Minimal PLQR demo data (oracle nuisances; no internal fitting) (experimental)

Generates data for a partially linear quantile regression (PLQR) model $$ Q_{\tau}(Y \mid D, U) \;=\; D^{\top}\,\theta_{0} \;+\; g_{0}(U) \, , $$ with a user-chosen design for the nonparametric shape nuisance $g_{0}$; the demo specializes to $U = X$. Errors follow an Asymmetric Laplace distribution (ALD) at level $\tau$, so the conditional $\tau$-quantile equals the right-hand side.

Usage

plqr_demo_data(
  n = 300,
  p = 2,
  p_d = 1,
  tau = 0.5,
  sigma = 0.5,
  design = c("linear", "sinusoidal", "bump"),
  seed = NULL,
  x0 = NULL,
  inject = NULL,
  inject_col = c("Y", "g_oracle", "D1", "mD1", "rD1")[1],
  idx_inject = 3L
)

Arguments

n: Integer; sample size.
p: Integer; number of features in $X$ (recommend $p \ge 2$).
p_d: Integer; dimension of $D$ (number of partially linear regressors).
tau: Quantile level in $(0,1)$.
sigma: Positive ALD scale for the regression error (larger means noisier $Y$).
design: Character; one of "linear", "sinusoidal", "bump" for $g_{0}$.
seed: Optional integer seed.
x0: Optional target point in $\mathbb{R}^{p}$ for localization (defaults to the zero vector).
inject: Optional, one of NULL, "na", "inf"; if provided, inject a single non-finite into inject_col at row idx_inject. Useful for testing runtime guards.
inject_col: Character; which column to corrupt when inject is not NULL. One of "Y", "g_oracle", "D1", "mD1", "rD1" (extend as needed).
idx_inject: Integer row index to corrupt (default 3).

Value

A list with:

data: a data.frame with columns X1..Xp, D1..Dp_d, Y; oracle nuisances g_oracle (the value of $g_{0}(X)$), mD1..mDp_d (components of $m_{D}(X)$), residuals rD1..rDp_d (components of $D - m_{D}(X)$), and density_oracle, the true conditional density of $Y$ at the quantile threshold. Because the demo's ALD errors are independent of $(X, D)$ and homoskedastic, this density is constant, $f(0) = 4\tau(1-\tau)/\sigma$.
x0: the target point used.
truth: a list with theta_true (length p_d), g_fn(x) and mD_fn(x) closures to evaluate ground truth at new $X$, and density_fn(v), the error density at signed distance $v$ from the quantile threshold (density_fn(0) is the density_oracle value).
g_x0: the true value $g_{0}(x_{0})$.

Details

The function also returns the oracle $m_{D}(U) \equiv \mathbb{E}[D \mid U]$ to build the orthogonal PLQR score $$ \psi(W;\theta) \;=\; (\tau - \mathbf{1}\{\,Y \le D^{\top}\theta + g_{0}(U)\,\})\, (D - m_{D}(U))\, . $$

Lifecycle

Experimental. PLQR functionality is outside the CATE and regression workflow focus of the initial public release. Its API and inference interfaces may change in later releases.

Examples

demo <- plqr_demo_data(
  n = 300, p = 2, p_d = 1, tau = 0.5,
  design = "sinusoidal", seed = 1
)
head(demo$data)
#>           X1         X2         D1          Y    g_oracle        mD1
#> 1 -0.6264538  0.8936737 -0.9379820 -1.0859139 -0.09347465 -0.7333418
#> 2  0.1836433 -1.0472981  1.4305600  0.9953984  0.36551477  0.5291053
#> 3 -0.8356286  1.9713374 -0.9729275  0.1560512  0.60068363 -1.2899121
#> 4  1.5952808 -0.3836321  1.4359361  1.2727712  0.53664353  1.1106213
#> 5  0.3295078  1.6541453 -0.5459575  0.6313299  0.84583783 -0.4639535
#> 6 -0.8204684  1.5122127 -1.7792064 -0.6906623  0.20596416 -1.0971661
#>           rD1 density_oracle
#> 1 -0.20464019              2
#> 2  0.90145472              2
#> 3  0.31698463              2
#> 4  0.32531481              2
#> 5 -0.08200401              2
#> 6 -0.68204031              2
demo$truth$theta_true
#> [1] 0.5
demo$g_x0
#> [1] 0