GLBFP

GLBFP is an R package for histogram-based nonparametric density estimation. It implements:

Averaged Shifted Histogram estimators: ASH(), ASH_estimate()
Linear Blend Frequency Polygon estimators: LBFP(), LBFP_estimate()
General Linear Blend Frequency Polygon estimators: GLBFP(), GLBFP_estimate()

The package supports pointwise density estimation, regular-grid estimation, 1D and 2D plotting, sparse-prefix grid-count computation, S3 summaries and predictions, and plug-in bandwidth selection. The GitHub development version also includes fixed-grid leave-one-out D_i diagnostics.

Release status

Source	Version	Fixed-grid `D_i` diagnostics
CRAN	0.5.2	Not included
GitHub `main`	0.5.2.9000	Development only: `compute_Di()`

CRAN 0.5.2 is the stable density-estimation release. The leave-one-out diagnostic developed in Nicosia, Duchesne and Carbon (2026) is available only in the GitHub development version while its software interface and CRAN integration are being finalized. The article studies the single-grid LBFP case. The development package also exposes the same fixed-grid deletion diagnostic for ASH and GLBFP as software extensions.

The article's project-specific replication package uses a separate internal R package, LOOLBFP, for the single-grid calculations reported in the paper. In an audit comparison, LOOLBFP and GLBFP::compute_Di(..., estimator = "LBFP") agreed to floating-point precision when given equivalent fixed grids. Their default grid anchors differ, however, so calls using both packages' defaults need not return identical numerical scores. Use LOOLBFP for exact reproduction of the submitted article results.

Part of the research ecosystem

This repository is part of Aurélien Nicosia's open research and teaching ecosystem in computational statistics, scientific R software, reproducible data science and statistical education.

Research Lab: https://aureliennicosiaulaval.github.io/web_site/research-lab.html
GitHub profile: https://github.com/AurelienNicosiaULaval
Related projects: grid-density-sparse-traversal

Installation

Install the stable CRAN release, which does not include D_i:

install.packages("GLBFP")

Install the GitHub development version to use D_i:

install.packages("remotes")
# remotes::install_github("AurelienNicosiaULaval/GLBFP")
install.packages("GLBFP", repos = c('https://aureliennicosiaulaval.r-universe.dev', 'https://cloud.r-project.org'))

Quick start

library(GLBFP)

set.seed(2026)
x <- matrix(rnorm(300), ncol = 1)
b <- compute_bi_optim(x, m = 1)

fit <- glbfp(x = 0, data = x, b = b, m = 1)
fit
summary(fit)
predict(fit)

Uppercase function names remain available and are the historical API:

fit_upper <- GLBFP(x = 0, data = x, b = b, m = 1)
identical(fit$estimation, fit_upper$estimation)

Two-dimensional workflow

library(GLBFP)

data("ashua")

river_data <- ashua[, c("flow", "level")]
b <- c(8, 0.4)
x0 <- c(mean(river_data$flow), mean(river_data$level))

point_fit <- glbfp(x = x0, data = river_data, b = b, m = c(1, 1))
point_fit

grid_fit <- glbfp_estimate(
  data = river_data,
  b = b,
  m = c(1, 1),
  grid_size = 20
)

summary(grid_fit)
head(as.data.frame(grid_fit))
plot(grid_fit, contour = TRUE)

Leave-one-out diagnostics (development version only)

The following example uses the single-grid LBFP setting studied in the article. The grid and bandwidth remain fixed when each observation is deleted.

scores <- compute_Di(river_data, b = b, estimator = "LBFP")
summary(scores)
head(as.data.frame(scores))
plot(scores)

D_i measures local self-support under the fitted estimator. It is a diagnostic score, not an estimated probability that an observation is an outlier.

Main functions

Task	Functions
Pointwise density estimation	`ASH()`, `LBFP()`, `GLBFP()`
Grid-based density estimation	`ASH_estimate()`, `LBFP_estimate()`, `GLBFP_estimate()`
Lowercase aliases	`ash()`, `lbfp()`, `glbfp()`, `ash_estimate()`, `lbfp_estimate()`, `glbfp_estimate()`
Leave-one-out diagnostics	`compute_Di()`
Bandwidth helper	`compute_bi_optim()`
Bandwidth constants	`K_mi()`, `G_i()`, `compute_G_star()`
S3 helpers	`print()`, `summary()`, `predict()`, `plot()`, `as.data.frame()`

Documentation

The pkgdown site is organized as a reading path:

Getting started with GLBFP
Package overview and workflow map
Brief methodological background
Choosing between ASH, LBFP and GLBFP
Two-dimensional density estimation
Sparse-prefix computation
Leave-one-out D_i diagnostics
Objects, summaries and plotting
Validation and comparison
Legacy estimation example

The first five articles introduce the package and the estimators. The next three articles document implementation diagnostics and S3 behavior. The validation article gives a lightweight reproducible benchmark, while the legacy vignette is kept for backward compatibility.

References

General background on frequency polygons, averaged shifted histograms, and multivariate density estimation is available in:

Carbon, M., and Duchesne, T. (2024). Multivariate frequency polygon for stationary random fields. Annals of the Institute of Statistical Mathematics, 76(2), 263-287. doi:10.1007/s10463-023-00883-5.
Scott, D. W. (1992). Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley. doi:10.1002/9780470316849.
Terrell, G. R., and Scott, D. W. (1985). Oversmoothed Nonparametric Density Estimates. Journal of the American Statistical Association, 80(389), 209-214. doi:10.1080/01621459.1985.10477163.

The complete bibliographic record for the original GLBFP methodological article has not yet been verified in this repository. It is tracked in dev/references_to_verify.md and should be added before journal submission.

Citation

To cite the package from R:

citation("GLBFP")

The repository also includes CITATION.cff for software citation metadata.

Development checks

devtools::document()
devtools::test()
devtools::check()
rcmdcheck::rcmdcheck(args = c("--as-cran"))

Benchmarks are stored in benchmarks/ and are not run automatically during R CMD check.

Contributing

Please use GitHub issues and pull requests: https://github.com/AurelienNicosiaULaval/GLBFP/issues

License

GPL (>= 3).