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.

Status

The package is prepared for CRAN submission. Development-only features remain on GitHub until their methodology and documentation are ready for release.

Installation

Install the development version from GitHub:

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

If the package is accepted on CRAN, installation will use:

install.packages("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)

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()`
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
Objects, summaries and plotting
Validation and comparison
Legacy estimation example

The first five articles introduce the package and the estimators. The next two 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).