Stats Estimator

Stats estimator — stochastic-rs-stats

A "stats estimator" in stochastic-rs-stats consumes a 1-D series (ArrayView1<T>), optionally a second covariate / regressor, and returns a typed XxxResult struct with named fields plus a converged / p-value indicator.

This SKILL covers MLE, MoM, Hurst estimators, stationarity tests, fractal-dimension estimators, and bootstrap variants. The pattern is uniform: the user receives a data type they can introspect (rather than a tuple of unnamed f64s) and the test reports its own diagnostic without hidden state.

1. Function signature

// stochastic-rs-stats/src/foo_estimator.rs

use ndarray::ArrayView1;
use crate::traits::FloatExt;

pub fn estimate<T: FloatExt>(
    samples: ArrayView1<T>,
    /* extra parameters: m_window, lag, alpha, etc. */
) -> FooResult { /* ... */ }

Three rules:

• Input is ArrayView1<T>, never &[T]. ndarray slices interop with the rest of the stats / quant pipeline; raw slices are ergonomic but the boundary cost shows up in benchmarks.
• Generic over T: FloatExt so f32 and f64 callers share code. The estimator typically internally lifts to f64 for accumulation (.to_f64().unwrap()) and returns f64 in the *Result struct.
• Return a typed struct, never a tuple. Estimators evolve (a future version might add iterations, pvalue, confidence_interval); a named struct can grow a field without breaking existing call sites.

2. The *Result struct

#[derive(Debug, Clone)]
pub struct FooResult {
    /// Point estimate.
    pub estimate: f64,
    /// Optional p-value (parametric / asymptotic).
    pub pvalue: Option<f64>,
    /// 95% confidence interval; None when bootstrap not requested.
    pub ci_95: Option<(f64, f64)>,
    /// Number of optimiser iterations (None for closed-form estimators).
    pub iterations: Option<usize>,
    /// Whether the optimiser converged (true for closed-form).
    pub converged: bool,
    /// Optional bootstrap p-value (separate from the parametric one
    /// because the asymptotic form may not apply on small samples).
    pub bootstrap_pvalue: Option<f64>,
}

Debug + Clone is mandatory. Calibrators and downstream pipelines clone results into pipelines; Debug is what dumps to logs.

3. Parametric vs bootstrap p-values

Two distinct fields, deliberately not collapsed:

• pvalue — analytic / asymptotic. E.g. ADF unit-root test: Mackinnon (1996) regression coefficients give p-value as a function of sample size + the test statistic.
• bootstrap_pvalue — non-parametric resampling. Slower (typical: 1000 bootstrap replicates) but valid on any DGP.

Estimators with an exact / asymptotic formula populate pvalue only. Bootstrap-only estimators populate bootstrap_pvalue only. Estimators where both make sense populate both, and document the difference in the struct doc.

4. openblas-gating

Estimators that need LAPACK (linear regression, SVD, eigendecomposition) gate behind #[cfg(feature = "openblas")]:

#[cfg(feature = "openblas")]
pub fn estimate_lapack<T: FloatExt>(samples: ArrayView1<T>) -> FooResult {
    use ndarray_linalg::SVD;
    // ...
}

The non-openblas baseline must always compile (and be the default build). If the openblas-only path is strictly more accurate, provide a closed-form fallback that's slower but always available. Don't make the user discover at runtime that they need a feature flag.

5. Paper citation header

The source file's //! header must name the paper:

//! # Foo estimator
//!
//! Implements the <Name> (<Year>) estimator for <quantity>:
//!
//! \[LaTeX block of the canonical formula\]
//!
//! Reference: <Author, Year>, "<Title>", *<Journal>* <vol>(<num>), <pages>.

For Hurst estimators specifically, also cite the Mandelbrot & Van Ness (1968) prior so users orienting themselves can map between estimators.

6. Reference-comparison test

Mandatory: at least one test that compares to a manually-computed reference (R, scipy, Mathematica, or a published paper Table). Pinned seed, named tolerance:

#[cfg(test)]
mod tests {
    /// Reference: Hurst & Co. (2024), Table 3 row 2 — H = 0.7 ± 0.02.
    #[test]
    fn hurst_recovery_matches_paper_table3() {
        let mut rng = StdRng::seed_from_u64(42);
        let series = simulate_fbm(0.7, 5_000, &mut rng);
        let result = estimate_hurst(series.view());
        assert!(
            (result.estimate - 0.7).abs() < 0.02,
            "H = {}, expected 0.7 ± 0.02",
            result.estimate
        );
    }
}

The feedback_test_batching memory entry says "when adding many tests write all first, then run cargo test once". For estimators that take seconds per test (large Monte Carlo runs), batch the tests and watch for parallel-execution flakes (the rc.2 Fukasawa fix taught us this).

7. Python wrapper

Expose as #[pyfunction] (preferred for stateless estimators) or #[pyclass] (when the estimator carries state — e.g. a fitted model that supports predict):

// stochastic-rs-quant/src/python.rs (yes, the Python wrappers for
// stats estimators live in the quant crate's python.rs because that's
// where stochastic-rs-py registers them; alternative is direct
// registration from -stats but the existing pattern is via -quant).

#[pyfunction]
#[pyo3(signature = (samples))]
pub fn estimate_foo<'py>(samples: numpy::PyReadonlyArray1<'py, f64>) -> PyResult<PyFooResult> {
    let result = stochastic_rs_stats::foo::estimate(samples.as_array());
    Ok(PyFooResult { inner: result })
}

#[pyclass(name = "FooResult", from_py_object, unsendable)]
#[derive(Clone)]
pub struct PyFooResult {
    pub inner: stochastic_rs_stats::foo::FooResult,
}

#[pymethods]
impl PyFooResult {
    #[getter] fn estimate(&self) -> f64 { self.inner.estimate }
    #[getter] fn pvalue(&self) -> Option<f64> { self.inner.pvalue }
    // ... one getter per field ...
}

Then register both in stochastic-rs-py/src/lib.rs.

8. Anti-patterns

• Do not return a tuple (f64, f64, bool). Always return a typed struct.
• Do not silently fall through to a slow path when openblas isn't available. Either gate explicitly with #[cfg(feature = "openblas")] or provide a documented closed-form fallback.
• Do not roll your own ADF / KPSS regression. If you need linear regression, use the helpers in stochastic-rs-stats::stationarity.
• Do not depend on statrs for distribution math — write closed forms via stochastic_rs_distributions::DistributionExt. See feedback_no_statrs_distributions memory entry.
• Do not combine parametric and bootstrap p-values into a single field. They have different validity domains; users need both.

9. Reference impls

• fukasawa_hurst::estimate (fukasawa_hurst.rs) — rough-vol Hurst via L-BFGS-B + Paxson + Eq. 16 corrections; paper-Table 1 validation test.
• stationarity::adf::adf_test (stationarity/adf.rs) — Augmented Dickey-Fuller with Mackinnon p-values + test-statistic struct.
• stationarity::kpss::kpss_test — KPSS with bandwidth-aware long-run variance estimator.
• mle::* — MLE family (gamma / lognormal / NIG / Heston) with closed-form score / Fisher info where available.

Related SKILLs

• add-diffusion-process — when validating an estimator on simulated process samples.
• python-bindings — for the PyFooResult / estimate_foo wrappers.
• integration-test-writing — for reference-comparison test conventions.

Source: rust-dd/stochastic-rs — distributed by TomeVault.