Kaplan-Meier Z-estimator map — morie_survival

\(\Psi(S)(t) = S_0(t)L(t) + \int_0^t [S_0(u)/S(u)]dG(u)S(t) - S(t)\) (Eq. 2.11, p. 26), implemented exactly as printed.

Usage

morie_survival_psi(S, t_grid, S0, L, G)

Arguments

S: candidate survival function on t_grid.
t_grid: the grid everything is supplied on.
S0, L, G: the section's components, on t_grid.

Value

list: t_grid, psi, sup_norm, parameter_is, norm, components_supplied, n, method.

Details

\(S_0\), \(L\) and \(G\) are SUPPLIED rather than inferred. The section fixes them for its own censoring model, and the passage stating (2.11) does not define them unambiguously enough to reconstruct; plausible empirical stand-ins were tried and do NOT make Kaplan-Meier a root, so guessing would have produced a module that looked right and was wrong.

Survival analysis becomes Z-ESTIMATION: the estimator is characterised as the zero of a map between function spaces, and Chapter 2's theory then supplies consistency, weak convergence and the bootstrap at once. The parameter is a FUNCTION and the norm is uniform. Mirrors morie.fn.ksr047.

References

Kosorok, Ch. 2, Eq. (2.11), p. 26.

Examples

g <- seq(0.1, 2, length.out = 20)
morie_survival_psi(exp(-g), g, exp(-g), exp(-0.5 * g),
                   1 - exp(-0.3 * g))$sup_norm
#> [1] 0.05258647