LogDensity

(logf, β) = logdensity( X, x, h; various optional arguments )

Computes estimates of the log density and its derivatives of the data 
in the vector X evaluated at the elements in the vector x, using the 
bandwidth h. Returns a tuple ( logf, β ) where logf is a vector whose
elements correspond to the evaluation points and β a matrix with rows 
corresponding to the evaluation points and columns to the derivatives;  
this is a matrix even if S = 1.

Mandatory arguments

• X::Vector{T}: vector of data
• x::Vector{T}: vector of evaluation points
• h::T: bandwidth

T is a floating point type

Optional arguments

• g::Function=g: the function g to be used (see Pinkse and Schurter)
• dg::Function=dg: its derivative
• S::Int=1: the number of derivatives to be computed
• minx::T=0.0: the left hand side of the support
• maxx::T=Inf: the right hand side of the support
• logf::Bool=true: whether the log density itself should be computed
• mz::Function=LogDensity.epanechnikov: the kernel to be used for the log density itself
• anal::Bool=true: whether to run many sanity checks

Other choices for the kernel are: LogDensity.quartic LogDensity.gaussian LogDensity.triweight LogDensity.uniform LogDensity.cosinus

β = logdensityderivatives( X, x, h; various optional arguments )

Computes estimates of the derivatives of the log density of the data 
in the vector X evaluated at the elements in the vector x, using the 
bandwidth h. Returns a matrix β with rows corresponding to the 
evaluation points and columns to the derivatives.  This is a matrix
even if S = 1.

Mandatory arguments

• X::Vector{T}: vector of data
• x::Vector{T}: vector of evaluation points
• h::T: bandwidth

T is a floating point type

Optional arguments

• g::Function=g: the function g to be used (see Pinkse and Schurter)
• dg::Function=dg: its derivative
• S::Int=1: the number of derivatives to be computed
• minx::T=0.0: the left hand side of the support
• maxx::T=Inf: the right hand side of the support
• anal::Bool=true: whether to run many sanity checks