crshat: CRS Hat Operator

Description

Construct or apply the linear hat operator for fixed-structure CRS mean regression fits. The helper is intended for fixed-\(X\) workflows such as fast plot bootstrapping and constrained-estimation diagnostics.

Usage

crshat(object, ...)
# S3 method for crs
crshat(object, 
       newdata = NULL, 
       y = NULL,
       output = c("matrix", "apply", "constraint"), 
       deriv = 0,
       deriv.index = 1, 
       rcond.min = 1e-08, 
       use.svd.fallback = TRUE, 
       ...)

Value

For output="matrix", a matrix of dimension nrow(newdata) x nrow(training data). For output="apply", fitted values produced by applying the operator to y. For output="constraint", the transpose operator scaled by the supplied one-column response vector.

Arguments

object: A fitted mean-regression object of class "crs".
newdata: Optional evaluation data. If omitted, the training data are used.
y: Optional response vector or matrix. Required for output="constraint"; when supplied with output="apply", the operator is applied directly without returning a dense hat matrix.
output: One of "matrix", "apply", or "constraint".
deriv: Non-negative integer derivative order. deriv=0 returns the fitted-mean hat operator. Positive values return the derivative hat operator for continuous predictor deriv.index.
deriv.index: Positive integer identifying the continuous predictor whose derivative operator is requested.
rcond.min: Minimum reciprocal condition number used by the weighted least-squares primitive before falling back to QR/SVD policy.
use.svd.fallback: Logical value controlling the weighted least-squares fallback policy.
...: Additional arguments, currently unused.

Details

For a fitted CRS mean-regression object, crshat() returns the linear operator mapping the training response to fitted values at newdata. The default output="matrix" returns a dense matrix with class c("crshat", "matrix"). The output="apply" route applies the same operator to y and is preferable when many right-hand sides are needed.

The helper preserves the fitted object's fixed spline/kernel structure, including basis family, degree, segments, pruning state, categorical-kernel bandwidths, weights, and the package's weighted least-squares rank policy. It does not run bandwidth or degree selection.

For deriv > 0, crshat() returns the derivative operator \(H^{(s)}\) such that \(H^{(s)} y\) matches the corresponding CRS gradient prediction at newdata. This is the CRS analogue of npreghat's derivative-selector behavior in np. Derivative operators are available for fixed-structure mean CRS fits across additive, tensor, and GLP bases, including categorical-kernel fits. If the requested derivative order exceeds the fitted spline degree for that predictor, the returned operator is zero.

Quantile CRS objects remain intentionally unsupported because quantile estimation is not linear in the response.

Examples

Run this code

set.seed(42)
x <- runif(30)
y <- sin(2 * pi * x) + rnorm(30, sd = 0.1)
fit <- crs(y ~ x, cv = "none", degree = 2, segments = 1,
           display.warnings = FALSE, display.nomad.progress = FALSE)
nd <- data.frame(x = seq(0.1, 0.9, length.out = 5))
H <- crshat(fit, newdata = nd)
drop(H %*% fit$y)
crshat(fit, newdata = nd, output = "apply")
Hd <- crshat(fit, newdata = nd, deriv = 1, deriv.index = 1)
drop(Hd %*% fit$y)