moderndid.compute_cck_ucb#

moderndid.compute_cck_ucb(y, x, w, x_eval=None, alpha=0.05, boot_num=99, basis='tensor', j_x_degree=3, k_w_degree=4, knots='uniform', ucb_h=True, ucb_deriv=True, deriv_index=1, deriv_order=1, w_min=None, w_max=None, x_min=None, x_max=None, seed=None, selection_result=None)[source]#

Compute honest and adaptive UCBs.

Implements the data-driven uniform confidence band (UCB) construction from [1]. These UCBs are honest, guaranteeing uniform coverage over a class of data-generating processes, and adaptive, contracting at or near the minimax optimal rate.

The UCB for \(h_0\) is constructed as

\[C_n(x) = \left[\hat{h}_{\tilde{J}}(x) \pm \text{cv}^*(x) \hat{\sigma}_{\tilde{J}}(x)\right],\]

where \(\tilde{J}\) is the data-driven dimension choice. The critical value \(\text{cv}^*(x)\) is a combination of a bootstrap quantile \(z_{1-\alpha}^*\) and a penalty term involving the critical value from the dimension selection step, \(\theta_{1-\hat{\alpha}}^*\).

For models in the “mildly ill-posed” regime (including nonparametric regression), the critical value is

\[\text{cv}^*(x) = z_{1-\alpha}^* + (\log\log\tilde{J}) \theta_{1-\hat{\alpha}}^*.\]

The quantile \(z_{1-\alpha}^*\) is the \((1-\alpha)\) quantile of

\[\sup_{(x,J) \in \mathcal{X} \times \hat{\mathcal{J}}_-} |D_J^*(x) / \hat{\sigma}_J(x)|\]

ensuring robustness to the choice of \(J\). A similar construction applies to the derivatives of \(h_0\). This method provides efficiency improvements over traditional undersmoothing by adapting to the data.

Parameters:

ynumpy.ndarray: Dependent variable vector.
xnumpy.ndarray: Endogenous regressor matrix.
wnumpy.ndarray: Instrument matrix.
x_evalnumpy.ndarray, optional: Evaluation points for X. If None, uses x.
alphafloat, default=0.05: Significance level (1-alpha confidence level).
boot_numint, default=99: Number of bootstrap replications.
basis{“tensor”, “additive”, “glp”}, default=”tensor”: Type of basis for multivariate X.
j_x_degreeint, default=3: Degree of B-spline basis for X.
k_w_degreeint, default=4: Degree of B-spline basis for W.
knots{“uniform”, “quantiles”}, default=”uniform”: Knot placement method.
ucb_hbool, default=True: Whether to compute confidence bands for function estimates.
ucb_derivbool, default=True: Whether to compute confidence bands for derivative estimates.
deriv_indexint, default=1: Index (1-based) of X variable for derivative computation.
deriv_orderint, default=1: Order of derivative to compute.
w_minfloat, optional: Minimum value for W range.
w_maxfloat, optional: Maximum value for W range.
x_minfloat, optional: Minimum value for X range.
x_maxfloat, optional: Maximum value for X range.
seedint, optional: Random seed for reproducibility.
selection_resultdict, optional: Result from data-driven selection.

Returns:

NPIVResult: NPIV results with CCK uniform confidence bands.