Numerical-bootstrap inference for a qfmix fit

Runs Algorithm 1 of Alvarez & Orestes (2024): draws Z_s ~ N(0, V_hat) from the L-moment covariance and re-solves the (local) program to obtain the sampling law of the weights, then forms confidence bands for the weights or for the mixture quantile function.

Usage

qfmix_boot(
  fit,
  S = 500L,
  kappa = "sqrt_n",
  level = 0.95,
  target = c("quantile", "weights"),
  band = c("pointwise", "uniform"),
  u = ppoints(100)
)

Arguments

fit

A "qfmix" object (fit on a numeric sample, so n is known).

S

Number of simulation draws. Default 500.

kappa

Local-set scaling for constrained sets; "sqrt_n" (default) or a number. Ignored when constraint = "unconstrained".

level

Confidence level. Default 0.95.

target

"quantile" (bands for Q_mu(u)) or "weights".

band

"pointwise" (default) or "uniform". The uniform band is a simultaneous (sup-t) band: a single critical value from the bootstrap distribution of the max studentized deviation, valid jointly over the grid by the anti-concentration argument of Chernozhukov, Chetverikov & Kato (the hyperrectangle validity the paper cites via Nazarov).

u

Probability grid for target = "quantile".

Value

A list with the point estimate, lower/upper bands, and the simulated delta.