Estimation Diagnostics

Start Here

On This Page

Overview

NNPIV includes estimator-agnostic diagnostics under nnpiv.diagnostics. These diagnostics are optional and non-invasive: they do not modify estimator objectives, but help characterize whether a DGP appears favorable for nested sequential vs simultaneous estimation before fitting models, and (optionally) how severe relative conditioning is on the realized first-stage error direction after estimation.

Assumptions

  • Data blocks are row-aligned for \((A, C, C')\) diagnostics and optional \(e_g\) post-estimation checks.

  • Diagnostics are finite-dimensional approximations over chosen feature maps (for example RFF or polynomial sieves).

  • Conditioning conclusions are empirical and should be read jointly with sieve-size and stabilization paths.

Notation

  • \(\kappa\): pre-estimation relative well-posedness diagnostic.

  • \(\kappa_{\mathrm{eff}}\): post-estimation diagnostic along error direction \(e_g = \hat{g} - g_0\).

  • \(\eta\): stabilization level in generalized-eigenvalue computations.

Progressive Recipe

# Step 1: prepare nested NPIV blocks
from nnpiv.diagnostics import relative_wellposedness_from_nested_npiv

# Step 2: run diagnostic A
out = relative_wellposedness_from_nested_npiv(
    A=A,
    D=C_prime,
    B=B,
    C=C,
    feature_map="rff",
    n_features=300,
    eta=1e-6,
    random_state=123,
)

# Step 3: inspect key outputs
print(out["kappa"], out["nullspace_violation_flag"], out["unstable_flag"])

Canonical Diagnostics Reference