Build 3D Parameter Arrays for Quantile Betting

Pre-computes the dynamic, pair-specific bounding arrays (c_array) and betting fractions (lambda_array) required to evaluate the Sequential Model Confidence Set for quantile forecasts under the strong null hypothesis.

Usage

build_quantile_betting_arrays(forecasts, scores, tau, eps = 1e-08)

Arguments

forecasts

A \(T \times m\) matrix of raw quantile forecasts.

scores

A \(T \times m\) matrix of positively-oriented tick-loss scores.

tau

Numeric scalar in (0, 1). The quantile level.

eps

Numeric. Safeguard against division by zero. Default: 1e-8.

Value

A list containing two \(T \times m \times m\) numeric arrays: c_array and lambda_array.

Note

Scale Translation: This function assumes forecasts and scores are evaluated on the raw, linear scale. To replicate the exact log-scale bounds used in the Arnold et al. (2026) Covid-19 case study, the forecast matrix and outcomes must be log-transformed prior to passing them to this pipeline.

Examples

set.seed(3)
fcsts <- matrix(runif(150), nrow = 50, ncol = 3)
y <- rbinom(50, 1, 0.5)
scores <- matrix(0, nrow = 50, ncol = 3)
for(i in 1:3) scores[, i] <- tick_loss(fcsts[, i], y, tau = 0.5)

arrays <- build_quantile_betting_arrays(fcsts, scores, tau = 0.5)
dim(arrays$c_array) # 50 x 3 x 3
#> [1] 50  3  3