_condExpectation(Y, X, h = 0.1)

# Visualize
plot(fit_reg)

Working with Results

Both functions return S3 objects with standard methods:

# Extract parameters (A, r, B, h)
coef(fit)

# Get confidence intervals
confint(fit)

# Detailed summary
summary(fit)

# For regression: fitted values
fitted(fit_reg)

Learning More

Citation

If you use rbbnp, please cite the package (run citation("rbbnp") for the current version):

Dai, X. and Schennach, S. M. (2026). rbbnp: A Bias Bound Approach to Non-Parametric Inference. R package version 1.1.0. https://CRAN.R-project.org/package=rbbnp

@Manual{rbbnp,
  title  = {rbbnp: A Bias Bound Approach to Non-Parametric Inference},
  author = {Xinyu Dai and Susanne M. Schennach},
  year   = {2026},
  note   = {R package version 1.1.0},
  url    = {https://CRAN.R-project.org/package=rbbnp},
}

The package implements the method introduced in Schennach (2020).

Getting Help