dot-get_B_gaussian_nocorr: Path 2: Gaussian Identity Link, No Correlation

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Path 2: Gaussian Identity Link, No Correlation

Description

For the canonical Gaussian case without correlation structures, the unconstrained estimate has the closed form \hat{\boldsymbol{\beta}}_k = \mathbf{G}_k \mathbf{X}_k^{\top} \mathbf{y}_k and the constrained estimate follows by a single Lagrangian projection. No iteration is needed.

Usage

.get_B_gaussian_nocorr(
  Xy,
  Ghalf,
  GhalfInv,
  A,
  K,
  p_expansions,
  R_constraints,
  constraint_value_vectors,
  family,
  return_G_getB,
  quadprog,
  qp_Amat,
  qp_bvec,
  qp_meq,
  qp_score_function,
  parallel_aga,
  parallel_matmult,
  parallel_qr,
  cl,
  chunk_size,
  num_chunks,
  rem_chunks,
  X,
  y,
  Lambda,
  order_list,
  observation_weights,
  iterate,
  tol,
  glm_weight_function,
  schur_correction_function,
  need_dispersion_for_estimation,
  dispersion_function,
  unique_penalty_per_partition,
  L_partition_list,
  VhalfInv,
  homogenous_weights,
  initial_active_ineq = integer(0),
  ...
)

Arguments

Xy	List of cross-products \mathbf{X}_k^{\top}\mathbf{y}_k by partition.
Ghalf, GhalfInv	Lists of \mathbf{G}^{1/2}_k and \mathbf{G}^{-1/2}_k matrices by partition.
A	Constraint matrix \mathbf{A}.
K, p_expansions, R_constraints	Integer dimensions.
constraint_value_vectors	Constraint RHS list encoding \mathbf{A}^{\top}\boldsymbol{\beta} = \mathbf{c}.
family	GLM family object.
return_G_getB	Logical; return covariance components.
quadprog	Logical; apply QP refinement for inequality constraints.
qp_Amat, qp_bvec, qp_meq	QP constraint specification.
qp_score_function	Score function for QP step.
parallel_aga, parallel_matmult	Logical flags.
cl, chunk_size, num_chunks, rem_chunks	Parallel parameters.
X, y, Lambda, order_list, observation_weights	Standard arguments passed through for optional QP refinement.
iterate, tol, glm_weight_function, schur_correction_function	need_dispersion_for_estimation,dispersion_function, unique_penalty_per_partition,L_partition_list,VhalfInv, homogenous_weights Standard arguments passed through.
...	Passed to sub-functions.

Details

When K = 0 and there are no inequality constraints or nonzero constraint values, the function returns \hat{\boldsymbol{\beta}} = \mathbf{G}\mathbf{X}^{\top}\mathbf{y} directly without forming the full P-dimensional OLS system.

Value

Same structure as get_B.

lgspline documentation built on Aug. 5, 2026, 1:10 a.m.