KernSmooth

About

KernSmooth.jl is the a partial port of the R package KernSmooth, (v2.23-10.) The R package carries an unlimited license.

Currently the locpoly and dpill functions are ported. locpoly uses local polynomials to estimate pdf of a single variable or a regression function for two variables, or their derivatives. dpill provides a method to select a bandwidth for local linear regression.

Other functionality provided by the R package but not ported to KernSmooth.jl pertains to univariate and bivariate kernel density estimation. Univariate and bivariate kernel density estimation is provided by the kde function in StatsBase.jl.

Usage

locpoly - Estimate regression or density functions or their derivatives using local polynomials

The method signatures:

locpoly(x::Vector{Float64}, y::Vector{Float64}, bandwidth::Union(Float64, Vector{Float64});
    drv::Int = 0,
    degree::Int=drv+1,
    kernel::Symbol = :normal,
    gridsize::Int = 401,
    bwdisc::Int = 25,
    range_x::Vector{Float64}=Float64[],
    binned::Bool = false,
    truncate::Bool = true)

locpoly(x::Vector{Float64}, bandwidth::Union(Float64, Vector{Float64}); args...)

• x - vector of x data
• y - vector of y data. For density estimation (of x), y should be omitted or be an empty Vector{T}
• bandwidth - should be a scalar or vector of length gridsize
• Other arguments are optional. For their descriptions, see the R documentation

A (Vector{Float64}, Vector{Float64}) is returned. The first vector is the sorted set of points at which an estimate was computed. The estimates are in the second vector.

dpill - Direct plug-in method to select a bandwidth for local linear Gaussian kernel regression

The method signature

function dpill(x::Vector{Float64}, y::Vector{Float64};
               blockmax::Int = 5,
               divisor::Int = 20,
               trim::Float64 = 0.01,
               proptrun::Float64 = 0.05,
               gridsize::Int = 401,
               range_x::Vector{Float64} = Float64[],
               truncate = true)

• x - vector of x data
• y - vector of y data.
• Other arguments are optional. For their descriptions, see the R documentation

Regression example

Estimate regression using different bandwidths, including the bandwidth selected by dpill.

xgrid2, yhat0_5 = locpoly(x, y, 0.5)
yhat1_0 = locpoly(x, y, 1.0)[2]
yhat2_0 = locpoly(x, y, 2.0)[2]
h = dpill(x, y)
yhath = locpoly(x, y, h)[2]

A plot of the estimates and true regression:

The full code for the example is here.