hessian_solver {aspline}

Inverse the hessian and multiply it by the score

Description

Inverse the hessian and multiply it by the score

Usage

hessian_solver(par, XX_band, Xy, pen, w, diff)

Arguments

par

The parameter vector

XX_band

The matrix X^T X where X is the design matrix. This argument is given in the form of a band matrix, i.e., successive columns represent superdiagonals.

Xy

The vector of currently estimated points X^T y, where y is the y-coordinate of the data.

pen

Positive penalty constant.

w

Vector of weights. Has to be of length

diff

The order of the differences of the parameter. Equals degree + 1 in adaptive spline regression.

Value

The solution of the linear system:

(X^T X + pen D^T diag(w) D) ^ {-1} X^T y - par