Unconditional Density Hat Operator

Constructs the unconditional density hat operator associated with npudens bandwidth objects. The returned operator maps a right-hand side y to \(H y\); with y = 1 this reproduces the fitted unconditional density.

Usage

npudenshat(bws,
           tdat = stop("training data 'tdat' missing"),
           edat,
           y = NULL,
           output = c("matrix", "apply"))

Arguments

Data, Bandwidth Inputs And Formula Interface

These arguments identify the fitted bandwidth object, training data, and evaluation data.

bws

A fitted unconditional density bandwidth object of class "bandwidth".

edat

Optional evaluation data. If omitted, the operator is built on the training data.

tdat

Training data used to construct the operator.

Operator Output

These arguments control whether the operator is returned as a matrix or applied directly.

output

Either "matrix" for the hat matrix or "apply" for direct application to y.

y

Optional right-hand side vector or matrix with one row per training observation.

Details

For output = "matrix", the return value is a matrix with class c("npudenshat", "matrix") and attributes storing the bandwidth object, training data, evaluation data, and call metadata.

For output = "apply", the function returns H y directly. Matrix right-hand sides are applied column-wise.

This helper is intended for object-fed repeated evaluation once a bandwidth object has already been constructed. It does not perform bandwidth selection.

Value

Either a hat matrix of class "npudenshat" or the applied result H y, depending on output.

Examples

if (FALSE) { # \dontrun{
data(cps71)
tx <- data.frame(age = cps71$age)

bw <- npudensbw(dat = tx, bwtype = "fixed",
                bandwidth.compute = FALSE, bws = 1.0)

H <- npudenshat(bws = bw, tdat = tx)
dens.hat <- npudenshat(bws = bw, tdat = tx,
                       y = rep(1, nrow(tx)),
                       output = "apply")
dens.core <- fitted(npudens(bws = bw, tdat = tx))

head(cbind(dens.core, dens.hat), n = 2L)
} # }