KernSmooth

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.

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.

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

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.