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GeneralizedLeastSquares

Generalized least squares with a caller-supplied error covariance and the inference table on top of it, at statsmodels.api.GLS parity.

public static class GeneralizedLeastSquares

Example — ten readings whose errors are correlated with their neighbours, 0.6^|i−j|.

using Lodestar.Stats.Regression;

double[] time = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0];
double[] reading = [2.4, 3.6, 6.9, 7.1, 10.8, 11.2, 15.1, 14.6, 19.3, 19.9];
double[] covariance = new double[100];
for (int i = 0; i < 10; i++)
{
    for (int j = 0; j < 10; j++)
    {
        covariance[(i * 10) + j] = Math.Pow(0.6, Math.Abs(i - j));
    }
}

OlsSummary fit = GeneralizedLeastSquares.Fit(time, reading, covariance, featureCount: 1);

double slope = Math.Round(fit.Coefficients[1], 4);      // => 1.9712
double error = Math.Round(fit.StandardErrors[1], 4);    // => 0.2924

Remarks — the same rows fitted by OrdinaryLeastSquares.Fit report a slope standard error of 0.1102, less than half: ten correlated readings carry less information than ten independent ones, and the ordinary table counts them as independent.

Applies to — net10.0, netstandard2.0.

See also — OlsSummary, WeightedLeastSquares, the generalized least squares index.

Members

Member	What it does
GeneralizedLeastSquares.Fit	Fits a linear model under a given error covariance and reports what a summary table holds.