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Package {debiasedInference}

Type: Package
Title: Bootstrap Inference with Debiased Nonparametric Estimators
Version: 0.1.0
Description: Implements debiased kernel density and local-linear regression estimators with empirical-bootstrap simultaneous confidence bands, as proposed by Cheng and Chen (2019) <doi:10.1214/19-EJS1575>. Also provides bandwidth selectors and grid-based confidence sets for density level sets and inverse regression.
License: MIT + file LICENSE
Encoding: UTF-8
Depends: R (≥ 4.1.0)
Suggests: testthat (≥ 3.0.0)
Config/testthat/edition: 3
URL: https://github.com/mathcg/debiased-inference, https://doi.org/10.1214/19-EJS1575
BugReports: https://github.com/mathcg/debiased-inference/issues
NeedsCompilation: no
Packaged: 2026-09-19 05:37:24 UTC; runner
Author: Gang Cheng [aut, cre], Yen-Chi Chen [aut]
Maintainer: Gang Cheng <mathchenggang@gmail.com>
Repository: CRAN
Date/Publication: 2026-09-29 14:10:10 UTC

Debiased kernel density estimation and confidence bands

Description

Evaluate the Gaussian debiased KDE in equation (3) of Cheng and Chen or construct its empirical-bootstrap simultaneous confidence band (Figure 2).

Usage

debiased_kde(x, points = NULL, bandwidth = NULL, tau = 1,
  grid_size = 200L)

kde_confidence_band(x, points = NULL, bandwidth = NULL, tau = 1,
  confidence = 0.95, n_boot = 999L, studentized = FALSE,
  random_state = NULL, grid_size = 200L)

Arguments

x

Numeric observations or a numeric matrix with observations in rows.

points

Optional evaluation vector or matrix; required for multivariate data.

bandwidth

Positive isotropic bandwidth selected for the ordinary KDE.

tau

Positive ratio h/b; the paper recommends one.

grid_size

Generated grid size for one-dimensional data.

confidence

Confidence level strictly between zero and one.

n_boot

Positive number of empirical-bootstrap replicates.

studentized

Whether to use the variable-width band in Remark 1.

random_state

Optional local random seed; the caller's RNG state is preserved.

Value

debiased_kde() returns a di_estimate; kde_confidence_band() returns a di_band.

References

Cheng, G. and Chen, Y.-C. (2019). Nonparametric Inference via Bootstrapping the Debiased Estimator. Electronic Journal of Statistics, 13(1). doi:10.1214/19-EJS1575.

Examples

x <- rnorm(50)
fit <- debiased_kde(x, bandwidth = 0.4)
band <- kde_confidence_band(x, bandwidth = 0.4, n_boot = 19,
                            random_state = 1)

Debiased local-linear regression and confidence bands

Description

Fit the debiased local-linear estimator in equation (5) of Cheng and Chen or construct its paired-bootstrap simultaneous confidence band (Figure 3).

Usage

debiased_local_linear(x, y, points = NULL, bandwidth = NULL, tau = 1,
  grid_size = 200L, n_folds = 5L, random_state = 0L)

regression_confidence_band(x, y, points = NULL, bandwidth = NULL,
  tau = 1, confidence = 0.95, n_boot = 999L, random_state = NULL,
  grid_size = 200L, n_folds = 5L, max_attempts = NULL)

Arguments

x

Numeric one-dimensional covariates.

y

Numeric responses of the same length as x.

points

Optional numeric evaluation grid.

bandwidth

Positive bandwidth selected for the ordinary smoother.

tau

Positive ratio h/b; the paper recommends one.

grid_size

Generated grid size when points is omitted.

n_folds

Number of cross-validation folds for bandwidth selection.

random_state

Optional local random seed.

confidence

Confidence level strictly between zero and one.

n_boot

Positive number of paired-bootstrap replicates.

max_attempts

Maximum resamples attempted if singular fits occur.

Value

A di_estimate or di_band object.

References

Cheng, G. and Chen, Y.-C. (2019). Nonparametric Inference via Bootstrapping the Debiased Estimator. Electronic Journal of Statistics, 13(1). doi:10.1214/19-EJS1575.

Examples

x <- seq(-1, 1, length.out = 50)
y <- sin(pi * x) + rnorm(50, sd = 0.1)
fit <- debiased_local_linear(x, y, bandwidth = 0.3)
band <- regression_confidence_band(x, y, bandwidth = 0.3,
                                   n_boot = 19, random_state = 1)

Bandwidth selectors for ordinary nonparametric estimators

Description

Select the bandwidth on the ordinary estimator, as required by the debiasing method. Density estimation uses a normal-reference rule and regression uses K-fold cross-validation of the ordinary local-linear smoother.

Usage

density_bandwidth(x, method = "normal_reference", candidates = NULL,
  block_size = 512L)

regression_bandwidth(x, y, candidates = NULL, n_folds = 5L,
  random_state = 0L)

Arguments

x

Numeric observations or covariates.

y

Numeric responses.

method

For density estimation, either "normal_reference" or "cv".

candidates

Optional positive candidate bandwidths for cross-validation.

block_size

Positive pairwise-computation block size for density cross-validation.

n_folds

Number of cross-validation folds.

random_state

Optional local random seed.

Value

A positive numeric scalar.

Grid-based level-set utilities

Description

Estimate equality level sets on a one-dimensional or rectangular two- dimensional grid, invert a simultaneous band to obtain a confidence set, or calculate finite-point-cloud Hausdorff distance.

Usage

level_set(estimate, level)

invert_confidence_band(band, level)

hausdorff_distance(a, b)

density_level_set(x, level, points = NULL, bandwidth = NULL, tau = 1,
  grid_size = 200L)

density_level_set_confidence(x, level, points = NULL, bandwidth = NULL,
  tau = 1, confidence = 0.95, n_boot = 999L, method = "hausdorff",
  random_state = NULL, grid_size = 200L, max_attempts = NULL)

inverse_regression(x, y, level, points = NULL, bandwidth = NULL,
  tau = 1, grid_size = 200L, n_folds = 5L, random_state = 0L)

inverse_regression_confidence(x, y, level, points = NULL,
  bandwidth = NULL, tau = 1, confidence = 0.95, n_boot = 999L,
  method = "hausdorff", random_state = NULL, grid_size = 200L,
  n_folds = 5L, max_attempts = NULL)

Arguments

estimate

A di_estimate object.

band

A di_band object.

level

Finite target level.

a

First non-empty numeric vector or point matrix.

b

Second non-empty numeric vector or point matrix.

x

Numeric observations or covariates.

y

Numeric responses for inverse regression.

points

Optional evaluation grid. Density level sets accept a vector or a complete rectangular two-dimensional point matrix; inverse regression accepts a vector.

bandwidth

Optional positive bandwidth.

tau

Positive ratio h/b.

grid_size

Generated grid size when points are omitted.

confidence

Confidence level strictly between zero and one.

n_boot

Positive number of bootstrap replicates.

method

Either "hausdorff" or "inversion"; inverse regression additionally supports "normal" for a unique crossing.

random_state

Optional local random seed.

max_attempts

Maximum resamples attempted when sets are empty.

n_folds

Cross-validation folds for a regression bandwidth.

Value

Level-set and inverse-regression functions return a di_set; hausdorff_distance() returns a nonnegative scalar.

Print debiasedInference result objects

Description

Compact summaries of estimates, confidence bands, and level sets.

Usage

## S3 method for class 'di_estimate'
print(x, ...)

## S3 method for class 'di_band'
print(x, ...)

## S3 method for class 'di_set'
print(x, ...)

Arguments

x

A result object.

...

Unused.

Value

The input object, invisibly.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.