Stat

Statistical foundations: convergence modes, limit theorems, concentration inequalities, and minimax lower-bound tools.

Sample 52 to review 69 core · 49 supporting · 6 submodules This file provides the library's causal-agnostic model of an independent and identically distributed sample on a common ambient probability space. Limit 15 core · 21 supporting · 6 submodules Convergence concepts: convergence in probability and distribution, continuous mapping, and Slutsky-style composition rules. CLT 24 core · 20 supporting · 9 submodules Central limit theory: iid and triangular-array CLTs, Lindeberg conditions, and vector-valued versions used by the estimation layer. Empirical­Process 20 core · 13 supporting · 5 submodules Empirical-process theory: Rademacher complexities, maximal inequalities, moduli of continuity, and uniform laws for function classes. MEstimation 17 core · 12 supporting · 10 submodules M- and Z-estimation: consistency, asymptotic normality, and influence-function representations. Minimax 19 to review 64 core · 122 supporting · 18 submodules Minimax lower-bound machinery: risk definitions, maximal couplings, coordinatewise overlap, Le Cam two-point methods, Pinsker/KL bridges, and rate statements for estimation problems. Quantile 33 core · 48 supporting · 6 submodules Quantile processes: empirical quantiles, Bahadur representations, and joint sample-quantile asymptotics. UStatistic 22 to review 66 core · 86 supporting · 4 submodules Collects the U-statistic library: order-2 Hoeffding and variance tools, fixed-order m infrastructure, Hájek expansions, remainder negligibility, and the fixed-order CLT. Bootstrap 9 core · 2 supporting · 3 submodules Bootstrap foundations: resampling distributions and consistency of bootstrap approximations. Concentration 59 to review 158 core · 242 supporting · 12 submodules Vendored concentration-of-measure library (a port of auto-res/lean-rademacher; see UPSTREAM.md). Coupling 26 core · 36 supporting · 1 submodule This module collects coupling-based statistical primitives. GMM 15 core · 9 supporting · 4 submodules Generalized method of moments: identification, consistency, and asymptotic normality of GMM estimators. Inference 21 core · 24 supporting · 9 submodules Inferential tooling: delta methods (scalar, functional, Hadamard), Wald/chi-squared statistics, and Slutsky ingredients. Nonparametric 7 to review 135 core · 144 supporting · 7 submodules Top barrel for reusable nonparametric statistical methods: approximation theory, weighted least squares, local-polynomial and series/sieve estimators, and higher-order influence-function tools. Orthogonality 4 core · 5 supporting · 2 submodules Neyman orthogonality as a statistical property: definitions and the second-order remainder characterization. Polynomial­Tail 23 core · 33 supporting · 7 submodules Polynomial lower-tail moment analysis: the polynomial small-value tail law for a bounded positive variable, truncated inverse first/second moment asymptotics, the trimming-bias bound, and the bias-variance rate-balancing algebra. Privacy 9 core · 8 supporting · 1 submodule Differential privacy via the Laplace mechanism: the centered Laplace distribution and its density-ratio bound, scalar and finite-dimensional additive-noise release, pure and approximate ε-differential-privacy guarantees, post-processing closure, and Laplace-noise moment bounds. Sample­Split 8 to review 23 core · 24 supporting · 7 submodules This module is the public import point for sample-splitting infrastructure used by cross-fitting and fold-based estimation arguments.