densityLP

Local Polynomial Density Estimation on Complicated Domains

densityLP implements the nonparametric local polynomial density estimator of Bertin, Klutchnikoff and Ouimet (Bernoulli, forthcoming) for multivariate densities on known domains of arbitrary dimension, including domains with sharp concavities, holes, and polynomial sectors. The C++ backend (RcppArmadillo) provides a ×10 speedup over a pure-R implementation.

Installation

# Development version
remotes::install_github("nklutchnikoff/densityLP")

Quick start

Local linear estimation on the unit square

library(densityLP)

set.seed(1L)
n <- 500L
X <- matrix(runif(n * 2L), n, 2L)   # uniform on [0,1]^2

is_square <- function(x, y) x >= 0 & x <= 1 & y >= 0 & y <= 1
dom       <- domain_from_indicator(is_square)

grid  <- seq(0.1, 0.9, length.out = 20L)
t_grid <- as.matrix(expand.grid(x = grid, y = grid))

fit <- density_lp(X, t_grid = t_grid, h = 0.2, m = 1L,
                  domain = dom, N_quad = 500L)
plot(fit, main = "Local linear estimate — unit square")

## Warning in plot.density_lp(fit, main = "Local linear estimate — unit square"):
## plot.density_lp: no default graphical method for d = 2. Using scatter plot.

Spatial point pattern on an L-shaped domain

density_lp_ppp() accepts any ppp object from spatstat. It derives the evaluation grid and the integration domain automatically from Window(pp) and returns a spatstat.geom::im pixel image.

library(spatstat.geom)

## Loading required package: spatstat.data

## Loading required package: spatstat.univar

## spatstat.univar 3.1-7

## spatstat.geom 3.7-3

library(spatstat.random)

## spatstat.random 3.4-5

# L-shaped window and inhomogeneous Poisson process
L_win <- owin(poly = list(x = c(0, 2, 2, 1, 1, 0),
                          y = c(0, 0, 1, 1, 2, 2)))

lambda_fun <- function(x, y) {
  400 * exp(-4 * ((x - 1.5)^2 + (y - 0.4)^2)) +
    150 * exp(-4 * ((x - 0.3)^2 + (y - 1.5)^2))
}

set.seed(2L)
pp  <- rpoispp(lambda_fun, win = L_win)
fit <- density_lp_ppp(pp, h = 0.3, m = 1L, N_quad = 500L)

plot(fit, main = "Local linear estimate — L-shaped domain")
plot(pp, add = TRUE, pch = ".", col = "#00000050")

Pixels outside the window are automatically set to NA.

Vignettes

Vignette	Description
convergence	MSE convergence study on the cube and a polynomial sector
benchmark	R vs C++ timing: gram_matrix and full pipeline
spatstat	density_lp_ppp on synthetic spatial point patterns

Reference

Bertin, K., Klutchnikoff, N. and Ouimet, F. (forthcoming). Local polynomial estimation of the density on complicated domains. Bernoulli.