biasBound_density {rbbnp}

Bias bound approach for density estimation

Description

Estimates the density at a given point or across a range, and provides visualization options for density, bias, and confidence intervals.

Usage

biasBound_density(
  X,
  x = NULL,
  h = 0.09,
  alpha = 0.05,
  resol = 100,
  xi_lb = NULL,
  xi_ub = NULL,
  methods_get_xi = "Schennach",
  if_plot_density = TRUE,
  if_plot_ft = FALSE,
  ora_Ar = NULL,
  kernel.fun = "Schennach2004",
  if_approx_kernel = TRUE,
  kernel.resol = 1000
)

Arguments

X

A numerical vector of sample data.

x

Optional. A scalar or range of points where the density is estimated. If NULL, a range is automatically generated.

h

A scalar bandwidth parameter.

alpha

Confidence level for intervals. Default is 0.05.

resol

Resolution for the estimation range. Default is 100.

xi_lb

Optional. Lower bound for the interval of Fourier Transform frequency xi. Used for determining the range over which A and r is estimated. If NULL, it is automatically determined based on the methods_get_xi.

xi_ub

Optional. Upper bound for the interval of Fourier Transform frequency xi. Similar to xi_lb, it defines the upper range for A and r estimation. If NULL, the upper bound is determined based on the methods_get_xi.

methods_get_xi

A string specifying the method to automatically determine the xi interval if xi_lb and xi_ub are NULL. Options are "Schennach" and "Schennach_loose". If "Schennach" the range is selected based on the Theorem 2 in Schennach2020, if "Schennach_loose", it is defined by the initial interval given in Theorem 2 without selecting the xi_n.

if_plot_density

Logical. If TRUE, plots the density estimation.

if_plot_ft

Logical. If TRUE, plots the Fourier transform.

ora_Ar

Optional list of oracle values for A and r.

kernel.fun

A string specifying the kernel function to be used. Options are "Schennach2004", "sinc", "normal", "epanechnikov".

if_approx_kernel

Logical. If TRUE, uses approximations for the kernel function.

kernel.resol

The resolution for kernel function approximation. See fun_approx.

Value

A list containing various outputs including estimated values, plots, and intervals.

Examples

# Example 1: Specifying x for point estimation with manually selected xi range from 1 to 12
biasBound_density(
  X = sample_data$X,
  x = 1,
  h = 0.09,
  xi_lb = 1,
  xi_ub = 12,
  if_plot_ft = TRUE,
  kernel.fun = "Schennach2004"
)

# Example 2: Density estimation with manually selected xi range from 1 to 12 xi_lb and xi_ub
# biasBound_density(
#   X = sample_data$X,
#   h = 0.09,
#   xi_lb = 1,
#   xi_ub = 12,
#   if_plot_ft = FALSE,
#   kernel.fun = "Schennach2004"
# )

# Example 3: Density estimation with automatically selected xi range via Theorem 2 in Schennach 2020
#  biasBound_density(
#   X = sample_data$X,
#   h = 0.09,
#   methods_get_xi = "Schennach",
#   if_plot_ft = TRUE,
#   kernel.fun = "Schennach2004"
# )