Fit the tensor-design quantile regression — fit_tensor_quantile

Inner function to fit the spline coefficients of the alternating quantile algorithms: one large quantile regression of the vectorised data on the tensor-product design built from the current scores and the spline basis.

Usage

fit_tensor_quantile_regression(
  Y.vector,
  Y.mask,
  scores,
  spline.basis,
  quantile.value,
  method,
  intercept = TRUE,
  penalized = FALSE,
  lambda.ridge = 0,
  return.model = FALSE
)

Arguments

Y.vector: vectorised version of Y, the \((N \times T)\) matrix of observed time instants.
Y.mask: Mask matrix of the same dimensions as Y indicating which observations in Y are known.
scores: Matrix of scores (and / or regressors) scaling the spline blocks.
spline.basis: The spline basis matrix.
quantile.value: The quantile considered.
method: Method used in the resolution of the quantile regression model. It currently accepts the methods c('conquer', 'quantreg').
intercept: Boolean. If TRUE (default) the model contains a functional intercept; if FALSE the fit has no intercept of any kind (used by the mfqpca within level).
penalized: Boolean indicating if the smoothness should be controlled using a second derivative penalty (conquer only).
lambda.ridge: Hyper parameter controlling the penalization on the second derivative of the splines. Only used when penalized=TRUE.
return.model: Boolean. If TRUE, returns a list with the fitted model object, the spline coefficient matrix, the flat coefficient vector and the dense tensor design matrix (needed for the fosqr variance estimation).

Value

The matrix of spline coefficients (with npc + 1 columns when intercept=TRUE, npc otherwise), or the extended list when return.model=TRUE.