Nonparametric Regression Hat Operator

Constructs nonparametric regression hat operators for npreg-compatible bandwidth objects. The returned operator \(H^{(s)}\) maps responses to fitted values or derivative estimates via \(H^{(s)} y\).

Usage

npreghat(bws, ...)

# S3 method for class 'formula'
npreghat(bws, 
         data = NULL, 
         newdata = NULL, 
         ...)

# S3 method for class 'rbandwidth'
npreghat(bws,
         txdat = stop("training data 'txdat' missing"),
         exdat, y = NULL,
         output = c("matrix", "apply", "constraint"),
         basis = NULL,
         bernstein.basis = NULL,
         degree = NULL,
         deriv = NULL,
         leave.one.out = FALSE,
         ridge = 0,
         s = NULL, 
         ...)

# S3 method for class 'npregression'
npreghat(bws, 
         txdat, 
         y, 
         ...)

# S3 method for class 'npreghat'
predict(object, 
        newdata = NULL, y = NULL,
        output = c("matrix", "apply", "constraint"),
        s = attr(object, "s"),
        leave.one.out = attr(object, "leave.one.out"),
        deriv = NULL, 
        ...)

Arguments

Data, Bandwidth Inputs And Formula Interface

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

bws: An object of class rbandwidth or npregression.
data: A data frame used with the formula interface.
exdat: Optional evaluation predictors.
newdata: Optional evaluation data for formula and predict methods.
txdat: Training predictors.

Local-Polynomial Controls

These arguments control local-polynomial basis, degree, derivatives, leave-one-out behavior, and ridge stabilization.

basis: Local polynomial basis: "glp", "additive", or "tensor".
bernstein.basis: Logical; use Bernstein basis for LP terms.
degree: Optional local polynomial degree vector override (LP path).
deriv: Convenience alias for s.
leave.one.out: Logical; if TRUE, compute in-sample leave-one-out hat weights. This cannot be combined with explicit exdat/newdata.
ridge: Base diagonal regularization used when local systems are ill-conditioned. The ridge sequence starts at 0 (no regularization) and then increments by 1/n.train as needed for stable solves.
s: Derivative multi-index over continuous predictors.

Method Objects

This argument identifies a fitted hat-operator object supplied to an S3 method.

object: An object returned by npreghat.

Operator Output

These arguments control whether the operator is returned as a matrix, applied directly, or returned as a quadratic-programming constraint design matrix.

output: Either "matrix" for the hat matrix, "apply" for direct application to y, or "constraint" for the row-weighted transpose t(H) * y.
y: Optional response vector or matrix for apply mode. For output = "constraint", y is required and must be a vector or one-column object.

Additional Arguments

Further arguments are passed to methods.

...: Additional arguments passed to methods.

Details

For output = "matrix", the return value is a matrix with class c("npreghat", "matrix") so it can be used directly in matrix products, e.g. H %*% y. Attributes on the matrix store metadata used by predict.npreghat.

For output = "apply", the function returns H^{(s)} y directly and accepts matrix right-hand sides for one-shot bootstrap-style calculations.

For output = "constraint", the function returns t(H^{(s)}) * y, the row-weighted transpose commonly used as the design matrix in shape-constrained quadratic-programming examples. This is a convenience route that is exactly equivalent to obtaining H with output = "matrix" and then computing t(H) * y; it does not solve a constrained estimation problem.

Value

Either a hat matrix (class "npreghat") or the applied result H^{(s)} y, or the constraint design matrix t(H^{(s)}) * y, depending on output.

Examples

if (FALSE) { # \dontrun{
data(cps71)
bw <- npregbw(xdat = cps71$age, ydat = cps71$logwage,
              regtype = "ll", bandwidth.compute = FALSE, bws = 1.0)
H <- npreghat(bws = bw, txdat = data.frame(age = cps71$age))
H.fitted <- H 
A <- npreghat(bws = bw, txdat = data.frame(age = cps71$age),
              y = cps71$logwage, output = "constraint")
all.equal(A, t(H) * cps71$logwage)
ghat <- npreg(bws = bw)
head(cbind(fitted(ghat), H.fitted), n = 2L)
} # }