nx_estimator_diagnostics.nx

nx_estimator_diagnostics.nx -- substrate primitive for bias-variance decomposition of estimator outputs. THEORY (cited from first principles, NOT folklore): For an estimator T̂ of a true parameter θ, the Mean Squared Error decomposes as: MSE(T̂) = E[(T̂ - θ)²] = Var(T̂) + [Bias(T̂)]² where Bias(T̂) = E[T̂] - θ and Var(T̂) = E[(T̂ - E[T̂])²]. Source: Lehmann & Casella, "Theory of Point Estimation" 2nd ed., Springer 1998, eqs. 1.5.1, 1.5.2. Same decomposition appears in every statistics textbook (Casella-Berger §7.3, Wasserman §6.3). Interpretation for an HLL-vs-DS comparison: - If our mean_err > DS mean_err but our max_err < DS max_err, we have HIGHER BIAS but LOWER VARIANCE. The math says we should debias the estimator. Fix class: FX11 RecalibrateTable, or post-hoc bias correction term. - If our mean_err < DS mean_err but our max_err > DS max_err, we have LOWER BIAS but HIGHER VARIANCE. Add ensemble averaging (HIP estimator) or shrinkage. - If both worse: estimator class is fundamentally weaker; consider algorithm swap (FX02). Beyond the first two moments, we expose: - skewness: (third central moment) / sigma³ -- detects asymmetric error - excess kurtosis: (fourth central moment) / sigma⁴ - 3 -- detects heavy tails (matters for max-error comparison) All computed in i64 fixed-point at PPB (parts per billion) precision. genealogy_id: lehmann_casella_1998 + pearson_skewness_1895 lineage_id: estimator_theory + moment_method