info_cox: Compute Cox Observed Information Matrix

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Compute Cox Observed Information Matrix

Description

Negative Hessian of the Cox partial log-likelihood under the Breslow approximation for tied event times. Data must be sorted by ascending event time.

Usage

info_cox(X, eta, status, y = NULL, weights = 1)

Arguments

X	Design matrix (N x p), sorted by ascending event time.
eta	Linear predictor vector.
status	Event indicator (1 = event, 0 = censored).
y	Optional numeric vector of observed event/censor times, same length and order as eta. When supplied, tied event times are handled with the Breslow approximation. When omitted, the function assumes there are no ties.
weights	Observation weights (default 1).

Details

Under the Breslow approximation, the observed information is

\sum_g d_g^{(w)} \Bigl[\frac{S_{2g}}{S_{0g}} - \Bigl(\frac{S_{1g}}{S_{0g}}\Bigr) \Bigl(\frac{S_{1g}}{S_{0g}}\Bigr)^{\top}\Bigr]

where S_{0g} = \sum_{j \in R_g} w_j e^{\eta_j}, S_{1g} = \sum_{j \in R_g} w_j e^{\eta_j}\mathbf{x}_j, and S_{2g} = \sum_{j \in R_g} w_j e^{\eta_j}\mathbf{x}_j\mathbf{x}_j^{\top}.

Value

Symmetric p x p observed information matrix.

lgspline documentation built on May 8, 2026, 5:07 p.m.