icm_subset_cpp: Iterative Convex Minorant (ICM) Subset Algorithm

In iclogcondist: Log-Concave Distribution Estimation with Interval-Censored Data

Iterative Convex Minorant (ICM) Subset Algorithm

Description

This function implements the ICM algorithm for solving the sub-problem in the active set algorithm. This is a support of the active set algorithm, computing the optimal values phi_tilde with reduced number of knots in the sub-problem. It uses backtracking to ensure convergence (Jongbloed, 1998).

Usage

icm_subset_cpp(
  phi_tilde_initial,
  is,
  tau_no_Inf,
  L_Rc,
  Lc_R,
  Lc_Rc,
  ri,
  li,
  weight,
  tol = 1e-10,
  max_iter = 500
)

Arguments

phi_tilde_initial	A numeric vector representing the initial values of the reduced variables phi_tilde.
is	A numeric vector indicating the nodes with unequal left-hand slope and right-hand slope.
tau_no_Inf	A numeric vector containing the unique time points, excluding infinity.
L_Rc	Indices of observations where the event is in the intersection of L group and the complement of R group. The L group consists of samples with left intervals time <= min(all right intervals time). The R group consists of samples with infinity right interval time.
Lc_R	Indices of observations where the event is in the intersection of the complement of L group and R group.
Lc_Rc	Indices of observations where the event is in the intersection of the complement of L group and the complement of R group.
ri	A numeric vector of indices corresponding to the right bounds of the intervals in tau_no_Inf.
li	A numeric vector of indices corresponding to the left bounds of the intervals in tau_no_Inf.
weight	A numeric vector representing the weights for each observation.
tol	A numeric value specifying the tolerance for convergence. Default is 1e-10.
max_iter	An integer specifying the maximum number of iterations. Default is 500.

Value

A list containing:

phi_tilde_hat

The estimated values of the reduced variable phi_tilde at the end of the ICM iterations.

References

Jongbloed, G.: The iterative convex minorant algorithm for nonparametric estimation. J. Comput. Gr. Stat. 7(3), 310–321 (1998)

iclogcondist documentation built on April 4, 2025, 5:18 a.m.