Solve \(P(Y \le g(X) \mid W = w) = \tau\) for g. The quantile
restriction replaces the mean restriction of ordinary NPIV, and it
makes the problem NONLINEAR in g – the operator equation cannot
simply be inverted. The same ill-posedness is present and the same
regularisation is required; what changes is that linear-inverse
intuition no longer transfers directly. Mirrors
morie.fn.hrznqiv.
Usage
morie_npiv_quantile(T, tau_target, K = NULL, tau = 0.5)
Arguments
- T
numeric matrix, the discretised operator.
- tau_target
numeric target conditional probabilities.
- K
sieve truncation.
- tau
quantile level in (0, 1), recorded.
Value
list: g, K, residual_norm, tau, nonlinear, method.
References
Horowitz, Ch. 5, Sec. 5.5.1.
Examples
morie_npiv_quantile(diag(4), rep(0.5, 4))$nonlinear
#> [1] TRUE
