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, fixed-grid leave-one-out D_i scores, S3 summaries and predictions, and plug-in bandwidth selection.

Status

The package is available on CRAN. The GitHub development version may include features that are not yet part of the CRAN release while their methodology and documentation are being finalized.

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 CRAN release:

install.packages("GLBFP")

Install the development version from GitHub:

install.packages("remotes")
remotes::install_github("AurelienNicosiaULaval/GLBFP")

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

scores <- compute_di(river_data, b = b, m = c(1, 1), estimator = "GLBFP")
summary(scores)
head(as.data.frame(scores))
plot(scores)

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(), 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:

1. Getting started with GLBFP
2. Package overview and workflow map
3. Brief methodological background
4. Choosing between ASH, LBFP and GLBFP
5. Two-dimensional density estimation
6. Sparse-prefix computation
7. Leave-one-out D_i diagnostics
8. Objects, summaries and plotting
9. Validation and comparison
10. 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).