Fit the Low-Level LHWR Model from Lorentz kNN Neighborhoods

Fit adaptive k-nearest-neighbor LHWR directly from Lorentz hyperboloid coordinates without constructing a full pairwise distance matrix. This is a low-level performance-oriented routine. For compact kernels such as "bisquare", "tricube", and "boxcar", it is algebraically equivalent to hgwr.fit() with bandwidths equal to the Lorentz radius of the kth nearest neighbor at each focal point.

Usage

hgwr.fit.knn(
  y,
  X,
  Z,
  k,
  kernel = c("bisquare", "tricube", "boxcar"),
  return_hat = TRUE,
  tol = 1e-06,
  check = TRUE,
  n_threads = 1L
)

Arguments

y

Numeric response vector of length n.

X

Numeric n x p model matrix.

Z

Numeric n x 3 Lorentz hyperboloid coordinate matrix.

k

Adaptive nearest-neighbor count. The local fit uses the focal observation and its k nearest neighbors under Lorentz distance.

kernel

Compactly supported kernel. Available exact choices are "bisquare", "tricube", and "boxcar".

return_hat

Logical. If TRUE, compute hat-matrix diagnostics and unscaled local standard-error components.

tol

Numerical tolerance used in Lorentz distance clipping.

check

Logical. If TRUE, validate that Z lies on the upper Lorentz hyperboloid before fitting.

n_threads

Number of OpenMP threads used by the kNN local fitting loop when OpenMP is available. The default 1 gives deterministic serial execution and is used automatically on systems without OpenMP support.

Value

A list in the same format as hgwr.fit(), with an additional bandwidth vector containing the focal Lorentz kNN radii.

Examples

set.seed(7)
H <- simulate_H2(50, r_max = 3)
X <- cbind(Intercept = 1, x = rnorm(50))
y <- 1 + 2 * X[, "x"] + rnorm(50, sd = 0.2)
fit <- hgwr.fit.knn(y, X, H$Z, k = 20)
head(fit$beta_hat)