VarianceEstimatorFunction

VarianceEstimatorFunction
is an option for LinearModelFit and NonlinearModelFit which specifies the variance estimator to use.

DetailsDetails

  • VarianceEstimatorFunction defines the function for estimating the error variance scale for linear and nonlinear models with assumed normally distributed errors.
  • With the setting VarianceEstimatorFunction->f, the variance scale is estimated by where is the list of residuals and w is the list of weights, as specified by the setting for the Weights option.
  • The default setting Automatic estimates the variance scale by where is the weight for the th data point, is the th residual, is the number of data elements, and is the number of parameters in the model.
  • With VarianceEstimatorFunction->(1&) and Weights->{1/Δy12,1/Δy22,}, is treated as the known uncertainty of measurement and parameter standard errors are effectively computed only from the weights. »

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

Use the default unbiased estimate of error variance:

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Assume a known error variance:

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Estimate the variance by the mean squared error:

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Introduced in 2008
(7.0)