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Generic weight builder for parametric GWAS

make_weights_generic.Rd

Constructs a tau-by-K weight matrix \(W\) for an arbitrary parametric family, mapping RIF tau-slopes \(b(tau)\) into parameter effects.

Usage

make_weights_generic(
  taus,
  q_tau,
  dist_cdf,
  dist_pdf,
  params,
  grad_funcs,
  tiny = 1e-12
)

Arguments

taus

Numeric vector of quantile levels (length T).

q_tau

Numeric vector of baseline quantiles at taus (length T).

dist_cdf

Function (y, params) -> numeric. CDF of the distribution.

dist_pdf

Function (y, params) -> numeric. PDF of the distribution.

params

Named list of baseline parameters (e.g., list(mu = 0, sd = 1)).

grad_funcs

Named list of gradient functions. Each element is a function (y, params) -> numeric giving derivative of F(y; params) wrt that parameter. Can be analytic, or constructed with make_fd_grad().

tiny

Small positive floor to stabilize divisions (\(f(q_tau)\) clamped).

Value

A T x K numeric matrix of weights with columns named by parameter.

Details

The generic approach uses the identity: $$W_j(tau) = - (dF/dtheta_j)(q_tau; params) / f(q_tau; params),$$ where \(F\) is the CDF and \(f\) is the PDF.

Examples

taus <- seq(0.1, 0.9, 0.1)
y <- rnorm(5000, 2, 1)
q_tau <- as.numeric(quantile(y, taus, type = 8))

dist_cdf <- function(y, params) pnorm(y, mean = params$mu, sd = params$sd)
dist_pdf <- function(y, params) dnorm(y, mean = params$mu, sd = params$sd)
grad_mu  <- function(y, params) -dnorm((y - params$mu)/params$sd)/params$sd
grad_sd  <- function(y, params) { z <- (y - params$mu)/params$sd; -(z*dnorm(z))/params$sd }

W <- make_weights_generic(
  taus, q_tau, dist_cdf, dist_pdf,
  params = list(mu = 2, sd = 1),
  grad_funcs = list(beta_mu = grad_mu, beta_sd = grad_sd)
)