statsmodels → .NET

Verdict: mixed, and read rather than assumed. The foundation (linear regression, distributions, basic tests) exists, and the OLS summary table is now native. Past it the answer differs by subject, which is what the readings in decisions/0004 and decisions/0004 settled: forecasting is already first-party and is delegated; the GLM table is now native too, the time-series diagnostics — serial correlation, stationarity and seasonal decomposition — are native in Lodestar.Stats.TimeSeries; mixed models have no .NET package at all and wait for a caller; instrumental-variable and panel estimators have none either and reproduce exactly in linearmodels, so they could be written (decision 0004). decisions/0004 read Meta.Numerics and the commercial Numerics.NET on top, and each carries part of what this page used to call absent.

statsmodels need	.NET
Linear regression, least squares	Math.NET Numerics (Fit, MultipleRegression) — the estimate only
OLS(...).fit() with its summary table	native: Lodestar.Stats.Regression
OLS(...).fit(cov_type="HC0".."HC3")	native: CovarianceType. The distribution moves with it as it does in statsmodels — z for the coefficients, F for the overall test; decisions/0004, #686
WLS(...).fit(), with cov_type="HC0".."HC3"	native: WeightedLeastSquares, the same OlsSummary table. Math.NET's WeightedRegression.Weighted returns the coefficients only; #768
GLS(...).fit() with a full sigma	native: GeneralizedLeastSquares, the same OlsSummary table; a vector sigma is WeightedLeastSquares with weights 1/σ. GLSAR is not here; #771
fit(cov_type="HAC") and fit(cov_type="cluster")	native: CovarianceType.Hac and CovarianceType.Cluster on OrdinaryLeastSquares and WeightedLeastSquares, one-way clusters and the Bartlett kernel. No free .NET library read computes either (Accord.Statistics, Math.NET Numerics, Meta.Numerics, NumFlat); #775
Distributions, basic hypothesis tests	Math.NET (Distributions) for the distributions; it ships no test. The tests are native in Lodestar.Stats, at scipy parity, and Meta.Numerics 4.2.0 (MS-PL, netstandard2.0) carries eight of its ten families, slower on all eight at n = 10,000, and asymptotic on Kolmogorov-Smirnov where this is exact (performance). ⛔ not Accord.NET — last package October 2017, last commit November 2020; README
GLMs with the inference table (logit, Poisson, …)	native: Lodestar.Stats.Regression, binomial, Poisson, negative binomial with a given alpha, and Gamma with its estimated scale, each with offset and exposure (#787). ML.NET fits them too, but reports coefficient statistics for binary logistic only; decisions/0004, #616
Forecasting, seasonality and anomaly detection	Microsoft.ML.TimeSeries 5.0.0 (ForecastBySsa, DetectSeasonality) — first-party and MIT; decisions/0004
acf, pacf, acorr_ljungbox	native: Lodestar.Stats.TimeSeries, with the confidence bands; #617. Meta.Numerics carries the autocovariance and Ljung-Box and no partial autocorrelation; Numerics.NET, commercial, carries all three
adfuller, kpss	native: Stationarity in Lodestar.Stats.TimeSeries, every regression and autolag, MacKinnon's p-value, and KPSS's clamped p-value as a property rather than a warning; #671
seasonal_decompose	native: SeasonalDecomposition, additive and multiplicative, period required. STL is not here; stlnet ships it under MIT
ARIMA / SARIMAX estimation, state-space	⛔ not written — decisions/0004: statsmodels' own optimisers disagree at 1e-4 on one series, so no corpus can pin them; Cortex.TimeSeries' ARIMA fits a pure autoregression under an ARIMA name
VAR(y).fit(p): vector autoregression with its table	native: VectorAutoregression in Lodestar.Stats.TimeSeries, at statsmodels parity — least squares on the stacked lags, the residual covariances and the four information criteria. Nothing in .NET estimated one; decisions/0004, #786
MixedLM: mixed and hierarchical models	⚠️ gap, and not written until a caller needs it — no .NET package fits one, free or commercial, across nine read. Accord's TwoWayAnovaModel.Mixed and NMath's OneWayRanova/TwoWayRanova are classical ANOVA with a random or repeated factor; Infer.NET can express a hierarchical model by hand but prints no REML table. decisions/0004 has the reading, and why MixedLM's own solvers disagree past what a frozen corpus can hold
MNLogit: unordered categories with the inference table	native: MultinomialLogit, at statsmodels parity. Accord's MultinomialLogisticRegression carries a table too, and is LGPL-2.1 and archived (decision 0004); ML.NET's maximum-entropy trainers return coefficients only; #788
OrderedModel: ordinal responses	⛔ not written — decisions/0004: its numerical Hessian and default Nelder–Mead do not reproduce at 1e-9, and no .NET package fits one
GLM(...).fit_regularized(): lasso, ridge and elastic net	delegated: Microsoft.ML's LbfgsLogisticRegression, LbfgsPoissonRegression and LbfgsMaximumEntropy fit the same optimum — MIT and first-party — once the penalty is scaled by the row count: L1Regularization = alpha·L1_wt·n, L2Regularization = alpha·(1 − L1_wt)·n. Measured identical to six decimals, selected variables included. The reference returns no inference table here, deliberately, so there is nothing for this package to add; decisions/0004, #789
IV2SLS, IVLIML, IVGMM (linearmodels; statsmodels.sandbox for IV2SLS)	⚠️ gap, writable — decisions/0004: no .NET package estimates one, free or commercial, across seven read; linearmodels 7.0 reproduces 2SLS, LIML and two-step GMM at 1e-15, so a lot could be written at parity. Iterated GMM moves at 1e-6 with its tolerance and is left out
PanelOLS, RandomEffects, BetweenOLS, FirstDifferenceOLS (linearmodels)	⚠️ gap, writable — the same record: nothing in .NET, and each estimator reproduces at 1e-15; the errors follow linearmodels' own small-sample factors, not statsmodels'

using MathNet.Numerics;

// OLS y = a + b·x
(double a, double b) = Fit.Line(xs, ys);
double r2 = GoodnessOfFit.RSquared(xs.Select(x => a + b * x), ys);

Pitfalls

• Math.NET returns the estimate, not the inference. Read through a MetadataLoadContext, every regression entry point in MathNet.Numerics 5.0.0 returns coefficients, and GoodnessOfFit adds five whole-model scalars. Nothing in its 5 333 exported members is a coefficient p-value, a confidence interval, an adjusted R-squared, an overall F or a VIF. That gap is what Lodestar.Stats.Regression fills, at statsmodels parity; decisions/0003 has the reading.
• Time series: the forecast is the part .NET has. Microsoft.ML.TimeSeries 5.0.0 reads 34 exported types, and they carry ForecastBySsa, DetectSeasonality and four change-point and spike detectors — first-party, MIT, maintained. Across those same 34 types a search for ARIMA, autocorrelation, stationarity, Ljung-Box or decomposition returns nothing, and Deedle 8.1.0 returns nothing for them across 2 132 members: it is the time index, not a model. So the gap is not the forecaster, it is the apparatus for deciding whether a series may be modelled at all — decisions/0004 has the reading, and replaces what this bullet used to claim. That gap is in the free, maintained packages only: the commercial Numerics.NET 10.7.0 exports the autocorrelation and partial autocorrelation functions, Ljung-Box, ADF and KPSS (decision 0004).
• A GLM exists in .NET three times, and none of them is usable here. Accord.Statistics 3.8.0 ships the whole stack — eleven link functions, IterativeReweightedLeastSquares, Wald tests, odds ratios, deviance — under LGPL-2.1, archived since 2017. Microsoft.ML 5.0.0 reports StandardError, ZScore and PValue, but for binary logistic only: a Poisson fit comes back with no statistics at all, there is no interval, no odds ratio and no AIC, and the standard errors live in Microsoft.ML.Mkl.Components behind a native MKL. cs-glm 1.0.1 has nine families and three IRLS solvers and installs no assembly — its lib/net461/Release/ layout is not a lib asset path. decisions/0004 has the member listings.

Before any native development beyond the tables that ship, weigh the real need: a regression plus a few tests is often enough, and that much now ships, with the GLM beside it since #616. One lot is scoped past them — #617 — and it starts from a reading rather than from a claim.

Guide to be expanded as real needs arise.

The table on a regularised fit's selected support

fit_regularized reports coefficients and nothing else, and refit=True reports the unpenalised fit on the variables the penalty kept. That second step is two calls here: take the columns whose penalised coefficient is not zero, and fit them through OrdinaryLeastSquares.Fit or GeneralizedLinearModel.Fit.

Read that table the way the reference's own docstring asks: the variables were chosen on the same rows the inference is computed from, so its standard errors are optimistic (decision 0004).